EPRI - Increased Power Flow Guidebook.pdf

Effective December 6, 2006, this report has been made publicly available in accordance with Section 734.3(b)(3) and published in accordance with Section 734.7 of the U.S. Export Administration Regulations. As a result of this publication, this report is subject to only copyright protection and does not require any license agreement from EPRI. This notice supersedes the export control restrictions and any proprietary licensed material notices embedded in the document prior to publication.

Increased Power Flow Guidebook Increasing Power Flow in Transmission and Substation Circuits

Increased Power Flow Guidebook: Increasing Power Flow in Transmission and Substation Circuits 1010627

Final Report, November 2005

EPRI Project Manager R. Adapa

ELECTRIC POWER RESEARCH INSTITUTE 3420 Hillview Avenue, Palo Alto, California 94304-1395 ▪ PO Box 10412, Palo Alto, California 94303-0813 ▪ USA 800.313.3774 ▪ 650.855.2121 ▪ [email protected] ▪ www.epri.com

DISCLAIMER OF WARRANTIES AND LIMITATION OF LIABILITIES THIS DOCUMENT WAS PREPARED BY THE ORGANIZATION(S) NAMED BELOW AS AN ACCOUNT OF WORK SPONSORED OR COSPONSORED BY THE ELECTRIC POWER RESEARCH INSTITUTE, INC. (EPRI). NEITHER EPRI, ANY MEMBER OF EPRI, ANY COSPONSOR, THE ORGANIZATION(S) BELOW, NOR ANY PERSON ACTING ON BEHALF OF ANY OF THEM: (A) MAKES ANY WARRANTY OR REPRESENTATION WHATSOEVER, EXPRESS OR IMPLIED, (I) WITH RESPECT TO THE USE OF ANY INFORMATION, APPARATUS, METHOD, PROCESS, OR SIMILAR ITEM DISCLOSED IN THIS DOCUMENT, INCLUDING MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE, OR (II) THAT SUCH USE DOES NOT INFRINGE ON OR INTERFERE WITH PRIVATELY OWNED RIGHTS, INCLUDING ANY PARTY'S INTELLECTUAL PROPERTY, OR (III) THAT THIS DOCUMENT IS SUITABLE TO ANY PARTICULAR USER'S CIRCUMSTANCE; OR (B) ASSUMES RESPONSIBILITY FOR ANY DAMAGES OR OTHER LIABILITY WHATSOEVER (INCLUDING ANY CONSEQUENTIAL DAMAGES, EVEN IF EPRI OR ANY EPRI REPRESENTATIVE HAS BEEN ADVISED OF THE POSSIBILITY OF SUCH DAMAGES) RESULTING FROM YOUR SELECTION OR USE OF THIS DOCUMENT OR ANY INFORMATION, APPARATUS, METHOD, PROCESS, OR SIMILAR ITEM DISCLOSED IN THIS DOCUMENT. ORGANIZATION(S) THAT PREPARED THIS DOCUMENT EPRI Power Delivery Consultants, Inc.

NOTE For further information about EPRI, call the EPRI Customer Assistance Center at (800) 313-3774 or email [email protected] Electric Power Research Institute and EPRI are registered service marks of the Electric Power Research Institute, Inc. Copyright © 2005 Electric Power Research Institute, Inc. All rights reserved.

CITATIONS This report was prepared by EPRI 115 East New Lenox Road Lenox, MA 01240 Principal Investigator B. Clairmont Power Delivery Consultants Inc. 28 Lundy Lane, Suite 102 Ballston Lake, NY 12019 Principal Investigators D. A. Douglass E. C. Bascom, III T. C. Raymond J. Stewart 59 St. Stephens Lane N Scotia, NY 12302 This report describes research sponsored by the Electric Power Research Institute (EPRI). The report is a corporate document that should be cited in the literature in the following manner: Increased Power Flow Guidebook: Increasing Power Flow on Transmission and Substation Circuits. EPRI, Palo Alto, CA: 2005. 1010627.

iii

PRODUCT DESCRIPTION

The Increased Power Flow (IPF) Guidebook is a state-of-the-art and “best practices” guidebook on increasing power flow capacities of existing overhead transmission lines, underground cables, power transformers, and substation equipment without compromising safety and reliability. The Guidebook discusses power system concerns and limiting conditions to increasing capacity, reviews available technology options and methods, illustrates alternatives with case studies, and analyzes costs and benefits of different approaches. Results & Findings The IPF Guidebook clearly identifies those cases where increasing power flow might be an alternative to upgrading the grid with major investment. The document reviews both established technologies and new developments in technologies with the potential to increase power flow— and addresses how to apply them for lines, cables, and substations. Because the guide compares the economic benefits of each available technology, it will assist utilities in making informed decisions in terms of what options for IPF are available and which options are most economical for application at their utility sites. By implementing one or more of the IPF technologies, utilities can obtain increased asset utilization with minimal cost. For example, if a utility decides to implement one of the IPF technologies, such as Dynamic Thermal Circuit Rating (DTCR) technology, that implementation will allow increased power flows on the order of 15-20% over the existing static ratings and, thus, increase utility revenue. Challenges & Objective(s) Motivations for increasing power flow limits on existing transmission facilities (rather than constructing new facilities) are economic, environmental, and practical. Due to limited incentives for new construction and time delays that may result from public opposition to new power facilities, utilities around the world are being forced to find new ways of relieving modest constraints or increasing power flow through existing transmission corridors with minimal investment. This Guidebook will be an excellent reference document for transmission and substation engineers since it provides all possible IPF options in one place for ease of use. Applications, Values & Use Training materials will be developed with the IPF Guidebook, including hands-on workshops at EPRI's full-scale laboratories. In addition, it is anticipated that, in the coming years, technical reports will be produced annually on new and updated aspects of IPF as well as new material on costing, economics, power storage, voltage upgrading, and case studies. This information will be incorporated into the Guidebook during subsequent work.

v

EPRI Perspective Due to limited incentives for new construction, utilities around the world are undergoing a major transformation that is redefining the use of existing power equipment in the electric transmission network. Under these circumstances, utilities are forced to find new ways of increasing power flow through the existing transmission corridors with minimal investments. EPRI’s Increased Transmission Capacity Program directly responds to the needs of owners and operators of the transmission grid to get the most out of existing equipment in today’s competitive electricity business while increasing the availability and reliability of transmission and substation equipment. This Program helps customers accomplish these goals strategically, without jeopardizing reliability and driving up costs. A number of projects have been undertaken by EPRI in this Program under the Project Set 38A—Increase Power Flow Capability in the Transmission Systems. One major effort under Project Set 38A is the IPF Guidebook, the only available utility compendium of “best practices” for increasing power flow in transmission circuits. Other major EPRI developments include DTCR (Dynamic Thermal Circuit Ratings) software to calculate dynamic ratings of transmission circuits and Video Sagometer to measure sag of transmission lines. Approach The Guidebook was developed by industry experts and draws on a combination of technology, documented case studies, and associated engineering and safety guidelines. Keywords Overhead transmission Substations Transmission capacity Underground transmission

vi

ABSTRACT The Increased Power Flow (IPF) Guidebook documents the state-of-science for increasing power flow capacities of existing overhead transmission lines, cables, and substation equipment. The Guidebook provides an overview of the electrical, mechanical, thermal, and system concerns that are important to increased power flow, presents all possible IPF options, uses case studies to illustrate the options, and compares their potential economic benefits. The Guidebook also provides an overview of dynamic thermal rating methods and summarizes other developments in hardware and software that are instrumental for IPF. The IPF Guidebook provides utilities with the only available compendium of “best practices” for increasing power flow. The Guidebook will assist utilities in making informed decisions in terms of what options for IPF are available and which options are most economical for application at their utility sites.

vii

Increased Power Flow Guidebook

Contents

Chapter 1

Increased Power Flow Fundamentals and Principles

1.1

INTRODUCTION

1-1

1.2

POWER SYSTEM ISSUES

1-2

1.3

LIMITING CONDITIONS

1-3

Circuit Power Flow Limits Surge Impedance Loading of Lines Voltage Drop Limitations Thermal Limits Environmental Limits Examples – Overhead Lines

1-3 1-4 1-5 1-6 1-7 1-8

1.4

CHAPTER PREVIEW Overhead Lines (Chapter 2) Underground Cables (Chapter 3) Power Transformers (Chapter 4) Substation Terminal Equipment (Chapter 5) Dynamic Rating and Monitoring (Chapter 6)

REFERENCES

Chapter 2 2.1

2.2

2.3

2.4

1-9 1-9 1-10 1-10 2.5 1-10 1-10 1-11

Overhead Transmission Lines

INTRODUCTION

2-1

Surge Impedance Loading Voltage Drop Thermal Limits Environmental Limits

2-2 2-2 2-2 2-2

UPRATING CONSTRAINTS

2-3

Introduction Sag-tension Calculations Limiting High Temperature Sag Uprating Constraints Related to Wind-Induced Conductor Motion Electrical Clearance Loss of Conductor Strength Constraints on Structural Loads Environmental Effects

2-3 2-3 2-5 2-8 2-10 2-12 2-13 2-15

LINE THERMAL RATINGS

2-15

Introduction Maximum Conductor Temperature Weather Conditions for Rating Calculation How Line Design Temperature Affects Line Ratings Heat Balance Methods Thermal Ratings— Dependence on Weather Conditions Transient Thermal Ratings

2-15 2-16 2-16 2-17 2-17 2-21 2-22

2.6

EFFECTS OF HIGH-TEMPERATURE OPERATIONS 2-23 Introduction Annealing of Aluminum and Copper Sag Tension Models for ACSR Conductors Axial Compressive Stresses Built–In Stresses Sag Tension Calculations Sag and Tension of Inclined Spans Calculation of Conductor High-Temperature Sag and Tension Results of High-Temperature Sag Tension Calculations Effects of Wind Speed on Thermal Ratings Thermal Elongation Creep Elongation Connectors at High Temperature Conductor Hardware

2-34 2-40 2-41 2-42 2-46 2-49

2.8

2-32

UPRATING WITHOUT RECONDUCTORING

2-51

Introduction Deterministic Methods Probabilistic Methods Development of a “Measure of Safety” as a Basis for Line Rating Comparison of Probabilistic Rating Methods Device for Mitigating Line Sag - SLiM

2-51 2-51 2-56 2-60 2-62 2-62

RECONDUCTORING WITHOUT STRUCTURAL MODIFICATIONS

2-65

Introduction TW Aluminum Wires – ACSR/TW or AAC/TW ACSS and ACSS/TW High-Temperature Aluminum Alloy Conductors Special Invar Steel Core Gapped Construction ACCR Conductor Conductors with Exotic Cores Comparing ACSS and High-Temperature Alloy Conductors 2.7

2-23 2-23 2-27 2-28 2-29 2-29 2-31

2-65 2-66 2-67 2-70 2-70 2-71 2-74 2-74 2-74

DYNAMIC MONITORING AND LINE RATING

2-75

Introduction Dynamic Ratings Versus Static Ratings Advantages of Dynamic Rating Disadvantages of Dynamic Rating Real-time Monitors Dynamic Rating Calculations Field Test Results Summary

2-75 2-75 2-76 2-76 2-77 2-79 2-82 2-84

CASE STUDIES

2-84

Introduction Selecting a Line Uprating Method Preliminary Selection of Uprating Methods Uprating Test Cases—Preliminary Uprating Study Economic Comparison of Line Uprating Alternatives

2-84 2-84 2-85 2-87 2-95

ix

Contents

2.9

Detailed Comparison of Uprating Alternatives— An Example Conclusions

2-99 2-103

REFERENCES

2-104

Chapter 3 3.1 3.2

3.3

3.4

3.5

3.6

3.7

x


Cupric Oxide Strand Coating Voltage Upgrading Superconducting Cables 3.8

Underground Cables

INTRODUCTION CABLE SYSTEM TYPES

3-1 3-2

High-Pressure Pipe-Type (Fluid- and Gas-Filled) Extruded Dielectric Self-Contained Liquid-Filled (SCLF) Other Cable Types

3-2 3-5 3-8 3-10

POWER FLOW LIMITS AND SYSTEM CONSIDERATIONS

3-11

3.9

3.10

3-44 3-45 3-45

DYNAMIC RATINGS OF UNDERGROUND CABLE SYSTEMS

3-46

Background EPRI Dynamic Ratings on Cables Benefit of Dynamic Ratings Required Monitoring Quasi-Dynamic (Real-Time) Ratings

3-46 3-46 3-49 3-51 3-51

CASE STUDIES FOR UNDERGROUND CABLE CIRCUITS

3-51

CenterPoint Energy United Illuminating Company

3-51 3-53

SUMMARY OF UPRATING AND UPGRADING APPROACHES AND ECONOMIC FACTORS

3-55

Thermal, Stability, and Surge Impedance Loading Limits Load Flow Considerations Uprating Hybrid (Underground and Overhead) Circuits

3-11 3-14

REFERENCES Appendix 3.1

Pipe-Type Ampacity Example

3-58

3-14

Appendix 3.2

Extruded Ampacity Example

3-65

UNDERGROUND CABLE RATINGS

3-15

Introduction Concept of Ampacity Losses Equivalent Thermal Circuit and Thermal Resistances Calculating Ampacity Effect of Various Parameters on Ampacity Emergency Ratings Inferring Conductor Temperatures from Measured Temperatures

3-15 3-15 3-16

Chapter 4

Power Transformers

3-26

UPRATING AND UPGRADING CONSTRAINTS

3-26

Direct Buried Cable Systems Fluid-Filled Cable Systems Duct Bank Installations Trenchless Installations Other Installation Locations Hot Spot Identification Accessories Hydraulic Circuit

3-26 3-26 3-27 3-27 3-27 3-28 3-28 3-28

3-19 3-23 3-24 3-25

INCREASING THE AMPACITY OF UNDERGROUND CABLES 3-28 Route Thermal Survey Review Circuit Plan and Profile Evaluate Daily, Seasonal, or Other Periodic Load Patterns Temperature Monitoring Ampacity Audit Remediation of “Hot Spots” Active Uprating Shield/Sheath Bonding Scheme

3-36 3-38 3-40 3-40 3-40 3-43

RECONDUCTORING (UPGRADING)

3-43

Introduction Larger Conductor Sizes

3-43 3-44

4.1 4.2

4.3

4.4

4.5

3-56

INTRODUCTION

4-1

TRANSFORMER DESIGN

4-2

General Construction Types of Cooling Losses Factory Testing

4-2 4-5 4-5 4-6

RISKS OF INCREASED LOADING

4-9

Short-Term Risks Long-Term Risks Additional Risks

4-9 4-11 4-18

THERMAL MODELING

4-21

Mechanisms of Heat Transfer Top Oil Model (IEEE C57.91-1995, Clause 7) Bottom Oil Model (IEEE C57.91-1995, Annex G) IEC Model (IEC 354-1991) Proposed IEC Model

4-21 4-24 4-26 4-30 4-32

THERMAL RATINGS

4-33

Ambient Air Temperature Load Rating Type and Duration Rating Procedure Condition-Based Loading Maintenance Considerations

4-34 4-34 4-35 4-35 4-36 4-37

4.6

WINDING TEMPERATURE MEASUREMENT

4-38

4.7

MODEST INCREASES IN CAPACITY FROM EXISTING TRANSFORMERS

4-39

EXAMPLES

4-39

3-28 3-36

4.8

REFERENCES

4-43

Contents

Chapter 5


Substation Terminal Equipment

Chapter 6

5.1

INTRODUCTION

5.2

SUMMARY—EQUIPMENT TYPES AND IPF OPPORTUNITIES

5-2

Equipment Rating Parameters Thermal Rating Parameter Comparison

5-2 5-4

THERMAL MODELS FOR TERMINAL EQUIPMENT

5-4

5.3

Bus Conductors Switch (Air Disconnect) Air-core Reactor Oil Circuit Breaker SF6 Circuit Breaker Bushings (Oil-immersed Equipment Only) Current Transformers Line Traps Other Types of Terminal Equipment 5.4

5.5

5.6

5-1

5-4 5-6 5-8 5-9 5-10 5-10 5-11 5-11 5-12

UPRATING OF SUBSTATION TERMINAL EQUIPMENT

5-12

Monitoring and Communications Maintenance and Inspection Procedures Reliability and Consequences of Failure

5-13 5-13 5-13

THERMAL PARAMETERS FOR TERMINAL EQUIPMENT

5-14

Manufacturer Test Report Data

5-14

CONCLUSIONS AND SUMMARY

5-14

REFERENCES

Dynamic Thermal Ratings Monitors and Calculation Methods

6.1

INTRODUCTION

6.2

ISSUES RELATED TO DYNAMIC THERMAL RATING METHODS 6-2

6.3 6.4

Where Should Dynamic Thermal Circuit Rating Calculations Be Performed? Costs—Capital and Otherwise Why Dynamic Ratings Go With Increased Utilization

6-2 6-3 6-4

POWER EQUIPMENT CONDITION ASSESSMENT AND REAL-TIME MONITORS

6-4

DYNAMIC THERMAL RATING MODELS FOR POWER EQUIPMENT 6-5 Accounting for Heat Storage (Pre-load Monitoring) Overhead Lines Power Transformers Underground Cables Substation Terminal Equipment

6.5

6.6

5-15

6.7

6.8

6-1

6-5 6-6 6-7 6-10 6-11

EPRI'S DTCR TECHNOLOGY

6-13

Power Circuit Modeling DTCR Output DTCR is a Calculation Engine for SCADA Modeling Complex Interfaces—California “Path 15” Conclusions about the Dynamic Rating of Complex Interfaces

6-13 6-13 6-14 6-14 6-16

OPERATING WITH DYNAMIC THERMAL RATINGS

6-16

Traditional Rating Definitions Traditional Operating Rules Operating with Dynamic Ratings

6-16 6-17 6-17

FIELD STUDIES OF DYNAMIC RATINGS

6-19

Overhead Lines Power Transformers Underground Cables Substation Terminal Equipment Power Circuits Communications and Monitoring

6-19 6-20 6-20 6-20 6-20 6-21

CONCLUSIONS

6-21

REFERENCES

6-22

Glossary

G-1

Index

I-1

xi


CHAPTER 1

Increased Power Flow Fundamentals and Principles

1.1

INTRODUCTION

The purpose of this guidebook is to provide technical information and explain concepts that may aid power transmission company technical personnel in finding economic, technically sound ways to increase the power flow capacity of existing circuits without compromising safety or reliability. The motivations for increasing the power flow limits on existing transmission facilities (rather than constructing new facilities) are economic, environmental, and practical. The methods discussed are generally modest in cost—ranging from virtually free to about 30% of the cost of equipment replacement. The corresponding increase in equipment rating is similarly modest, usually between 5% and 30% (with the exception of overhead lines where reconductoring may yield an increase of over 100%). The methods are practical since the environmental and/or visual impact is normally low, regulatory approval and public hearings may not be needed, and extended power outages are often avoided. Given the extended time delays that may result from public opposition to the construction of new power transmission facilities or even to any visible, physical modification of existing facilities, the use of increased power flow (IPF) methods may offer the only practical solution to relieving modest constraints on power flow. Determining the degree to which maximum power flow constraints can be eased on existing power equipment (overhead lines, power transformers, etc.), power circuits (multiple power equipment elements in series), and power system interfaces (multiple “parallel” power circuits connecting power system regions) can be quite complex. For example, consider the following:

• For an overhead line, any increase in power flow capacity is dependent on its length, the original design assumptions, present-day environmental concerns, the condition of its existing structures, and the type of conductors originally selected. Depending on these multiple factors and which of the IPF methods suggested in Chapter 2 is applied, the resulting increase in the line’s thermal rating could be as little as 5% or as much as 100%.

• But overhead lines are only part of the transmission path (circuit). The lines are terminated at substations by air disconnects, circuit breakers, line traps, etc. The power flow through all of the circuit elements must be limited to avoid damaging the line or the terminating equipment, and the maximum allowable power flow over this circuit may be limited by any one of the circuit elements.

• Finally, when seen as part of a power system interface, any increase in maximum allowable power flow through any component circuit or circuit element does not necessarily yield a higher rating for the complex interface.

1-1

Chapter 1: Increased Power Flow Fundamentals and Principles

In general, it may be stated that maximum power flow on the transmission system is a function of the overall system topology (transmission lines, transformers, generation, series and shunt compensation, and load), and that many non-thermal system considerations can also limit the maximum power flow on a specific transmission circuit. Therefore, transmission circuit ratings are often developed on a system basis, rather than on an individual line basis. The overall limit may be between operating areas irrespective of ownership or individual lines, and may change during a day based on system conditions. Chapter 1 provides an overview of the electrical, mechanical, thermal, and system concerns that are important to increased power flow. The chapter includes three sections:


2834 MW from A to B. Given this level of transfer, the power flows would be as shown in Figure 1.2-2. Notice in Figure 1.2-2 that, even though load area C is not importing power, the lines connecting load area C to the other areas are carrying almost half of the total power transferred. Now let us assume that the customers in load area B would like to buy even more than 2834 MW from the low-cost generator in load area A. Consequently, they contest the limit of 2834 MW set by the system operator, noting that the emergency rating of the lines is 1000 MW. The power system operator explains that the limitation on power import to load area B is not due to nor-

• Section 1.2, Power System Issues, presents a simple power flow example to illustrate several principles about increasing power flow.

• Section 1.3, Limiting Conditions, describes limits on power flow imposed by circuit power flow, surge impedance loading, voltage drop, thermal factors, and environmental constraints.

• Section 1.4, Chapter Previews, presents brief descriptions of the chapters in this guidebook. 1.2

POWER SYSTEM ISSUES

The power transmission system, in any region, is a complex combination of lines (including underground cable) and substations. With the exception of relatively short “radial” lines connecting generating stations to the system, power flow reaching any load point in the system flows over multiple “parallel” paths (circuits). In any path (circuit), the power flow moves through multiple series elements.

Figure 1.2-1 Base system operating "normally" with local generation being similar in cost and able to supply all local load.

This can be illustrated by the following simple power system (NERC 1995) shown in Figure 1.2-1. There are three load areas (A, B, and C). Each load area has sufficient generation to supply the local load. With the system operating “normally,” there is no net power transfer between load areas. Nonetheless, as a result of the available electrical paths connecting the load areas, the diagram shows a “loop” flow of 200 MW. This loop flow occurs even though there is no net power transfer to any of the areas. Consider the situation where power generated in load area A is considerably less expensive than local generation in load area B. It would then be advantageous for power customers in load area B to buy power from the generators in load area A. In doing this, the power transmission system operator sets a transfer limit of

1-2

Figure 1.2-2 Base system operating "normally" with local generation at A being much cheaper than at B, causing a net power transfer of 2834 MW.



limits and electrical impedance of interconnected power circuits.

mal power flows but rather to the emergency power flow through one of the lines (#2) between A and C, as shown in Figure 1.2-3! With line #1 out of service, the redistributed power flow through line #2 reaches the emergency thermal limit of 1000 MW. Thus the imposed power transfer limit of 2834 MW from A to B.

• Note that these observations do not depend on the

As shown in Figure 1.2-3, if the net power transfer from A to B with all lines in service had exceeded the transfer limit of 2834 MW then, under this single contingency loss of line #1 between A and C, the power flow in line #2 from A to C would have exceeded the line’s emergency thermal limit.

1.3

LIMITING CONDITIONS

1.3.1

Circuit Power Flow Limits

One can reach a number of conclusions regarding power flow limits from this simple example:

• Economic power transfers can be limited by circuits that do not directly connect the low-cost generation source and the customer.

• A 5% increase (50 MW) in the emergency rating of lines #1 and #2 connecting A and C from 1000 MW to 1050 MW might allow a similar 5% increase (141 MW) in the power transfer limit from 2834 to 2975 MW.

• A 5% increase in the emergency rating of either line #1 or #2 between A and B would not allow any increase in power transfer from A to B.

• The long-term value of projects to increase the power flow in any particular circuit is dependent on changes in the cost of generation and the power flow

reason for the power flow limit in any of the circuits. They would be equally valid whether the limitation on power flow is due to equipment temperature limits, limits on voltage drop, or electrical phase shift stability issues.

Power circuits consist of series and parallel combinations of electrical equipment (each subjected to mechanical, electrical, and thermal stresses) whose collective purpose is to transmit power safely and reliably under widely varying operational situations. Each element of such circuits is typically specified to have certain power flow limits that allow their safe, reliable operation for an extended period of time (e.g., 40 years). Increased power flow inevitably means increased electrical current flow or increased circuit voltage since power is the product of these quantities. In general, for substation equipment and underground cables, increasing the operating voltage is difficult or impossible, whereas increasing the maximum electrical current is both possible and economic. Overhead lines are often capable of either higher voltage or higher current levels if certain modifications are undertaken. Power transmission circuits are typically bimodal in terms of power flow. Under normal operation, it is not unusual for power transformers and lines to operate at much less than half of their power flow capacity, only approaching their operational limits under relatively rare emergency events. There are basically three methods of increasing power flow: load control, improved modeling and monitoring, and physical modification of existing circuits. Improved models may allow operation of equipment with reduced safety factors without reducing safety and reliability. Examples are the “bottom oil” model in Annex G of the IEEE loading guide and the improved models for high-temperature sag of ACSR conductor.

Figure 1.2-3 Base system operating in response to a “single contingency” outage of line #1 between A and C while there is a power transfer of 2834 MW from A to B.

Similarly, monitoring of environmental factors (air temperature, wind speed, humidity, etc.) may allow the use of less conservative assumptions, again without reducing safety and reliability.

1-3


With monitors communicating data in real-time, it may be possible to run equipment at higher power levels most of the time by avoiding the use of “worst case” assumptions. This approach is called dynamic thermal ratings. It is unlikely that such real-time monitoring would allow any increase in non-thermal operating limits. Overhead transmission lines are the primary means of power transfer over long distances. They have thermal ratings just as power transformers, substation terminal equipment, and underground cables but, for long lines, power flow limits may also be necessary to avoid excessive voltage drop or system stability problems. In addition, since the public has access to the area under lines, there may also be limits on voltage and current related to environmental effects. This section concerns the relationship between the various types of power flow limits for overhead lines. 1.3.2

Surge Impedance Loading of Lines

Sometimes a power transmission line possesses a definite power flow limit based on the design parameters for the specific line, but at other times, the line as a component of the overall transmission system determines the limit. System limits can result from factors such as voltage drop, possibility of voltage collapse, and system stability, both steady state and transient. System limits are functions of transmission line reactances in relation to the overall power system. Series reactance, shunt admittance, and their combination, surge impedance, are relevant to system transfer limits. System planners have long recognized this relationship, particularly where there are prospects of changing the line surge impedance, either by adding equipment (e.g., series capacitors) or by modifying the line itself (e.g., reconductoring, voltage uprating, etc.). Transmission line series inductive reactance is determined by conductor size, phase spacing, number of conductors, relative phasing (double-circuit lines), and line configuration. In transmission lines the series reactance is significantly larger than the series resistance, and is the dominant factor in a first-order explanation of system behavior. For this reason, simple reconductoring of a transmission line results in only minor changes in system power flows. Power flow on a transmission line, neglecting resistance of the line, is given by Equation 1.3-1, which can be derived from a simple circuit consisting of sending and receiving end voltage sources connected by a series reactance.

1-4


V1 •V2 • sin(δ ) X 1.3-1 Where: P = Real power transfer on the transmission line. V1 = Magnitude of sending end bus voltage. V2 = Magnitude of receiving end bus voltage. X = Line series inductive reactance between V1 and V 2. δ = Phase angle difference between V1 and V2. P=

Increasing voltage magnitude for the same line voltage and same phase difference between ends increases the power flow. By increasing the voltages V 1 and V 2 together, the power transmitted increases by the square of the voltage for the same phase angle. Power flow increases for the same end voltage magnitudes are accommodated by an increase in the phase angle difference between the voltages at the two line ends. Equation 1.3-1 imposes a fundamental limit on the amount of power that can be carried by a transmission line corresponding to a phase difference between line ends of 90°. Further increases in angle result in decreases in power flow. This is an unstable situation that can be realized in practice in two ways. If the steady-state power flow were to slowly increase to the point that the angle reached 90°, an attempt to further increase power flow would actually decrease the power flow. An increase in the power angle δ when δ is in the range from 90° to 180° results in a decrease in sin(δ) and a consequent decrease in power flow. The condition trying to increase the flow on the line actually results in a decreased flow, and system instability. Secondly, a system disturbance—for example, tripping of a line—causes a redistribution of power flow among the remaining lines, and consequent changes in the bus voltage angles. It is insufficient that the new angle differences on all the lines are less than 90°, because the angle differences must remain lower than 90° during all the transient system swinging from the time of the disturbance until the system settles in its new operating state. If a line were to experience its angle difference momentarily passing 90°, it would try to accommodate the power requirement by opening up the angle beyond 90°, decreasing the power flow. This is an unstable situation, and would cause the line to pass through the electrical point where its relay protection would sense a fault (even though none exists on the line), and result in a line trip and probable system separation. Surge impedance loading (SIL), defined in Equation 1.3-2) provides a useful rule of thumb measure of trans-



mission line loading limitation as a result of the effects of series reactance.

SIL =

V2 ZS

1.3-2

Where V is the line voltage, and ZS is the surge impedance of the transmission line given by:

ZS =

L C

1.3-3

Surge impedance ZS is a resistance in ohms. L and C in Equation 1.3-3 are positive sequence inductance and capacitance in henries per mile and farads per mile, respectively. Surge impedance loading is that loading on a three-phase power transmission line that it would have if it were loaded by a Y-connected set of resistances of ZS ohms per phase. This is the same physical condition as a radio frequency transmission line impedance matched to its termination (72 ohm coaxial cable terminated in 72 ohms in television cable). In electromagnetic theory, it corresponds to a pure TEM wave. The reactive power (vars) generated in the line capacitance is exactly canceled by the vars absorbed in the line inductance in a power transmission line at surge impedance loading (neglecting line resistance and real power losses). Surge impedance loading thus is a loading value based on physical principles related to the line design itself. Surge impedance loading is a handy tool for estimating the relative loading capabilities of lines of different voltages, constructions, and lengths from a system standpoint (St. Clair 1953). SIL is oversimplified for use in specifying actual line ratings on an operating system. However, it is a useful guide both for assessing actual loading limits and for understanding the different factors that limit line loading. Figure 1.3-1 gives a curve of line loadability in per unit of SIL as a function of line length for heavy loading conditions. Slightly different versions of Figure 1.3-1 have been published, but they are all very similar (Dunlop et al. 1979, Gutman 1988). The fundamental observation from Figure 1.3-1 is that transmission line loadability decreases as length of the line increases. Three different regions come into play in derivation of Figure 1.3-1. Short lines tend to be thermally limited, irrespective of system conditions. As line length increases, voltage drop considerations frequently come into play. At longer line lengths, stability factors may dominate. Short lines are often loaded at 2 or 2.5 times SIL and thus need reactive power (var) support to maintain the voltage. Long lines may be limited to 1.0 times SIL or less.

An important observation from Equation 1.3-2 is that surge impedance loading is a function of the square of line voltage. This has been a driving force in increased transmission voltages over the years, especially for longer lines. For an overhead transmission line, typical surge impedance is on the order of 300 ohms, while for a cable it may be 50 ohms or less. At 345 kV, SIL of an overhead line is on the order of 400 MW. Short lines may be able to carry 800 MW or more, while long lines of exactly the same construction may be limited to less than 400 MW by system considerations. Because of limitations on heat dissipation, underground transmission cables always operate very far below SIL. A consequence is that underground transmission cables are a net source of vars to the system, a condition that must be considered in system design. 1.3.3

Voltage Drop Limitations

Voltage control on the power system is of concern as system loadings increase. The system voltage distribution is affected by the series inductance and shunt capacitance of the transmission lines, and is related to the flow of reactive power in the system. Depending on the relative real and reactive power flow on a given transmission line, the voltage may increase or decrease from one end to the other. It is not desirable for voltage to vary more than 5%, or at most 10%, from one end to

Figure 1.3-1 Line loadability in terms of surge impedance loading (Dunlop et al. 1979).

1-5


the other. In some cases, a voltage drop limit is placed on power flow corresponding to the maximum allowable decrease in voltage magnitude. The longer the line or cable, generally the lower the power flow required to reach a voltage drop limit. Voltage control is a system problem, and is not generally solved by modifications to any one transmission circuit. Methods to improve voltage control on transmission circuits may take a variety of forms: 1. In some cases, bundled conductors have been in overhead lines used for short lower voltage lines to reduce series reactance, where the use of bundled conductors is required neither for thermal or corona reasons. 2. Supply of vars at various points on the system can be used to control voltage. The supply can be fixed, switched, or adjustable. In former years synchronous condensers were used to supply vars in a continuously adjustable basis. Capacitor banks are commonly used, and may be switched on or off depending on the local voltage. Static var compensators (SVCs) are also used to control voltage on the bulk power system. 3. Shunt reactors may be used for long EHV lines where the var supply from the line capacitance is greater than the system can absorb. Because voltage drop is primarily a function of line reactance rather than resistance, simple reconductoring does very little to decrease the voltage drop per unit length. Reconductoring an existing 230-kV line by replacing the original 636 kcmil Hawk ACSR with a 954 kcmil Rail ACSR only increases the voltage drop limit by 5%. For an overhead line, adding a second conductor per phase to form two conductor bundles results in a more significant reduction in series reactance, and a greater improvement in voltage drop power limit.


ular transmission line may be limited in its power-handling capacity by system voltages and var flows irrespective of the thermal capacity of the line conductors. In some cases, it is possible to increase the line flows by addition of capacitors or similar measures. Flexible AC Transmission (FACTS) is a scheme where thyristor-controlled devices are arranged to provide realtime control of transmission line flows in excess of those that would normally be allowed by system voltage and stability considerations. While voltage drop has long been known as a transmission limitation, attention has also been focused in more recent years on voltage collapse, which is a system instability that can occur under heavy loading conditions. Figure 1.3-2 shows a voltage collapse condition following a system disturbance, where the 115-kV voltage drops to 50% of the nominal operating voltage (0.5 p.u.). Voltage collapse can occur for several reasons on a heavily loaded system where there is insufficient var support. An example is the geomagnetic storm of March 13, 1989, with its resulting voltage collapse and blackout. The March 1989 storm increased attention to system problems that result from solar activity. Utilities in areas subject to geomagnetic disturbances monitor solar activity (Lesher et al. 1994), and can re-dispatch generation to reduce loading on affected lines during times of high geomagnetic activity. However, geomagnetic disturbances are not the only cause of voltage collapse. 1.3.4

Thermal Limits

Thermal limits are discussed in considerable detail later in this guidebook (see, for example, Section 2.3). In brief, the current-carrying capacity (thermal rating) of an overhead transmission circuit is determined by the assumed “worst-case” weather conditions, assumed

Shunt reactors may be applied for reasons other than voltage control—for example, to control transient overvoltages during line switching. Series capacitors may be used to partially compensate for the line series reactance, but this is usually reserved for the longest lines in relation to system stability. Whenever capacitors are installed in series with the transmission line inductance, the possibility of a series resonant condition exists. Subsynchronous resonance has been the cause of generator/turbine shaft failure and is a serious consideration for a series capacitor installation. Other problems present themselves with series capacitors—for example, provision for passage of fault current without causing failure of the capacitors. The overall effect of the concern with system voltage is that a partic-

1-6

Figure 1.3-2 Voltage collapse condition following a system disturbance.


conductor parameters, and the maximum allowable conductor temperature. Some of the specific thermal rating parameters are:

• Conductor construction: outside diameter, conductor strand diameter, core strand diameter, number of conductor strands, and number of core strands.

• Conductor AC resistance, which itself is a function of the conductor temperature.

• Conductor surface condition: solar absorptivity and


as 5 minutes. Emergency ratings are typically calculated for higher temperatures, and allow for some equipment deterioration in order to avoid load interruptions under unusual operating conditions. Broader voltage tolerances may also be appropriate under contingency conditions compared to normal operation. Lower voltage may be acceptable for a short time. Likewise, conductor resistive power losses are inconsequential during emergencies.

emissivity.

• Line location: latitude, longitude, conductor inclina-

1.3.5

Environmental Limits

tion, conductor azimuth, and elevation above sea level.

The electric field produced by overhead power transmission lines is influenced by the following factors:

• Weather: incident solar flux, air temperature, wind

• Line voltage. • Height of conductors above ground. • Configuration of conductors (line “geometry,” con-

speed, and wind direction. The temperatures experienced by terminal equipment must also be limited. In certain circuits, the thermal rating of substation equipment, in series with an overhead line, may determine the “circuit” rating. Disconnect switches, wave traps, current transformers, and other substation equipment all have current ratings that can be lower than those of the line. An example of terminal equipment limitations on older lines is 600 A disconnect switches. At EHV, bundled conductors are employed to reduce the conductor surface electric field and consequent corona phenomena of radio, television, and audibl e n o i s e. B u n d l e d c o n d u c t o r s we re o ri g i n a l ly introduced to lower line reactance and increase the line loadability, and their use for noise reduction was recognized later. Especially at the higher transmission voltages of 500 and 765 kV, the thermal current-handling capacity of a bundled conductor may be far in excess of the ratings of the circuit breakers. In such cases, the thermal limit of the circuit is entirely dominated by the terminal equipment. A survey of utility 345-kV circuit thermal limits in New York State gave the following limitations:

• 41% of the circuits were limited by the line or cable. • 18% of the circuits were limited by current transformers.

• 4% of the circuits were limited by wave traps. • 4% of the circuits were limited by the bus-work. • 3% of the circuits were limited by disconnect

ductor spacing, relative phasing of multi-circuit lines, and use of bundled conductors).

• Lateral distance from the center line of the transmission line.

• Height above ground at the point of field measurement.

• Proximity of conducting objects (trees, fences, buildings) and local terrain. The electric field near ground level produced by an overhead transmission line induces voltages and currents in nearby conducting objects. These objects are typically the size of people, animals, motor vehicles, sheds, and similar-sized bodies. Electric field coupling is capacitive coupling, and can be represented by a current source in parallel with a high source impedance (Norton equivalent circuit). The allowable electric field is limited by the maximum allowed induced current and voltage. For example, the National Electrical Safety Code specifies a maximum of 5 mA short-circuit current induced into the largest vehicle that could be stopped under the line, based on human susceptibility to loss of muscular control (letgo). Thus, if an existing line induces 4.9 mA on a large tractor-trailer, it would not be possible to increase the voltage without taking other measures to limit the electric field.

switches.

• 4% of the circuits were limited by the circuit breakers. Lines and substation equipment may have different thermal ratings for normal and for emergency system conditions. Emergency ratings typically apply for a limited period of time, not exceeding 24 hours and as short

Electric field levels are limited by law in some jurisdictions. Some regulations are specified at the edge of the right-of-way for public exposure. Other regulations are maximum levels on the right-of-way based on induction to an assumed size object. These regulations may restrict

1-7


voltage increases on presently existing transmission lines without taking electric field reduction measures. Magnetic field is affected by the same variables as electric field, except line current replaces line voltage, and nearby objects generally have minimal impact on the magnetic field. Magnetic field coupling is generally of significance for objects that parallel the transmission line for a long distance. Such objects include pipelines, telephone and railway signal circuits, and metal fences. Because magnetic field is a function of line current, and current increases during fault conditions, it may be necessary to evaluate magnetic field effects under both normal operation and faults. Magnetic field coupling is inductive coupling, and generally produces low voltages with low source impedances. Increasing current on a transmission line increases the magnetic field, and thus increases magnetically induced voltages and currents. This may be significant in cases such as when a transmission line parallels a railroad right-of-way. This is the inductive coordination problem that has been around since the dawn of the power industry with respect to telephone and railroad signal facilities. Increasing current flow on existing lines may require coordination with parallel infrastructure. In some jurisdictions, maximum magnetic field levels are specified by regulation. If an existing transmission line is operating near the magnetic field limit set by regulation, the ability to increase line current may be impaired, unless measures are taken to reduce the magnetic field levels.


Electric fields can be shielded by conducting objects. Vegetation is sufficiently conductive to reduce electric field levels. Grounded wires can be strung under the phase conductors at road crossings to reduce electric field levels. Grounding measures can be taken for fixed objects to eliminate induced voltages. On the other hand, magnetic field shielding is significantly more difficult than electric field shielding. Shielding a transmission line by magnetic materials is impractical. Flux canceling loops have been developed, but incur power loss and complexity in actively driven loops. Shielding is less practical as a mitigation measure for magnetic fields than it is for electric fields. 1.3.6

Examples – Overhead Lines

Figure 1.3-3, adapted from (Gutman 1988), repeats the generalized SIL curve of Figure 1.3-1 with the addition of a curve for thermal limitation. Superimposed on the SIL curve are curves for:

• Thermal limit for a single 1414 kcmil conductor per phase.

• Voltage drop limitation of 5%. • Steady-state stability margin of 35%. The thermal and voltage drop limitation curves cross at a line length of approximately 110 miles. The voltage drop and stability limitation curves cross at a line length of approximately 190 miles. Based on the thermal, voltage, and stability curves, three regions are identified in Figure 1.3-3.

Figure 1.3-3 Three line loading limits: thermal limit, voltage drop, and steady-state stability.

1-8



• Less than approximately 110 miles line length, the line is thermally limited.

• Between approximately 110 and 190 miles line length, the line is limited by voltage drop.

• Beyond approximately 190 miles, the line is stability limited. Figure 1.3-3 thus illustrates the three regimes of lineloading limits. Figure 1.3-3 further illustrates that, for a specific transmission line example, the data points for the line fall near, but not on, the generalized SIL curve. The fact that the values are similar, but not identical, illustrates the point that the SIL curve is a handy reference for sanity checking and rule of thumb analysis, but is not to be considered exact for any specific line. Sample surge impedance and thermal loading values for transmission lines of different voltages are given in Table 1.3-1. For comparison with the 345-kV example in Figure 1.33, the 230-kV example in Table 1.3-1 has a thermal rating of 440 MW and surge impedance loading of 145 MW. Stability and voltage control limits for this line depend on the system to which it is connected. As an example of voltage drop, assume the 230-kV line is 100 miles long. Further assume that the sending end bus has a voltage of 1.0 per unit, and the receiving end bus has a voltage of 0.95 per unit, a 5% difference. Also assume the 230-kV line is at 1.0 power factor at the receiving end, neither taking nor supplying vars to the bus. In this case, the 230-kV line flow would be 220 MW, about 1.5 times SIL, but half the thermal rating. This result is in line with the 345-kV example given in Figure 1.3-3. Because SIL is primarily related to transmission line series reactance rather than resistance, simple reconductoring would produce only a minor effect on SIL limits such as voltage drop. In this 230-kV example of 5% voltage drop, reconductoring from Cardinal to Falcon ACSR would increase the loading from 220 MW to 230

MW, a minor difference. Adding a second Cardinal conductor per phase to make two conductor bundles would increase the loading to 310 MW. Adding a second conductor per phase has a greater impact on surge impedance, and thus on SIL and line loading. Full use of the 230-kV line’s thermal rating would require system changes to provide var support at the receiving end of the line. The thermal limit is determined by line current and line voltage. Equation 1.3-2 shows that surge impedance loading is proportional to the square of the line voltage. Doubling line voltage doubles the thermal rating of the line, but multiplies SIL by a factor of 4. This has been the driving force during the history of the electric power industry for increasing voltage levels, and sometimes a motivation for voltage upgrades of existing lines. 1.4

CHAPTER PREVIEW

1.4.1

Overhead Lines (Chapter 2)

Overhead transmission lines are the predominant method of transporting power in any but the most urbanized power systems such as the New York City area. Of all the types of power equipment, overhead lines offer the largest opportunities for increased power flow at modest cost. Limits are placed on power flow through overhead lines in order to limit electrical phase shift, avoid excessive voltage drop, and limit the temperature of the current-carrying conductors. The emphasis in this book is on the latter of these limits. Chapter 2 discusses the reasons for limiting the temperature of overhead lines and the consequences of exceeding such limits. The chapter also covers the techniques for modifying the clearance of existing lines, reconductoring them without rebuilding structures, and real-time monitoring of weather and line sag-tensions. A number of interesting case studies are included at the end of the chapter.

Table 1.3-1 Power Flow Limits on Lines and Cables System kV

XL (Ω/mi)

XC (Ω/km)

(MΩ-mi)

Surge Impedance

SIL

Thermal Rating

(Ω)

(MW)

(MW)

(MΩ-km)

Transmission Line Characteristics 230

0.75

0.47

0.18

0.29

367

145

440

345

0.60

0.37

0.15

0.24

300

400

1500

500

0.58

0.36

0.14

0.26

285

880

3000

765

0.56

0.35

0.14

0.26

280

2090

8000

39

3050

2100

Transmission Cable Characteristics 345

.25

.16

.0060

.0097

1-9


1.4.2

Underground Cables (Chapter 3)

Chapter 3 provides an overview on underground cable systems and a very brief background on each of the major transmission cable types. As with overhead lines, the discussion on underground cable considers aspects external to a specific cable circuit that may limit power flow regardless of the cable circuit’s rating. The chapter also includes an overview on cable system ampacity, including worked examples. The major barriers to increased underground cable rating are inherent to each cable system type or installation location. Methods for increasing the rating of underground cable—such as surveying the soil thermal resistivity along the route and removing thermal bottlenecks due to other cable circuits or external heat sources—are discussed in some detail. Given the relatively long thermal time constant of underground cables, dynamic rating methods are very attractive ways of increasing the rating. The chapter discusses monitoring methods and the necessary real-time data required for dynamic rating calculations with underground cable. Case studies are included for actual cable uprating projects, and the chapter provides a summary comparison of uprating methods. 1.4.3

Power Transformers (Chapter 4)

Power transformers represent a significant portion of capital investment costs. Under existing conditions in the industry, utility budgets are reduced and networks are being forced to support greater power transfer over existing transmission circuits than ever before. As such, there is increased interest in safely utilizing all available capacity of power transformers. In general, transformer load capacity is limited by equipment (winding and oil) temperatures. Industry standards (IEEE C57.12.00 in the U.S.) specify a maximum average winding rise that defines the rated load. In other words, when operating at rated nameplate current, the average winding rise shall not exceed the given value. Chapter 4 describes the general construction of power transformers, outlines short- and long-term risks related to the loading of transformers, provides an overview of heat transfer mechanisms and describes the four most prevalent thermal models, and discusses factors behind thermal ratings, including ambient air temperature, load, and maintenance considerations.

1-10


1.4.4

Substation Terminal Equipment (Chapter 5)

Substation terminal equipment consists of many different types and designs of power equipment. Included in this classification are line traps, oil circuit breakers, SF6 circuit breakers, rigid tubular bus, line disconnects, current transformers, bolted connectors, and insulator bushings. The increase in circuit rating, resulting from applying the various methods of increasing power flow in overhead transmission lines, underground cable, and power transformers is often limited by terminal equipment. In some cases, a large increase in circuit rating may be obtained for a very modest expenditure on terminal equipment rather than a relatively large investment in lines, cables, or transformers. Chapter 5 describes practical, rather simple methods of increasing the power flow through less capital-intensive equipment such as switches, bus, line traps, breakers, and power transformer auxiliary equipment. The chapter includes a summary of terminal equipment types, specific thermal models for each type of equipment, dynamic thermal rating of terminal equipment, and methods of determining specific thermal parameters from field test, laboratory test, and manufacturer heatrun tests. 1.4.5

Dynamic Rating and Monitoring (Chapter 6)

Since the mid-1980s, considerable attention has been paid to increasing the power flow of overhead lines, power transformers, underground cables, and substation terminal equipment by means of monitoring weather and the equipment thermal state and by developing more accurate thermal models. The resulting dynamic thermal rating techniques typically yield increases of 5 to 15% in capacity. Chapter 6 provides an overview of dynamic thermal rating methods. The chapter aims to present a balanced overall view of when dynamic rating methods are appropriate, how they are best implemented in a practical operational application, and how such methods can be applied to complex interconnections consisting of multiple circuits and many circuit elements. The chapter discusses concerns related to dynamic ratings; outlines the need for inspections and/or real-time monitors and the problems that may arise without them; provides an overview on models for overhead lines, transformers, underground cables, and substation terminal equipment; describes the use of DTCR software; identifies operating issues related to dynamic thermal ratings; and describes field studies of dynamic ratings used for overhead lines, transformers, underground cables, substation terminal equipment, and power circuits.


REFERENCES

Boteler, D. H. 1994. “Geomagnetically Induced Currents: Present Knowledge and Future Research.” IEEE Transactions on Power Delivery. Volume 9. Number 1. January. pp. 50-58. Dunlop, R. D., R. Gutman, and P. P. Marchenko. 1979. “Analytical Development of Loadability Characteristics for EHV and UHV Transmission Lines.” IEEE Transactions on Power Apparatus and Systems. Volume 98. Number 1. March/April. pp. 606-617. correction May/June. page 699. Federal Power Commission. 1964. National Power Survey. Part II-Advisory Reports. U. S. Government Printing Office. Washington, D. C. October.


Koessler, R. J. and J. W. Feltes. 1993. “Voltage Collapse Investigations with Time-Domain Simulation.” IEEE/NTUA Joint International Power Conference. Athens Power Tech Proceedings. Athens, Greece. September 5-8. Lesher, R. L., J. W. Porter, and R. T. Byerly. 1994. “Sunburst—A Network of GIC Monitoring Systems.” IEEE Transactions on Power Delivery. Volume 9. Number 1. January. pp. 128-137. North American Electric Reliability Council (NERC). 1995. “Transmission Transfer Capability.” St. Clair, H. P. 1953. “Practical Concepts in Capability and Performance of Transmission Lines.” AIEE Transactions on Power Apparatus and Systems. Volume 72. Part III. December. pages 1152-1157.

Gutman, R. 1988. “Application of Line Loadability Concepts to Operating Studies.” IEEE Transactions on Power Systems. Vol. 3. Number 4. November. pages 1426-1433.

1-11


CHAPTER 2

Overhead Transmission Lines

2.1

INTRODUCTION

The degree to which the maximum power flow can be increased on an existing overhead line depends on its length, the original design margins, environmental concerns, and many other issues. Because power flow on the transmission system is a function of the overall system topology (transmission lines, transformers, generation, series and shunt compensation, and load), system considerations can also limit the maximum power flow on a specific transmission line. Transmission line ratings are sometimes developed on a system basis rather than on an individual line basis. The overall limit may be between operating areas, irrespective of ownership or individual lines, and may change during a day based on system conditions. Sometimes a power transmission line possesses a definite power flow limit based on the design parameters for the specific line; at other times the line as a component of the overall transmission system determines the limit. System limits can result from factors such as voltage drop, possibility of voltage collapse, and system stability, both steady state and transient. Power system limits, on the power flow through individual overhead lines, are described in more detail in Chapter 1, which discusses power system limits on increased power flow. System limits are functions of transmission line reactances in relation to the overall power system. Series reactance, shunt admittance, and their combination, as well as surge impedance are relevant to system transfer limits. Transmission line series inductive reactance is determined by conductor size, phase spacing, number of conductors, relative phasing (double circuit lines), and line configuration. In transmission lines, the series reactance is significantly larger than the series resistance, and is the dominant factor in a first-order explanation of system behavior. For this reason, simple reconductoring of a transmission line results in only minor changes in system power flows. Critical factors related to power flow limits for overhead lines include:

• • • •

Surge impedance loading Voltage drop Thermal limits Environmental limits

2-1

Chapter 2: Overhead Transmission Lines

2.1.1


Surge Impedance Loading

• Conductor AC resistance, which itself is a function of

Surge impedance loading (SIL, defined in Equation 2.11) provides a useful rule-of-thumb measure of transmission line loading limitation as a result of the effects of series reactance.

SIL =

2.1-1

For an overhead transmission line, typical surge impedance is on the order of 300 ohms, while for a cable it may be 50 ohms or less. At 345 kV, SIL of an overhead line is on the order of 400 MW. Short lines may be able to carry 800 MW or more, while long lines of exactly the same construction may be limited to less than 400 MW by system considerations. 2.1.2

Voltage Drop

Voltage control on the power system is of concern as system loadings increase. The system voltage distribution is affected by the series inductance and shunt capacitance of the transmission lines. It is not desirable for voltage to vary more than 5%, or at most 10%, from one end to the other. In some cases, a voltage drop limit is placed on power flow corresponding to the maximum allowable decrease in voltage magnitude. The longer the line, generally the lower the power flow required to reach a voltage drop limit. Voltage control is a system problem, and is not generally solved by modifications to any one transmission line. Because voltage drop is primarily a function of line reactance rather than resistance, simple reconductoring does very little to decrease the voltage drop per unit length. Reconductoring an existing 230-kV line by replacing the original 636 kcmil (324 mm2) Hawk ACSR with a 954 kcmil (487mm2 ) Rail ACSR only increases the voltage drop limit by 5%. Adding a second conductor per phase, to form two conductor bundles, results in a significant reduction in series reactance, and yields an increase in the voltage drop power limit. 2.1.3

Thermal Limits

Thermal limits are discussed in considerable detail in this chapter. In brief, the current carrying capacity (thermal rating) of an overhead transmission circuit is determined by the assumed “worst case” weather conditions, assumed conductor parameters, and the maximum allowable conductor temperature. Some of the specific thermal rating parameters are:

• Conductor construction: outside diameter, conductor strand diameter, core strand diameter, number of conductor strands, and number of core strands.

2-2

• Conductor surface condition: solar absorptivity and emissivity.

• Line location: latitude, longitude, conductor inclination, conductor azimuth, and elevation above sea level.

2

V ZS

the conductor temperature.

• Weather: incident solar flux, air temperature, wind speed, and wind direction. 2.1.4

Environmental Limits

The electric field produced by overhead power transmission lines is influenced by the following factors:

• Line voltage • Height of conductors above ground • Configuration of conductors (line “geometry,” conductor spacing, relative phasing of multi-circuit lines, use of bundled conductors)

• Lateral distance from the center line of the transmission line

• Height above ground at the point of field measurement

• Proximity of conducting objects (trees, fences, buildings) and local terrain The electric field near ground level produced by an overhead transmission line induces voltages and currents in nearby conducting objects (St. Clair 1953, Federal Power Commission 1964, Dunlop et al. 1979, Koessler and Feltes 1993, Boteler 1994, Lesher et al. 1994, EPRI 2005). These objects are typically the size of people, animals, motor vehicles, sheds, and similar-sized bodies. Electric field coupling is capacitive coupling, and can be represented by a current source in parallel with a high source impedance (Norton equivalent circuit). Electric field levels are limited by law in some jurisdictions. Some regulations are specified at the edge of the right-of-way (ROW) for public exposure. Other regulations are maximum levels on the ROW based on induction to an assumed size object. These regulations may restrict voltage increases on presently existing transmission lines without taking electric field reduction measures. Magnetic field is affected by the same variables as electric field, except line current replaces line voltage, and nearby objects generally have minimal impact on the magnetic field. Magnetic field coupling is generally of significance for objects that parallel the transmission line for a long distance. Such objects include pipelines,



telephone and railway signal circuits, and metal fences. Because magnetic field is a function of line current, and current increases during fault conditions, it may be necessary to evaluate magnetic field effects under both normal operation and faults. Magnetic field coupling is inductive coupling, and generally produces low voltages with low source impedances (St. Clair 1953, Federal Power Commission 1964, Dunlop et al. 1979, Koessler and Feltes 1993, Boteler 1994, Lesher et al. 1994, EPRI 2005).

• Section 2.4, Effects of High-Temperature Operations,

Increasing current on a transmission line increases the magnetic field, and thus increases magnetically induced voltages and currents. This may be significant in cases such as when a transmission line parallels a railroad ROW. This is the inductive coordination problem that has been around since the dawn of the power industry with respect to telephone and railroad signal facilities. Increasing current flow on existing lines may require coordination with parallel infrastructure. In some jurisdictions maximum magnetic field levels are specified by regulation. If an existing transmission line is operating near the magnetic field limit set by regulation, the ability to increase line current may be limited, unless measures are taken to reduce the magnetic field levels.

• Section 2.7, Dynamic Monitoring and Line Rating,

Electric fields can be shielded by conducting objects. Vegetation is sufficiently conductive to reduce electric field levels. Grounded wires can be strung under the phase conductors at road crossings to reduce electric field levels. Grounding measures can be taken for fixed objects to eliminate induced voltages. On the other hand, magnetic field shielding is significantly more difficult than electric field shielding. Shielding a transmission line by magnetic materials is impractical. Flux canceling loops have been developed, but incur power loss and complexity in actively driven loops. Shielding is less practical as a mitigation measure for magnetic fields than it is for electric fields (St. Clair 1953, Federal Power Commission 1964, Dunlop et al. 1979, Koessler and Feltes 1993, Boteler 1994, Lesher et al. 1994, EPRI 1994, EPRI 2005). Chapter 2 includes seven sections:

• Section 2.2, Uprating Constraints, discusses constraints on electrical and mechanical safety, with information on sag-tension calculations, limiting high-temperature sag, constraints related to windinduced conductor motion, electrical clearance, loss of conductor strength, constraints on structural loads, and environmental effects.

• Section 2.3, Line Thermal Ratings, explores the calculation of line thermal ratings, and describes common heat balance methods.

describes annealing, calculation of sag and tension, thermal and creep elongation, and connectors and conductor hardware at high temperature.

• Section 2.5, Uprating without Reconductoring, discusses deterministic and probabilistic methods of uprating without reconductoring.

• Section 2.6, Reconductoring without Structural Modifications, reviews the various reconductoring choices using new commercially available conductors. introduces the principles of dynamic rating methods.

• Section 2.8, Case Studies, includes a number of uprating test cases and an economic comparison of line uprating alternatives. 2.2

UPRATING CONSTRAINTS

2.2.1

Introduction

Increasing the thermal rating of an existing line requires dealing with constraints on electrical and mechanical safety. The uprated line must remain safe under all electrical power flows up to its maximum without compromising the mechanical safety under severe ice and wind loads. This section discusses issues related to constraints on uprating, including determining what constitutes a constraint in various areas of design, operation, and the environment. 2.2.2

Sag-tension Calculations

Normally, “sag-tension” calculations are performed using numerical programs in order to determine the sag and the tension of a conductor catenary as a function of ice and wind loads, conductor temperature, and time. Calculation examples from a program like SAG10 are shown below to illustrate how tension limits are applied and how maximum conductor tension and maximum final high temperature sag are taken for the purposes of strain structure design and tower placement. Details of sag-tension calculation methods are not included, but examples and key references are cited. In the design, uprating, or simple maintenance of power transmission lines, the concern of primary importance is public safety. It is more important that a line be safe than it carry power. Other than designing the supporting structures such that they remain standing under even the most severe weather conditions, the safety of a line is essentially determined by the position of its energized conductors relative to nearby people, buildings, and vehicles. Maintaining minimum distances to nearby 2-3


objects and people is primarily a matter of limiting the sag of the energized conductors under high mechanical loads and high temperature conditions. In addition to making lines safe, other important constraints are the level of electric and magnetic fields produced (e.g., electric fields increase as the conductor gets closer to the ground), the maximum structure loads during occasional high wind and ice loads, and the maximum temperature at which the energized conductors are allowed to operate. Given standard “worst-case” weather conditions, the thermal rating of an existing line is determined by the maximum allowable conductor temperature. Thus, uprating such lines without reconductoring normally requires finding ways to maintain electrical clearances while operating at a higher conductor temperature.


ture is the minimum attachment height, which determines structure height and spacing. In a detailed line design that has many different spans, this sort of sagclearance calculation must be developed for all spans (Ehrenburg 1935, Winkleman 1959). Definitions of the labels in Figure 2.2-1 are as follows:

• “Init” is the initial installed unloaded (with no ice or wind) sag of the conductor. It is typically at a conductor temperature of 10°C to 25°C (50°F to 80°F). This is also typically referred to as the line “ruling span stringing sag.”

• “Final–STC” is the final sag of the conductor at 15oC (60oF) after an ice/wind-loading event has occurred for a short time—typically an hour. STC stands for “short-time creep.”

• “Final–LTC” is the final sag of the conductor at 15oC Figure 2.2-1 is a basic sag-clearance diagram, which illustrates how minimum ground clearance must be maintained under both heavy loading and high temperature events over the life of both new and re-rated transmission lines. The figure shows ground clearance and line sags under normal conditions, high ice/wind load, and high temperature conditions for a ruling (or “equivalent”) span. Note that the sum of the minimum ground clearance, the buffer, and the sag at maximum tempera-

(60oF) after an extended period—typically 10 years— where the conductor simply persists at a conductor temperature on the order of 15°C (59°F) without ice or wind. “LTC” stands for “long-time creep,” which occurs even if heavy ice and wind loads never occur.

• “Max Load” is the sag of the conductor during the specified maximum ice and wind loading at a reduced temperature—typically 18°C to 0°C (0°F to 32°F). Note that the sag prior to this event is normally assumed to be the Init sag and the sag after this event is the Final–STC sag.

• “TCmax” is the sag of the conductor when its temperature is the maximum for which the line is designed—typically 50°C to 150°C. The final sag at 15oC (60oF), prior to this high temperature event, is assumed to be the larger of the Final–STC and the Final–LTC sags. Figure 2.2-1 shows typical behavior of transmission conductors where the sag under maximum ice and wind load conditions is less than that at the maximum temperature. For small or weak conductors experiencing heavy ice loads, this may not be true. Note that the diagram illustrates the “snapshot” nature of traditional sag-tension calculations. The actual conductor sag position at any time in the life of the line depends on the actual mechanical and electrical load history of the line. If the high load event is more severe or persists for a longer time than assumed in determining the Max Load condition, then the corresponding sag at Max Load and the sag increase will be greater. The use of buffers is required because of such uncertainties. Figure 2.2-1 Sag diagram showing sags for various times and loading conditions.

2-4

For transmission conductors made up primarily of aluminum strands under tension, sag never stops increasing



with both time and high loading events throughout the life of the line (Aluminum Association 1974, Harvey and Larson 1972, Harvey 1979). That is, the sag at a given conductor temperature (e.g., 15.5°C, or 60oF) increases steadily over the years after construction. However, with moderate unloaded and loaded conductor tensions (typically 15% and 50% of rated strength), the rate of change in sag with each such event decreases over the life of the line. Thus, if a heavy ice load event occurs 10 years after installation, the permanent increase in sag is much smaller than if it occurred in the first 6 months after construction. Similarly, under everyday unloaded conditions, the rate of change in sag will decrease with time, over the life of the line.

important to the correct calculation of maximum tension. Use of a linear modulus will result in an overestimate of the maximum tension.

Tension-Elongation Diagram (Normal) The “tension-elongation” diagram shown in Figure 2.2-2 shows how the conductor tension changes corresponding to the changes in sag position with load, time, and temperature shown in the preceding sag diagram.

The thermal elongation of stranded conductors is essentially the same as that of its component strands. Therefore, for an all aluminum or copper conductor, once the sag at “final” everyday conditions is established, the sag at high temperatures can be calculated and limited with relatively small uncertainty.

The initial unloaded (“Init”) sag corresponds to the initial unloaded (Init) tension. In the design of a new overhead line, increasing this initial tension decreases maximum temperature (Tcmax) sag and can allow the use of fewer and shorter structures. However, increased everyday tension levels also increase the maximum (“Max”) tension loads (and thus the cost) on angle and dead-end structures, and decrease the mechanical selfdamping of the conductor, which can lead to Aeolian vibration-induced fatigue damage unless dampers are applied.

High Temperature Sag with All Aluminum Conductors For example, consider a line section of an all-aluminum, 37 strand (Arbutus) conductor having a ruling span of 600 ft (183 m) installed to meet the following constraints: maximum tension of 50%, 33% initial unloaded at 15°F and 25% final unloaded at 15°F (-9.4 °C). An equally typical SAG10 program line design sag-tension run is shown in Table 2.2-1.

As the temperature of the conductor increases, its length and the resulting sag increase while the line tension decreases. Errors in modeling the conductor modulus at high temperatures have little or no effect on the calculated sag, but the thermal elongation behavior of conductors at high temperatures is very important. As is noted in Section 2.4, the thermal elongation of ACSR can be particularly complex. 2.2.3

Limiting High Temperature Sag

With an older existing line that has reached its final sag, increasing the conductor tension reinitiates creep (though at a reduced rate). It also increases angle and dead-end structure loads (though perhaps not higher than they were upon initial installation) and is likely to increase Aeolian vibration activity. When reconductoring an existing line, an increase in the maximum tension load may lead to the need for reinforcement or replacement of angle and dead-end structures and may be a critical factor in determining whether reconductoring is an economic uprating solution. The modulus (actually the spring constant) of the conductor determines the increase in tension between unloaded and loaded states. Figure 2.2-2 shows typical behavior for a transmission conductor where the difference in tension between unloaded and loaded states may result in a tension increase by a factor of two or more. Specification of a realistic, nonlinear conductor modulus (stress-strain behavior) under high tension loads is

Figure 2.2-2 Tension diagram showing conductor tension for various times and loading conditions.

2-5



Table 2.2-1 Sag-Tension Calculations for 37 AAC (Arbutus) ALUMINUM COMPANY OF AMERICAN SAG AND TENSION DATA Conductor Arbutus

795.0 kcmil

37 Strands AAC

Area = 0.6234 sq in.

Dia + 1.026 in.

Wt = 0.746 lb/°F

RTS= 13900 lb

Span + 600.0 ft

Creep is a Factor

NESC Medium Load Zone

Design Points

Final

Initial

Temp (°F)

Ice (in.)

Wind (psf)

K (lb/°F)

Weight (lb/°F)

Sag (ft)

Tension (lb)

Sag (ft)

Tension (lb) 6140

15.

.25

4.00

.20

1.451

12.02

5446.

10.65

32.

.25

.00

.00

1.143

12.00

4294.

10.06

5118

0.

.00

.00

.00

.746

8.77

3833.

6.63

5067.

15.

.00

.00

.00

.746

9.67

3475.a

7.27

4621.

30.

.00

.00

.00

.746

10.58

3179.

7.98

4212.

60.

.00

.00

.00

.746

12.34

2727.

9.54

3524.

90.

.00

.00

.00

.746

13.99

2406.

11.19

3006.

120.

.00

.00

.00

.746

15.54

2167.

12.82

2624.

167.

.00

.00

.00

.746

17.78

1897.

15.24

2210.

212.

.00

.00

.00

.746

19.73

1711.

17.37

1941.

a. Design condition.

High Temperature Sag with ACSR Because steel elongates thermally at half the rate of aluminum, the thermal elongation rate of ACSR conductor is less than that of all aluminum conductor. Therefore, older lines (which often have relatively small conductors with high steel content) sag less than all aluminum conductors for the same change in temperature. The degree to which an ACSR conductor’s thermal expansion is less than that of an all aluminum conductor (AAC) is dependent on the ratio of the steel to aluminum area. This ratio, expressed as a percentage, is usually referred to as the ACSR “Type” number. Table 2.2-2 lists the composite thermal elongation of ACSR conductors with different type numbers. Typical values for the coefficient of thermal expansion (α) of an ACSR are shown in Table 2.2-2. Although we have listed composite thermal elongation coefficients for ACSR, in reality the aluminum strands elongate at twice the rate of the steel strands. The reduced thermal elongation coefficient of the composite Table 2.2-2 Coefficients of Thermal Expansion for Bare Stranded Conductors Conductor

Type Number

α (per degree C)

AAC

0

-6 23.0 x 10

36/1 ACSR

3

-6 22.0 x 10

18/1 ACSR

5

21.1 x 10

45/7 ACSR

7

-6 20.7 x 10

54/7 ACSR

13

-6 19.5 x 10

26/7 ACSR

16

-6 18.9 x 10

30/7 or 30/19 ACSR

23

17.5 x 10

2-6

-6

-6

is actually the result of both this difference in expansion with temperature and the change in component tensions that it produces.

Ignoring Aluminum Compression in ACSR at High Temperature Over the past 40 years, the Varney graphical method (Aluminum Company of America 1961) has been the basis of most sag-tension programs. The Alcoa SAG10 program is widely used. The sag-tension Table 2.2-3, taken from the SAG10 program, shows the sag and tension (total, aluminum, and steel component tensions) for initial and final conditions for 30/19, 795 kcmil (405 mm2) ACSR (Mallard) initially sagged so as not to exceed a final unloaded tension of 25% of Mallard’s Rated Breaking Strength at 60oF (15.5oC). NESC Medium Loading conditions and conductor temperatures up to 302oF (150oC) are included. Notice that the knee point temperature, where the aluminum tension goes to zero, under final conditions, occurs at only 90oF (32oC). Figure 2.2-3 shows final sag versus conductor temperature for ACSR (Mallard) in four different ruling span lengths. Note the change in slope of the curves below 50oC where the knee point is predicted to occur. Many older lines that are typical candidates for uprating were designed with high steel ACSR such as 30/19, 30/7, and 26/7. The low thermal elongation beyond the knee point temperature, illustrated in the preceding calculations, makes these older lines attractive candidates for operation at higher temperatures. In such design situations, the difference in predicted sag at high temperature can be very important.



Table 2.2-3 Sag-Tension Calculations for 30/19, 795 kcmil ACSR (Mallard) ALUMINUM COMPANY OF AMERICAN SAG AND TENSION DATA Conductor Mallard

795.0 kcmil

30/19 ACSR

Area = .7669 sq. in.

Dia + 1.140 in.

Wt = 1.235 lb/°F

RTS = 38400 lb

Span + 600.0 ft

Creep is a Factor


Design Points

Final

Initial

Temp (°F)

Ice (in.)

Wind (psf)

K (lb/°F)

Weight (lb/°F)

Sag (ft)

Tension (lb)

Sag (ft)

Tension (lb)

15.

.25

4.00

.20

1.955

7.80

11283. 3423.A 7859.S

6.83

12880. 4986.A 7894.S

32.

.25

.00

.00

1.667

7.68

9773. 2377.A 7395.S

6.36

11804. 4462.A 7342.S

0.

.00

.00

.00

1.235

5.30

10495. 3193.A 7302.S

4.45

12499. 4972.A 7527.S

15.

.00

.00

.00

1.235

5.79

9600.a 2508.A 7092.S

4.69

11864. 4623.A 7242.S

30.

.00

.00

.00

1.235

6.34

8775. 1860.A 6914.S

4.95

11241. 4277.A 6963.S

60.

.00

.00

.00

1.235

7.56

7357. 693.A 6664.S

5.54

10039. 3605.A 6435.S

90.

.00

.00

.00

1.235

8.65

6432. 0.A 6432.S

6.23

8921. 2966.A 5955.S

120.

.00

.00

.00

1.235

9.26

6010. 0.A 6010.S

7.03

7910. 2373.A 5537.S

167.

.00

.00

.00

1.235

10.27

5422.S 0.A 5422.S

8.45

6580. 1553.A 5027.S

212.

.00

.00

.00

1.235

11.27

4939. 0.A 4939.S

9.94

5600. 894.A 4706.S

257.

.00

.00

.00

1.235

12.30

4528. 0.A 4528.S

11.45

4864. 343.A 4522.S

302.

.00

.00

.00

1.235

13.34

4178. 0.A 4178.S

12.80

4352. 0.A 4352.S


Figure 2.2-3 Sag for a “strong” 30/19 ACSR conductor (calculated ignoring aluminum strand compression) as a function of conductor temperature and ruling span length.

2-7


Considering Aluminum Compression in ACSR at High Temperature Starting with the studies of Barrett at Ontario Hydro (Barrett et al. 1982), the assumption of zero compressive stress in ACSR beyond the knee point temperature has come into question. The question centers not on the correct calculation of the knee point temperature but on whether the aluminum strands can support compressive stresses above it. The Canadian Electrical Association’s STESS software program incorporated Barrett’s research. Inclusion of the compressive effects of the aluminum strands of high steel content conductors such as 26/7 ACSR (Drake) can add as much as 3 ft (0.91 m) to the sag at 150oC in a 1200 ft (366 m) span. The effect is less with smaller ruling spans and with lower conductor temperatures. Recent studies by Rawlins (Rawlins 1998) seem to confirm the existence of compressive effects as well as residual stresses (due to manufacturing) in aluminum strands at high temperatures. The effect on sag at high temperatures appears to be much smaller than those predicted by Barrett. The widely used SAG10 program has incorporated Rawlins’s studies as an optional calculation. In a 1200 ft (366 m) span, Rawlins’s method would add about 1 ft (30 cm) to the sag of a high steel conductor such as Drake at 150oC. Figure 2.2-4 shows a comparison of sag as a function of conductor temperature calculated with the following assumptions:

• The SAG10 computer program with an assumption


• The STESS computer program with the default assumption of 10 MPa (1450 psi) for maximum compressive stress and no residual stress. Figure 2.2-5 is a similar plot that shows the somewhat larger sag differences that occur in a 1200 ft (366 m) ruling span. At this point, there is no clear way to determine which of these methods is correct. Indeed, there is no way to be certain that the stress assumptions for any of the calculations is correct for all ACSR conductors installed in old and new lines. However, there is a distinct possibility that the original line design sag-tension calculations, assuming no compressive stress in the multiple aluminum layers, yielded sags above the kneepoint that were too small. The uncertainty centers on how much the sag should be increased to be certain that electrical clearances will be maintained at an increased maximum conductor temperature. 2.2.4

Uprating Constraints Related to WindInduced Conductor Motion

Transmission lines must be designed not only to provide adequate vertical clearance for electrical and safety considerations, but also to allow for adequate horizontal clearance to tall objects and buildings at the edge of the ROW under high wind conditions. This conductor displacement is termed conductor blowout and is normally at its maximum midway between conductor support points, as shown in Figure 2.2-6. Note that the horizontal displacement at midspan (XH) is determined in part by the conductor sag (D).

of zero compressive stress in the aluminum strands.

• The SAG10 computer program with the default assumption of 2500 psi (17.2MPa) residual stress and allowance for aluminum compression.

Figure 2.2-4 Sag at high temperatures calculated with and without aluminum compression.

2-8

The maximum displacement of the outermost conductors from the center of the ROW under high wind conditions can be one of the most important variables in

Figure 2.2-5 Final sags for Mallard ACSR in a 1200-ft span.



determining ROW width or for a given ROW width, determining the maximum structure spacing. In addition to blowout in strong cross-winds, wind can cause certain oscillatory conductor motions. See Table 2.2-4. By far the most common oscillatory windinduced motion is aeolian vibration since it occurs under low-speed everyday wind conditions. Unless it is controlled, aeolian vibration can accumulate millions of cycles, which cause fatigue failure of copper, aluminum, or steel strands. A less common, but more dramatic, form of wind-induced conductor motion is ice galloping. It occurs for strong winds in combination with ice on the conductors and can yield high amplitude, oscillatory conductor motions that result in repeated flashovers between the phase conductors or between a phase conductor and a shield wire. The amplitude of wind-induced conductor aeolian vibration is generally less than the conductor diameter. It can be measured with special monitors, but the calcu-

lation methods are complex. Two simple methods of control are widely used: (1) the tension of the line conductors under everyday conditions is limited and; (2) vibration dampers are clamped to the line conductors. In regions where aeolian vibration is a problem, transmission line conductor tensions are typically limited to between 15% and 20% of RBS during the coldest month of the year, and vibration dampers are routinely installed in every span. Ice galloping motions can be predicted in a crude way through the use of ice galloping ellipses. By comparing such ellipses to the spacing between the line conductors, the likelihood of flashovers from galloping can be minimized by providing sufficient phase spacing and by offsetting any vertical phases. Also, since the major axis of the galloping ellipse is proportional to the line conductor sag with ice and wind loading, the amplitude of ice galloping motions can be reduced by minimizing the sag of conductors in the typical span. Wind-induced subconductor oscillation only occurs for bundled phase conductors when wind speeds exceed a certain critical velocity. If uncontrolled, it can result in fatigue damage to spacers and suspension hardware. Oscillations are controlled by keeping bundled conductors at a spacing-to-diameter ratio of about 20 or more and by avoiding uniform spacer spacing. With regard to increasing maximum allowable power flow through existing lines, wind-induced conductor motions are a primary constraint on increasing the line operating voltage, on retensioning the existing conductors to allow operation at higher maximum conductor temperatures, on reconductoring the line with high– temperature, low-sag conductor, and on bundling (adding a second conductor per phase).

Figure 2.2-6 Illustration of midspan conductor blowout due to wind.

Table 2.2-4 Cyclic, Wind-induced Conductor Motions Aeolian Vibration

Ice Galloping

Subconductor Oscillation

Types of Overhead Lines Affected

All

All in regions with ice

Lines with bundled conductors

Approx. Frequency Range, Hz

3 to 150

0.08 to 3

0.15 to 10

Approx. Range of Vibration Amplitudes (Peak-topeak, Expressed in conductor diameters)

0.01 to 1.0

5 to 300

0.5 to 80

Weather Conditions Favoring Conductor Motion Wind Character: Wind Velocity: Conductor Surface: Damage Characteristics: Direct Causes of Damage:

Steady 1 to 7 m/sec (2 to 15 mph) Bare or uniformly iced

3 months to 20 years for damage to occur Conductor fatigue due to cyclic bending

Steady Steady 7 to 18 m/sec (15 to 40 mph) 4 to 18 m/sec (10 to 40 mph) Bare, Dry Asymmetrical, thin ice deposits 1 to 48 hours per occurrence 1 month to 8+ years for damage to occur Repeated Flashovers, High dynamic loads on structures, Conductor clashing, accelerated wear of hardware premature wear of hardware

2-9


HTLS conductors such as ACSS are particularly advantageous in reconductoring if they are prestressed. When prestressed, ACSS has much higher self-damping than standard ACSR. It can be installed with smaller initial sag, which reduces ice galloping motions and may allow operation of an existing line at higher voltage as well as higher current levels. In lines without vibration dampers, the addition of dampers may allow the line’s existing conductors to be retensioned and operated to a higher maximum temperature without the need for reconductoring. When bundling new conductors with old, the use of a vertical bundle can eliminate the problem of subconductor oscillation while keeping the bundle spacing to no more than 9 to 12 inches. Regardless of the uprating method, wind-induced motions must be thoroughly considered as part of the redesign. 2.2.5

Electrical Clearance

The National Electric Safety Code (National Electric Safety Code 1997) specifies minimum spacings from energized conductors to ground, to objects passing under the line, to buildings nearby, and to other conductors (“underbuild”). These clearances must be maintained under “The maximum conductor temperature for which the line is designed to operate” (NESC 232.A.2). Failure to maintain such minimum distances is a public safety issue of primary importance. The National Electric Safety Code also specifies minimum horizontal spacings from energized conductors to other conductors and objects such as buildings at the edge of ROW. When subjected to transverse wind, the conductor catenaries “blow out,” and the horizontal spacing of energized conductors to buildings, etc. is reduced. This reduction in horizontal clearance can be limited by using heavier conductors or shorter span lengths; reducing energized conductor sag under blowout conditions; using insulators such as V strings, horizontal V, and posts that do not move with wind; and providing generous right-of-way widths. Reducing sag under horizontal blowout conditions is limited by concerns about vibration, but is complementary to uprating methods such as retensioning. Minimum electrical clearances must be maintained under all line loading and environmental conditions. Since the actual sag clearance of transmission lines is seldom monitored, sufficient allowance for this clearance must be included in the process of initial design or in rerating of existing lines. 2-10


Applicable Code Clearances In all cases, national codes may apply. In the United States, the National Electric Safety Code (NESC) is applicable. State codes may also apply. Minimum horizontal and vertical distances from energized conductor (“electrical clearances”) to ground, other conductors, vehicles, and objects such as buildings are a function of three things: the line-to-ground voltage, the use of ground fault relaying, and type of object or vehicles. The NESC Rules covers both vertical and horizontal clearances. That is, the code sets minimum spacing for energized conductors both above and next to people, vehicles, and buildings. This chapter considers only vertical clearances since our focus is on high temperature operations (see Tables 2.2-5 and 2.2-6). Horizontal clearances are typically specified for high winds where the transmission line catenaries are horizontally displaced by the wind. In such cases, the conductor temperature is low due to high convection cooling. Ground clearance minimums listed in the NESC code are primarily due to the height of the object or person that may pass beneath the span. For example, a person with an overhead umbrella extended overhead at arm’s length may physically reach 10 ft (3 m) above ground, whereas a railroad car may be as much as 20 ft (6 m) high. The NESC code calls for a minimum ground clearance of 27 ft (8.2 m) for a low-voltage conductor over a railroad and only 16.5 ft (5 m) over “spaces or ways” accessible only to pedestrians. The difference in minimum ground clearance is due primarily to the height of the object under the line. In each case, the clearance between the low-voltage conductor and the top of the conflicting object is approximately the same. Essentially, the minimum vertical ground clearance for any “supply” conductor (0 to 750 V) is defined by the NESC code as 16.5 ft (5 m) for lines going over places such as roads, streets, driveways, parking lots, and farmland, or any other type of land which can be traversed by vehicles. Conductors passing over waterways must generally meet greater clearance requirements. The Influence of Line Voltage on Clearance For those lines having a line-to-ground voltage of 750 to 22 kV, the ground clearance for the 0 to 750 V supply conductor is increased by 2 ft to 18.5 ft (0.6 m to 5.6 m). For lines at higher voltages, the vertical clearance is increased by 0.4 in. (1 cm) for every kV increase in lineto-ground voltage above 22 kV. Note that the voltage used in these calculations of added electrical clearance are based on the maximum operating voltage, which is typically 5% or 10% above nominal.



Reduced Clearance for EHV Lines with Limited Switching Surge Levels For lines exceeding 98 kV line to ground, the code allows clearances to be calculated based on knowledge of switching surge levels. If the switching surge level is restrained to 2.2 p.u., the clearance at EHV voltages may be decreased. Power System Conditions when Clearances Apply It is impossible to be certain that clearances will be maintained under all foreseeable circumstances. For example, in certain regions, tornadoes may occur, which might cause conductors that are energized to fall to earth. However, it is irresponsible to design lines or line upgrades where clearance violations are likely to occur. The minimum ground clearances specified by the NESC code apply to energized conductors under the three conditions specified in Rule 232A where the temperatures specified are that of the conductor not the surrounding air:

• 50°C (122°F) with no wind displacement. • At the maximum operating temperature for which the line is designed to operate if greater than 50°C (122°F) with no wind displacement. Table 2.2-5 Minimum Vertical Ground Clearances According to NESC C2-1997, Rule 232C L-L/L-G

Basic Clearance @ 22 kV

kV

ft

m

69/40

18.5

5.6

138/80

18.5

161/93

18.5

Clearance Added for Voltage

m

0.7

19.2

5.8

5.6

2.1

20.6

6.3

5.6

2.5

21.0

6.4 6.8

230/133

18.5

5.6

3.9

22.2

18.5

5.6

7.0

25.5

7.8

500/290

18.5

5.6

9.9

28.4

8.7

765/440

18.5

5.6

15.5

34.0

10.4

Table 2.2-6 Minimum Vertical Ground Clearances According to NESC C2-1997, Rule 232D*

KV

Reference Minimum Height Listed in Alternate Clearance for Table 232-3 Clearance Adder Streets ft

m

ft

m

ft

m

69/40

-

19.2

5.9

138/80

-

20.6

6.3

21.0

6.4 6.4

161/93

ness of ice. Even in these days of heavily utilized transmission assets, it is unusual for lines to carry electrical loads that cause the energized conductors to be more than 5°C or 10°C above air temperature. However, given the relatively rare loss (outage) of a major generating station or EHV transmission circuit, electrical loading on HV lines can increase and cause much higher conductor temperatures. Thus, all lines are designed to meet clearances “at the maximum operating temperature for which the line is designed to operate” (see above). Heavy ice loads are also relatively rare events, but in any modern HV or EHV line, the energized conductor sag at 0°C (32°F) with maximum ice is typically less than the sag for high temperature, even when that maximum operating temperature is only 50°C (122°F). Thus, the assurance of adequate clearance involves the behavior of transmission conductors at high temperatures, not under heavy ice load. Transmission line operators typically meet minimum clearance requirements by limiting the current on the energized conductors. The specification of any relationship between the electrical current on the energized conductors and the conductor temperature is left to the discretion of the operator.

Streets ft

345/200

Nominal Voltage L-L/L-G

• 0°C (32°F), no wind displacement, with radial thick-

230/133

14

4.3

7.1

2.2

21.0

345/200

14

4.3

7.1

2.2

21.0

6.4

500/290

14

4.3

12.7

3.9

26.7

8.1

765/440

14

4.3

21.8

6.6

32.4

9.9

* In accord with Rule 232D4, the clearance calculated based on Rule 232D2-3 cannot be less than the clearance calculated for 98 kV under Rule 232C, which is 21.0 ft.

The NESC code describes the minimum clearances in considerable detail as a function of voltage and potentially conflicting activity. The code also prescribes the conditions under which the clearance minimums must be met. The code does not, however, specify: (1) how the temperature of the conductor is to be calculated; (2) how the physical position of the conductor above ground is to be related to this maximum operating temperature; nor (3) how adequate ground clearance can be confirmed under rare occasions of high electrical loading. Consequently, methods of ensuring adequate ground clearance vary widely between transmission line operators. Upgrading Buffers On older transmission lines, the structure placement along the ROW is fixed, and the final sag of the conductor is measurable. Thus any initial spacing buffer added because of uncertainties in structure placement and initial sag can be reduced in uprating. There are, however, certain irreducible uncertainties, and some clearance buffer must be maintained. The traditional method of determining clearances for existing transmission lines involves standard survey methods to determine the conductor attachment points and the sag at span mid-point for one or more spans in 2-11


each line section. These measurements are typically taken with the line out of service so that the conductor is at air temperature plus some solar rise. Vertical position errors of up to a foot (0.3 m) are easily made in determining the catenary’s position and the attachment heights. Additional errors may be expected in determining the ground clearance since the ground profile is only checked at a few points along the line. In more recent years, several photographic and laserbased methods have been developed. These methods help determine all attachment points at all structures, and provide a complete description of catenary profiles for all three-phase conductors with much better accuracy than is possible with conventional survey methods. Such measurements are seldom done with the line out of service, so the conductor temperature at the time of the survey measurements must be calculated or measured. The result of such detailed survey activity is very impressive and can easily convince the novice that buffers can be eliminated or reduced when upgrading existing lines. This is not the case. Knowing the exact ground clearance with perfect certainty at the conclusion of a laser survey does not mean that one can be certain of adequate clearance under maximum electrical loading. There still remain several uncertainties. 2.2.6


Figure 2.2-7 shows the reduction in tensile strength with time and temperature for a sample of 0.081 in. (0.2 cm) diameter hard drawn copper wire, as described in (Hickernell et al. 1949). There are 8760 hours in a year, so the diagram clearly shows that sustained operation at 65οC yields no measurable reduction of tensile strength, sustained operation at 100oC yields a 10% reduction in 600 hours (25 days), and that only 40 hours at 125 o C reduces the wire tensile strength by 10%. Figure 2.2-8 shows similar tensile strength reduction data for 1350-H19 “EC” hard drawn aluminum wire. It

Figure 2.2-7 Annealing of 0.081 in. diameter hard drawn copper wire.

Loss of Conductor Strength

Construction codes also require that maximum conductor tension not exceed a certain percentage of the energized conductor’s breaking strength. A significant reduction in the breaking strength can weaken the energized conductor and lead to a tensile failure during subsequent high ice and wind loading events. To avoid this, the conductor must not operate at a high enough temperature for a long enough period of time so as to reduce its breaking strength more than 10%, and it must not be installed at such a high everyday “unloaded” tension that its strands fatigue due to wind vibration. The American Society for Testing and Materials (ASTM) or the International Engineering Consortium (IEC) standards specify the minimum tensile strength of aluminum and copper wires, which is the stress at which the wire breaks. At temperatures above 75°C, the tensile strength decreases with time. Temperatures below 300°C do not affect the tensile strength of galvanized, aluminum-clad, or copper-clad steel wires. Thus, extended exposure of conductors made up largely of aluminum or copper wires to temperatures above 75oC can eventually lead to tensile failures during high ice and/or wind loading events.

2-12

Figure 2.2-8 Annealing of 1350-H19 hard drawn aluminum wire (Aluminum Association 1989).



is taken from (Aluminum Association 1989). In general, tensile strength reduction of aluminum wires at temperatures of less than 90 o C is considered negligible. At 100oC, the tensile strength of the wire is reduced by 10% after 5000 hours, and at 125 oC the tensile strength is reduced 10% after 250 hours. When compared to copper, aluminum appears to anneal somewhat more slowly, though the difference is probably not important in transmission line applications. The source of the copper wire data also noted a significant amount of variation in the annealing rates for wire obtained from different manufacturers. In applying these equations, the cumulative strength reduction for multiple exposures at the same conductor temperature may be found by simply adding up all the hours and calculating the residual strength. However, for multiple exposures at different conductor temperatures, the calculation process is more complex. To determine the cumulative strength reduction for a series of high temperature exposures at different temperatures and times, all exposures must be expressed in equivalent time at the highest temperature before adding. Thus, if an all aluminum conductor consisting of 370.1466 in. diameter strands is raised to 125oC for 100 hours and then at a later time for 50 hours, then the strength reduction can be calculated for 150 hours at 125 oC. If the same conductor is raised to 125oC for 100 hours and then at a later time is raised to 150oC for 50 hours, then the following calculation must be performed: For 100 hours @125oC,

RS = 100 × 100

⎡ ⎛ 0.1 ⎞ ⎤ − ⎢ (0.125 − 0.095 )• ⎜ ⎟⎥ ⎝ 0.1466 ⎠ ⎦ ⎣

= 91.0%

Before undertaking any uprating project, a review of the existing structures and operating records of the line is required. If structural failures at angle or dead-end structures have occurred, any attempt at increasing everyday installed tension is unlikely to succeed. Similarly, if occasional high temperature operations have yielded splice failures, increasing operating temperature levels without replacing or inspecting the line is unwise. On the other hand, if a review of structure and foundation capacity indicates that the line was conservatively designed, and that it has operated for many years without any structural or foundation failures, it may be possible to replace the existing conductor with a new larger conductor without structure modifications. When a conductor span is ice covered and/or exposed to high winds, the effective conductor weight per unit length increases. During occasions of heavy ice and/or wind load, the conductor tension increases dramatically, along with the loads on angle and dead-end structures. Both the conductor and its supports can fail unless these high-tension conditions are considered in the line design. The National Electric Safety Code (NESC) suggests certain combinations of ice and wind corresponding to heavy, medium, and light loading regions of the United States.

2.2-1

At 150oC, RS = 91.0% after 7.2 hours, so the cumulative loss of strength over the two high temperature exposures is equal to the remaining strength after 50 + 7.2 hours. It is 82.1% 2.2.7

For tangent structures, the governing transverse loads are primarily a function of the conductor diameter. Thus the replacement conductor diameter must be within about 10% of the existing conductor to avoid tangent structure modification. For angle and dead-end structures, the governing loads are primarily related to maximum conductor tension. The replacement conductor’s maximum tension should not exceed the original conductor’s initial maximum conductor tension unless these structures are to be reinforced.

Constraints on Structural Loads

Existing structures and foundations were designed for certain maximum transverse wind loads and, for strain structures, for maximum tension loads. Unless the existing structures are to be replaced, retensioning the existing conductor, or reconductoring the line with a new conductor, must be done without greatly exceeding the original design limits on structure loading. If many of the line structures must be replaced, the design solution is not the sort of minimal capital investment solution that this guide emphasizes.

The NESC Code (National Electric Safety Code 1997) also suggests that increased conductor loads due to high wind loads but no ice should be considered as noted in the last column of Table 2.2-7. Certain utilities in very heavy ice areas use glaze ice thickness as much as 2 to 3 in. (5 to 7.6 cm) in order to calculate iced conductor weight. This is especially true if they have experienced extensive line failures due to ice loads in excess of those recommended by the NESC. Similarly, utilities in regions where hurricane winds occur may use wind loads as high as 0.236 psi (1630 Pa). Ice Loading The formation of ice on overhead conductors may take several physical forms such as glaze ice, rime ice, or wet

2-13



Table 2.2-7 Definition of NESC Loading Areas Loading Districts

Therefore, small diameter conductors may need to have a higher elastic modulus and higher tensile strength than large conductors in heavy ice and wind loading areas to limit the sag.

Light

Extreme Wind Loading

6.5

0

0

318

165

0

0

Horizontal wind pressure (lb/ft2)

4

4

9

16 to 22

Horizontal wind pressure (Pa)

190

190

430

16 to 22

Temperature (°F)

0

+15

+30

+60

Temperature (°C)

-18

-10

-1

+15

angle suspension structures are often determined by infrequent high wind-speed loading.

Constant to be added to the resultant (all conductors) (lb/ft)

0.30

0.20

0.05

0.0

• Wind loading determines the permanent increase in

Constant to be added to the resultant (all conductors) (N/m)

4.40

Heavy Medium Radial thickness of ice (in.)

12.5

Radial thickness of ice (mm)

Wind Loading Wind loading on overhead conductors influences line design in a number of ways:

• The maximum span between structures may be determined by the need for horizontal clearance to the edge of the ROW during moderate winds.

• The maximum transverse loads for tangent and small

conductor sag in areas of light ice loads. 2.50

0.70

0.0

snow. The impact of lower density ice formation is usually considered in the design of line sections at high altitudes. The formation of ice on overhead conductors has the following influence on line design:

Wind pressure load on conductors, Pw, is commonly specified in lb/ft2. Equation 2.2-2 gives the relationship between Pw and wind velocity: Pw (lb / ft 2 ) = 0.00256 ⋅ [Vw ( mph )]

2

Pw ( Pascals ) = 0.0473 ⋅ [Vw ( km / h )]

2

2.2-2

Where Vw = the wind speed in miles per hour.

• Ice loads determine the maximum vertical conductor loads that structures and foundations must withstand.

• In combination with simultaneous wind loads, iced conductor may also yield the highest transverse design loads on structures.

• In regions of heavy ice loads, the maximum sags and the permanent increase in sag with time (difference between initial and final sags) may be due to ice loading. In addition to the NESC loading region, ice loads for use in designing lines may also derive from past experience, state regulations, and analysis of historical weather data. Mean recurrence intervals for heavy ice loadings are a function of local conditions along various routings. Line design software can be used to investigate the impact of a variety of assumptions concerning ice loading. The calculation of glaze ice loads on conductors is normally done with an assumed ice density of 57 lb/ft3 (913 kg/m3). The ratio of iced weight to bare weight depends strongly upon the conductor diameter. As shown in Table 2.2-8, for three different conductors covered with 0.5 in. (1.27 cm) radial glaze ice, this ratio ranges from 4.8 for #1/0 AWG to 1.6 for 1590 kcmil (811 mm 2 ) conductors.

2-14

The wind load per unit length of conductor, Ww, is equal to the wind pressure load, Pw, multiplied by the conductor diameter (including radial ice of thickness t, if any):

Ww (lb / ft ) = Pw ( psf ) Ww ( N / m ) = Pw

[Dc (in) + 2 ⋅ t(in)] 12

[D ( mm) + 2 ⋅ t( mm)] ( Pascals ) ⋅ c 1000

2.2-3

Combined Ice and Wind Loading If the conductor weight is to include ice and wind loading, the resultant magnitude of the loads must be deterTable 2.2-8 Ratio of Iced to Bare Conductor Weight ACSR Conductor

wbare+ wice --------wbare

D

wbare

wice

(in.)

(lb/ft)

(lb/ft)

#1/0AWG-6/1 “Raven”

0.398

0.1452

0.559

4.8

47-kcmil-26/7 “Hawk”

0.858

0.6570

0.845

2.3

1590-kcmil-54/19 “Falcon”

1.545

2.044

1.272

1.6



mined. Equation 2.2-4 gives the weight of a conductor under both ice and wind loading: w w +i = (w b + w i ) 2 + (Ww ) 2

2.2-4

Where wb = bare conductor weight per unit length. wi = weight of ice per unit length. ww = wind load per unit length. ww+i= resultant of ice and wind loads. 2.2.8

Environmental Effects

The public considers overhead transmission lines as very visible and, though most power engineers have difficulty in understanding why, unattractive. Thus, one of the primary environmental effects of any transmission line is their visual impact on their surroundings. A great deal of effort has been expended on making lines more visually acceptable with decidedly mixed results. Fortunately, when uprating existing lines, most of the normal opposition to new lines is avoided unless the appearance of the uprated line is significantly changed. Because lines are highly visible and perceived as unattractive, they can have a negative impact on property values. This is typically much less of an issue with the modification of existing lines than with new lines. Figure 2.2.9 shows a comparison of the relative importance of some of the major environmental issues involving overhead lines as deter mined by survey. It is interesting that the top three factors are primarily a matter of human perception or belief, while the three least important issues are matters of physics.

Figure 2.2-9 Median survey results as to why people oppose transmission lines.

Various attempts to reduce the visual impact of lines and the corresponding impact on property values have been made. There have been design competitions to find more visually acceptable structures and research into methods of compacting HV lines so they look more like distribution lines. Probably the most effective way to reduce public opposition to transmission lines concerns putting them away from where people live and work. Clearly, this is not always possible, but as shown in Table 2.2-9, it is quite effective. In the specific case of uprating, a variation on the classic physician’s ethic. “First, do no harm” makes sense. Specifically, uprating techniques that do not raise structure peaks or make conductors more visible from a distance are preferred. This guide emphasizes line uprating methods where the voltage of the line remains the same but current flow is increased. Most of the techniques covered herein will leave the original ground level electric field, electric induction, corona discharge levels and audible noise levels unchanged. However, the ground level magnetic field and magnetic induction levels will increase with the higher line currents. Both environmental effects are linear with current so that maximum original levels are easily estimated by scaling with the increase in rating. Table 2.2-9 The Impact of Distance on Public Opposition to Power Transmission Lines Distance from Line Feeling

Less than 1 mile

Like it

2.3%

3.2%

Don’t care

32.6%

71.3%

Dislike it

65.1%

25.3%

2.3

LINE THERMAL RATINGS

2.3.1

Introduction

More than 1 mile

The temperature and/or sag of overhead power transmission lines can be measured, but seldom are. Rather, in order to avoid excessive sag or loss of strength, a “maximum allowable conductor temperature” is typically specified, and the conductor temperature is kept below this maximum by placing limits on the level and duration of power transferred over the line (MVA or amperes). If such limits are based on worst-case weather conditions, they are called static ratings, and if based on actual weather conditions, they are called dynamic ratings. The calculation of thermal ratings for overhead lines is an essential part of the uprating process.

2-15


The electrical power conductors of overhead transmission lines carry relatively large electrical currents, are self-supporting, and energized at high voltage. They are stranded from wires of aluminum or copper, which may be reinforced with a steel core. As the current flowing through a conductor increases, its temperature increases, and it elongates. This elongation increases the sag of the conductor between support points, decreasing the clearance to people, ground, other conductors, buildings, and vehicles under the line. Beyond a certain “maximum allowable” sag, the line may flashover, resulting in either a power supply outage or injury to the public. If the conductor temperature remains high for an extended period of time, the strength of the conductor and tensioned connectors may decrease, resulting in mechanical failure during the next occurrence of ice or high wind loading. In the design of a new transmission line, the thermal rating required for reliable system operation can be attained either by selecting a large conductor at a moderate maximum operating temperature or by using a smaller conductor at a higher maximum temperature. The higher sag resulting from higher operating temperatures can easily be accommodated by using taller or more closely spaced structures. In uprating an existing line, it is unusual if the existing conductor can be replaced by a significantly larger conductor since this would increase both transverse wind loads and maximum tension loads, and require costly and time-consuming rebuilding of existing structures. It is also unusual if the existing conductor can simply be operated at a significantly higher temperature without raising the existing attachment points or retensioning the line, since this would lead to unacceptable violations of minimum electrical clearances under maximum electrical loading. 2.3.2

Maximum Conductor Temperature

Modern transmission conductors are typically stranded from aluminum wires with a steel core added where increased strength is required. The temperature limit on all-aluminum or ACSR conductors is based on the maximum sag or maximum loss of strength in the aluminum. Temperature limits for normal ACSR conductors in use today range from 50°C to 150°C (122°F to 302°F). The temperature limit is normally selected at the time the line is designed. The higher this temperature, the higher the thermal capacity of the line, the maximum conductor sag, and the higher (or closer) the structures required to maintain ground clearance. If aluminum or copper conductor temperatures remain high (above 95 °C, or 203 °F) for an extended period of 2-16


time, the strength of the conductors and tensioned connectors may decrease, which eventually results in mechanical failure during ice or high wind occurrences. Generally, rating durations are kept short if maximum conductor temperatures are high (e.g., 4 hour maximum at 115 °C [239 °F] and 15 minutes at 125 °C [257 °F]). These high temperature effects on conductor, hardware, and fittings are discussed in detail in Section 2.4. 2.3.3

Weather Conditions for Rating Calculation

Traditionally, power utilities use fixed “worst-case” weather conditions in order to calculate (static) line ratings. The impact of changes in these weather parameters upon thermal line ratings depends on the specific rating situation. Consider an overhead line with 795 kcmil (402 mm2) of aluminum, 26/7, “Drake” ACSR conductor, whose static rating is based upon a maximum allowable conductor temperature of 100oC with an air temperature of 40oC, full summer sun, and a wind blowing perpendicular to the conductor axis at 2 ft/sec (0.61 m/sec). The static rating under these conditions is 1000 A. Clearly, if the current in this conductor is 1000 A with the assumed weather conditions, the conductor temperature is 100 o C. Table 2.3-1 shows how the conductor temperature is affected by small changes in weather conditions. For example, the conductor temperature drops to 92oC if there is no solar heating. The table also shows how the thermal rating (i.e., the current which yields a temperature of 100oC) changes with small changes in weather. Note that with the conductor at a reasonably high temperature and near “worst-case” heat transfer conditions, the overhead line rating and conductor temperature are very sensitive to wind direction, modestly sensitive to Table 2.3-1 Variation in Conductor Temperature and Rating with Weather Conditions (for 795 kcmil [404 mm2], 26/7, “Drake” ACSR conductor with a maximum allowable conductor temperature of 100°C, an air temperature of 40oC, full summer sun, and a wind blowing perpendicular to the conductor axis at 2 ft/sec) Range in Weather Conditions

Line Rating @ 100°C

Conductor Temperature at 1000 A

(amperes)

(°C)

(°F)

None

1000

100

212

Air temp = 39°C

1010

99

210

No sun

1070

92

198

3 ft/sec (0.91m/sec)

1090

90

194

Parallel wind

750

133

271


changes in wind speed and solar heating, and less affected by small changes in air temperature. Other minor factors are gradual changes in emissivity and absorptivity of the conductor with age, and seasonal shifts in solar heating. 2.3.4

How Line Design Temperature Affects Line Ratings


sponds to an increase of 10oC in the line design temperature. For this ACSR conductor, the increase in sag for a 10oC increase in conductor temperature decreases with increasing line design temperature. It is clear from this table why simple physical line modifications (such as raising support points or using “floating” dead-ends) are an effective means of uprating older lines with relatively low design temperatures. Even modest increases in allowable sag result in relatively large increases in rating for such lines. It is also clear why such techniques are not usually helpful in uprating new lines having higher line design temperatures.

Line design temperature is the maximum allowable conductor temperature for a particular line. As noted previously, for normal conventional ACSR, it varies from 50oC to 150oC. The impact of changes in the line design temperature upon thermal line ratings depends on the specific rating situation, but certain observations are possible.

2.3.5

Until the early 1970s, the National Electric Safety Code (National Electric Safety Code 1997) suggested that minimum electrical clearances were to be met at conductor temperatures up to 120 ° F (49 o C). Line thermal capacity was typically calculated by conductor manufacturers for a conductor temperature of 75oC, a temperature sure to avoid possible annealing problems with aluminum and copper.

Around the world, utilities perform overhead line rating calculations in essentially the same way: by setting the heat input from Ohmic losses and solar heating equal to the heat loss due to convection and radiation (EPRI 1995). The specific formulas used to determine the heat balance terms vary somewhat, but normally one of three methods is used – the IEEE method (IEEE 1993), the CIGRE method (CIGRE 1992), or the EPRI DYNAMP method (Black et al. 1983).

In the 1970s, the NESC changed this position and stated that the electrical clearances listed were to be met at “the maximum conductor temperature for which the line was designed to operate, if greater than 50oC, with no wind displacement” (excerpted from Rule 232.A.2). Thus the maximum allowable conductor temperature (MACT) used in line rating calculations may vary from 50oC to 200oC according to available ground clearances, and consistency, with concerns about loss of tensile strength at temperatures above 90oC. Consider an existing overhead line with 795 kcmil (402 mm2) of aluminum, 26/7, “Drake” ACSR conductor, whose static rating is based upon an air temperature of 40oC, full summer sun, and a wind blowing perpendicular to the conductor axis at 2 ft/sec (0.61 m/sec). The rating of this existing line depends on the line design temperature as is shown in Table 2.3-2, where the line design temperature with this ACSR conductor ranges from 50°C to 150oC. For each line design temperature, the line rating is shown. Also shown is the increase in rating that corre-

Heat Balance Methods

Given the same assumed wind speed and direction, the same conductor temperature and the same conductor electrical and physical parameters, the thermal rating found with the three methods is similar if not identical. To illustrate typical values of the heat balance terms, the IEEE method is used in the following development for a Drake ACSR conductor at 100oC. Table 2.3-2 Variation in Line Rating with Design Temperature (for 795 kcmil [405 mm2], 26/7, “Drake” ACSR conductor with an air temperature of 35oC, full summer sun, and a wind blowing perpendicular to the conductor axis at 2 ft/sec [0.61 m/sec]) Increase in Line Rating for 10°C Change in Line Design Temperature

Line Design Temperature

Line Rating

(oC)

(amps)

(amps)

(%)

50

374

213

57

75

797

107

13

100

1039

78

7.5

125

1221

63

5.2

150

1370

54

3.9

2-17



Radiation Radiation of heat from an overhead conductor is modeled in terms of the absolute temperature of the conductor and its surroundings (taken as the air temperature):

4⎤ ⎡ ⎢ ⎛⎜ T c + 273 ⎞⎟ ⎥ ⎢ ⎝ 100 ⎠ ⎥ qr = 0.0178⋅ D ⋅ ε ⋅ ⎢ ⎥ ⎢ ⎛ T a + 273 ⎞ 4⎥ ⎢−⎜ ⎟ ⎥ ⎢⎣ ⎝ 100 ⎠ ⎥⎦ 4⎤ ⎡ ⎢ ⎛⎜ T c + 273 ⎞⎟ ⎥ ⎢ ⎝ 100 ⎠ ⎥ qr = 0.138⋅ D ⋅ ε ⋅ ⎢ ⎥ ⎢ ⎛ T a + 273 ⎞ 4⎥ ⎢−⎜ ⎟ ⎥ ⎣⎢ ⎝ 100 ⎠ ⎦⎥

100 + 40 = 70DC 2

ρf = 1.029 kg/m (28.14)

W/m

Tfilm =

3

100 + 40 = 70oC 2

ρf = 0.0643 lb/ft3

qc = 0.0205 (1.029)

0.5

qc = 0.283 (0.0643)0.5

0.75

(1.108)0.75

(100–40)1.25

(100-40)1.25 = 12.9 W/ft

= 42.4 W/m

Forced Convection With the IEEE 738 and the CIGRE methods, forced convection is calculated with two separate formulas, and the larger of the two values for forced convection heat loss is used.

W / ft

2.3-1

As an example of radiation heat loss from a bare overhead conductor, consider Drake ACSR at 100oC and an air temperature of 40oC: ⎡ 4 4⎤ ⎢⎛⎜ 373 ⎞⎟ − ⎛⎜ 313 ⎞⎟ ⎥ ⎜ 100 ⎟ ⎥ q = 0.0178 ⋅ 28.14 ⋅ 0.5⋅⎢⎜⎝ 100 ⎟⎠ ⎝ ⎠ ⎥ r ⎢ ⎢⎣ ⎥⎦

⎦⎥

⎡ ⎛ D ⋅ ρ ⋅V ⎢ f w ⎜ q = ⎢1.01+ 0.0372⋅⎜ c1 μ ⎜ ⎢ f ⎝ ⎢⎣ ⋅ k ⋅ (T − T ) W / m f c a ⎡ ⎛ D ⋅ ρ ⋅V ⎢ f w ⎜ q = ⎢1.01+ 0.371⋅⎜ c1 μ ⎜ ⎢ f ⎝ ⎣⎢

⎡ 4 ⎛ 4⎤ ⎛ 373 ⎞ 313 ⎞ ⎥ ⎟ −⎜ ⎟ q = 0.138 ⋅1.108 ⋅ 0.5⋅⎢⎜⎜ ⎜ 100 ⎟ ⎥ ⎢⎝ 100 ⎟⎠ r ⎝ ⎠ ⎣⎢

T film =

⋅k 2.3-2

qr = 24.44 W/m qr = 7.461 W/ft Convection Natural Convection With zero wind speed, natural convection occurs, where the rate of heat loss is:

q c = 0.0205 ⋅ ρ f0.5 ⋅ D 0.75 ⋅ (T c - T a )1.25W / m q c = 0.283 ⋅ ρ f0.5 ⋅ D 0.75 ⋅ (T c - T a )1.25 W / ft

f

⋅ (T − T ) W / ft c a

⎛ D⋅ρ f ⋅Vw ⎞ q = 0.0119⋅⎜ ⎟ c2 μ f ⎝ ⎠

(

⋅k ⋅ T −T f c a

)

(

)

0.52 ⎤ ⎥ ⎥ ⎥ ⎦⎥

0.52 ⎤ ⎥ ⎥ ⎥ ⎦⎥ 2.3-5

0.6

W /m

⎛ D⋅ρ f ⋅Vw ⎞ q = 0.1695⋅⎜ ⎟ c2 μ f ⎝ ⎠ ⋅k ⋅ T −T f c a

⎞ ⎟ ⎟ ⎟ ⎠

⎞ ⎟ ⎟ ⎟ ⎠

0.6

W / ft 2.3-6

2.3-3

Taking our example of Drake ACSR at 100oC, the natural convection heat loss is:

q = 0.0205 ⋅ ρ 0.5 ⋅ D 0.75 ⋅(T −T )1.25 (5s ) c f c a 0 . 5 1 . 25 ⋅(T −T ) q = 0.283⋅ ρ c f c a where: D = 28.14 mm Tc = 100°C Ta = 40°C

2-18

where: D = 1.108 in. TC = 100oC Ta = 40oC

2.3-4

The first two equations apply at low winds, but are too low at high speeds. The last two equations apply at high wind speeds, being too low at low wind speeds. At any wind speed, the larger of the two calculated forced convection heat loss rates is used. The convective heat loss rate is multiplied by the wind direction factor, Kangle, where φ is the angle between the wind direction and the conductor axis:

K angle = 1.194 - c os (φ ) + 0.194 cos (2φ ) + 0.368 sin (2φ ) 2.3-7



Referring once again to our example of Drake ACSR at 100oC we have: 0.52 ⎤ ⎡ ⎛ 28.14 ⋅1.029 ⋅ .6096 ⎞ ⎢ ⎥ ⎟ q c1 = ⎢1.01 + 0.0372 ⎜ ⎥ 5 − ⎜ ⎟ 2.04 ⋅10 ⎢ ⎥ ⎝ ⎠ ⎣ ⎦ .0295 ⋅ (100-40) = 82.295 W/m

According to the IEEE solar model, the maximum possible conductor solar temperature rise above air temperature is on the order of 15 o C (for still air). Field measurements of actual lines indicate that the typical solar rise is in the range of 5°C to 10°C.

0.52 ⎤ ⎡ ⎛ 1.108 ⋅ 0.643 ⋅ 7200 ⎞ ⎥ q c1 ⎢1.01 + 0.371⎜ ⎟ 0.0494 ⎢ ⎥ ⎝ ⎠ ⎣ ⎦ .00898 ⋅ (100-40) = 25.052 W/ft 2.3-8

⎛ 28.14 ⋅1.029 ⋅ .6096 ⎞ q c 2 = 0.0119 ⋅ ⎜ ⎟ ⎜ ⎟ 2.04 ⋅10 −5 ⎝ ⎠ .0295 ⋅ (100-40) = 76.88 W/m

0.6

⎛ 1.108 ⋅ 0.0643 ⋅ 7200 ⎞ q c 2 = 0.1695 ⋅ ⎜ ⎟ 0.0494 ⎝ ⎠ .00898 ⋅ (100-40) = 23.464 W/ft

0.6

With reference to Table 2.3-3, with a solar altitude of 70 degrees (noon in June in New York) and clear atmosphere, the solar heat flux to a surface perpendicular to the sun’s rays is approximately 1020 watts/ft 2 or 95 watts/m2. The maximum heat input to the conductor is therefore: qC = 0.5 ⋅1020 ⋅ 0.0281 = 14.3

2.3-9

Now select the larger of the two calculated convection heat losses. qc = 82.295 W/m

the angle of the solar beam relative to the line direction, and the conductor absorptivity (the fraction of incident solar radiation absorbed by the conductor). The resulting temperature rise above air temperature is a function of the conductor absorptivity and diameter as well as the wind speed and direction.

qc = 25.052 W/ft

Since the wind is perpendicular to the axis of the conductor, the wind direction multiplier, Kangle, is 1.0, and the forced convection heat loss is greater than the natural convection heat loss. Therefore, the forced convection heat loss will be used in the calculation of thermal rating. Notice that if the wind had been nearly parallel to the line at 10o from the line direction, the wind direction multiplier would be 0.517, and convection cooling would have been similarly reduced. Also, notice that the heat loss with no wind (natural convection) is much less than that for forced convection with even the low 2 ft/sec (0.61 m/sec) wind. Solar Heating Overhead conductors are typically 5oC to 10oC above air temperature due to solar heating alone, even if the current in the conductor is zero. The conductor heat balance described in these notes applies when there is only solar heat input as well as when the conductor carries electrical current. The solar heat into the conductor in direct sun is a function of the solar heat flux density,

W/m

qC = 0.5 ⋅ 95 ⋅ 0.092 = 4.4 W/ft

2.3-10

Ohmic Losses Conductor resistance per unit length and the electrical current on the line determine the Ohmic losses. The resistance of a stranded conductor is a function of the conductivity of the component wires, the frequency, the current density, the temperature of the wires, and the stranded construction. Resistance values at 25°C and 75oC are readily available from the manufacturer or the Aluminum Association.

The IEEE standard suggests that electrical resistance may be calculated solely as a function of conductor temperature, ignoring dependence on current density. For example, the values of conductor resistance at high temperature, Thigh, and low temperature, Tlow, may be taken from the tabulated values in the Aluminum Association Handbook (Aluminum Association 1989). The conduc-

Table 2.3-3 Total Heat Flux Received by a Surface at Sea Level Normal to the Sun’s Rays Solar Altitude, Hc

QS for a Clear Atmosphere

QS for an Industrial Atmosphere

Degrees

(w/m2)

(w/ft2)

(w/m2)

(w/ft2)

60

1000

92.9

771

71.6

70

1020

95.0

809

75.2

80

1030

95.8

833

77.4

90

1040

96.4

849

78.9

2-19



tor resistance at any other temperature, TC, is found by linear interpolation according to Equation 2.3-11. R(T c) =

⎡ R(T high) - R(T low)⎤ ⎢⎣ T high - T low ⎥⎦

* (T c - T low)+ R(T low)

2.3-11

This method of resistance calculation allows the user to calculate the high and low temperature resistance values by whatever means is appropriate. See, for example, references (Douglass and Rathbun 1985 and (Lewis and Tuttle 1958). In the example calculation, the resistance of the Drake ACSR conductor is calculated for a conductor temperature of 100oC:

⎛ R(75) − R( 25) ⎞⋅(100 − 25) R(100 ) = R( 25 ) +⎜ ⎟ 72 − 25 ⎝ ⎠ ⎡ 8.688⋅10 − 5 −7.283⋅10 − 5 ⎤ ⎥⋅ 75 =7.283⋅10 − 5 + ⎢ 50 ⎢ ⎥ ⎣ ⎦ −5 =9.390⋅10 Ω / m

⎛ R(75) − R( 25) ⎞⋅(100 − 25) ⎟ 72 − 25 ⎝ ⎠

R(100 ) = R( 25 ) +⎜

⎡ 2.648⋅10 −5 −2.220⋅10 −5 ⎤ =2.220⋅10 −5 + ⎢ ⎥⋅ 75 50 ⎣ ⎦ =2.862⋅10 −5 Ω / ft 2.3-12

Steady-State Thermal Rating Now that the radiation heat loss, the convective heat loss, the solar heat input and the resistance of the conductor have been determined, the steady-state thermal rating can be calculated as follows:

I=

qc + qr − qs R(100)

I=

qc + qr − qs R(100)

2.3-13

For the example case: qc = 82.295 W/m qr = 24.44 W/m qs = 14.0 W/m (from equations) R(100) = 9.390⋅10-5 Ω/m I=

82.295+ 24.44 −14.0 9.39010

= 994 A

2-20

−5

qc = 25.052 W/ft qr = 7.461 W/ft qs = 4.26 W/ft (from equations) R(100) =2.862·10-5Ω/ft I =

Thermal Rating – Dependence on Conductor Parameters The rating of bare overhead conductors depends on the various conductor parameters including (see Table 2.3-4):

• Outside diameter • Emissivity and absorptivity • Electrical resistance per unit length At the time of construction, the choice of conductor type and size defines the resistance and outside diameter. Normally, the emissivity and absorptivity of new aluminum conductor are initially in the range of 0.2 to 0.3 but increase to values close to 1.0 as the conductor ages. Figure 2.3-1 shows this increase in emissivity with time for energized conductors. The actual rate at which the conductor emissivity and absorptivity increase with time is a function of the line voltage and the density of particulates in the air. Two observations, however, can be made. The emissivity and absorptivity are correlated, so it is unlikely that one parameter will be high and the other low. Also, new conductors will have emissivity and absorptivity values in the range of 0.2 to 0.3, and old conductors will have values in excess of 0.5. As stated above, resistance and diameter are tightly correlated. Thus, aluminum stranded conductors of a given diameter will have a corresponding resistance per unit length. The exceptions to this are:

• The component strands have a different conductivity from that of standard aluminum (e.g., copper).

• Conducting strands are trapezoidal rather than round (e.g., TW conductor).

• The steel core strands are not used or are replaced by aluminum-clad steel wires (e.g., ACSR/AW). Table 2.3-4 Illustration of the Effect of Diameter, Resistance, Emissivity and Absorptivity on Thermal Rating Resistance Outside Emissivity Conductor Diameter @ 25 °C and Description (Ohms/mi) Absorptivity (in.)

Thermal Rating (A)

Drake

1.108

0.1170

0.5 & 0.5

996

Drake/TW

1.010

0.1170

0.5 & 0.5

976 (-2.0%)

Drake/AW

1.108

0.1129

0.5 & 0.5

1014 (+1.8%)

Arbutus AAC

1.026

0.1200

0.5 & 0.5

962 (-3.4%)

CU 500 kcmil

0.811

0.1196

0.5 & 0.5

909 (-8.7%)

Drake

1.108

0.1170

0.9 & 0.9

1046 (+5.0%)

Drake

1.108

0.1170

0.3 & 0.3

971 (-2.5%)

25.052 + 7.461 − 4.26 2.862 ⋅ 10 − 5

= 994 A



Figure 2.3-1 Transmission line conductor emissivity as a function of time (House et al. 1963)

2.3.6

Thermal Ratings—Dependence on Weather Conditions

It is clear from the preceding discussion that the thermal rating of an overhead line depends on the weather conditions along it, as well as on the type of conductor and its maximum allowable operating temperature. Many utilities around the world adjust their line ratings for seasonal variation in air temperature, recognizing that air temperature is lower and ratings can be higher in the winter than in the summer. Of course, in areas where the seasonal change is small (near the equator), or where the fluctuations in any season are larger than the seasonal average difference, this does not make sense. Other utilities adjust thermal ratings for day and night by including or ignoring solar heating, and others adjust the wind speed, using a more conservative (lower) wind speed for continuous ratings than for emergency ratings, which tend to have a low probability of occurrence. Many utilities have installed real-time monitoring systems, adjusting their line ratings for actual real-time wind speed, wind direction, solar heating, and air temperature. This technique is discussed in more detail in Section 2.8.

Table 2.3-5 Effect of Weather Conditions on Thermal Ratings. (In all cases, the conductor is 26/7 795 kcmil (0.61 mm2) ACSR (Drake) with emissivity = absorptivity = 0.5, Direct sun on June 10, clear air, at sea level, latitude = 40° with the conductor at 100°C.)

Air Temperature (°C)

Wind Speed (ft/sec)

Wind Direction Relative to the Line (90 = Perpendicular)

40

2

90

2 PM

996

40

2

90

12 PM

986 (-0.8%)

40

2

90

6 PM

1045 (+4.9%

30

2

90

2 PM

1081 (+8.5%)

40

0

90

2 PM

838 (-15.6%)

40

3

90

2 PM

1183 (+18.7%)

40

6

10

2 PM

968 (-2.8%)

Time of Day

Thermal Rating Amperes

In order to illustrate the effect of changing weather conditions on ratings, consider Table 2.3-5.

2-21



By reviewing this limited series of rating calculations, a number of important aspects of line rating dependence on weather can be drawn:

solar heating equals the heat loss by convection and radiation.

• Rating variation due to solar heating changes

Immediately after the current step change (t = 0+), the conductor temperature is unchanged (as are the conductor resistance and the heat loss rate due to convection and radiation), but the rate of heat generation due to Ohmic losses has increased. Therefore, at time t = 0+, the temperature of the conductor begins to increase at a rate given by the non-steady-state heat balance equation.

throughout the day is less than 5%.

• Air temperature variation is important. A difference of 10°C in air temperature causes a line rating change of nearly 10%.

• Relatively small differences in wind speed, in the range of 0 to 3 ft/sec (0.91 m/sec) can make a big difference in the line rating, generally 10% to 20%.

• The wind direction relative to the line is as important as the speed. A 6 ft/sec (1.8 m/sec) wind blowing near parallel to the line (10°) yields a slightly lower line rating than a 2 ft/sec (0.61 m/sec) wind blowing perpendicular to the line. 2.3.7

Transient Thermal Ratings

The need for increased thermal capacity in overhead lines is often driven by occasional, sharp increases in load after certain system contingencies. For example, an HV line might only reach high current levels after the loss of an EHV line or a critical generating facility. Since these occasions of high load occur infrequently and may persist for short time periods, it is often useful to consider transient thermal ratings for lines. The temperature of an overhead power conductor is constantly changing in response to changes in electrical current and weather. In this method, however, weather parameters (wind speed and direction, ambient temperature, etc.) are assumed to remain constant, and any change in electrical current is limited to a step change from an initial current, Ii, to a final current, If, as illustrated in Figure 2.3-2. Immediately prior to the current step change (t = 0–), the conductor is assumed to be in thermal equilibrium. That is, the sum of heat generation by Ohmic losses and

As time passes, the conductor temperature increases, yielding higher heat losses due to convection and radiation, and somewhat higher Ohmic heat generation due to the increased conductor resistance. After a large number of “thermal time constants”, the conductor temperature approaches its final steady-state temperature (Tf). The transient thermal rating is normally calculated by repeating the preceding calculations of Tc(t) over a range of If values, then selecting the If value that causes the conductor temperature to reach its maximum allowable value in the allotted time.

q c + q r + mC p

dT c = q s + I 2R (T c ) dt

1 dT c ⎡⎣R(T c ) I 2 + q s - q c - q r ⎤⎦ = dt mC p The transient thermal rating of an overhead line is dependent on the duration of the elevated current, the maximum temperature that the conductor is allowed to attain during the rating period, and on the starting temperature of the conductor. For example, with the Drake ACSR that was used for rating calculations previously, the transient ratings for various rating durations, maximum temperatures, and starting temperatures are as shown in Table 2.3-6. The advantage to using transient ratings is that the line can be loaded above its continuous rating without violating the constraints on sag clearance or annealing, but Table 2.3-6 Transient Ratings Versus Rating Duration

Figure 2.3-2 Temperature response of a bare overhead conductor to a step-change in current.

2-22

Rating duration

Maximum temp

Starting Temp

(Minutes)

(oC)

(oC)

(A)

continuous

100

N/A

1040

60

100

50

1045

30

100

50

1090 (+4.8%)

15

100

50

1230 (+18.3%)

15

100

75

1135 (+9.1%)

Rating



the drawback is that the load must be reduced to the continuous rating or below within a short time (15 to 30 min). See, for example, (Black and Rehberg 1985) and (Davidson 1969). 2.4

EFFECTS OF HIGH-TEMPERATURE OPERATIONS

2.4.1

Introduction

For any given high-voltage conductor, there are usually at least two current limits specified—the conductor’s normal rating, and the emergency rating (see Section 2.3). The conductor’s normal rating specifies how much current may flow in the circuit on a continuous basis, whereas the emergency rating specifies how much current can flow under emergency conditions for a specified amount of time—e.g., 30 minutes. A typical emergency rating may be applicable in the case where there is an unexpected outage on a parallel circuit requiring a short-duration increase in the load flow. The above “normal” current flow that is required during emergency loading will, if it remains unchecked, result in a thermal overload of the circuit, or significantly reduced clearances leading to a flashover of the circuit. Regardless of the case, the two issues that require attention are the loss of conductor strength and increased conductor sag. Ideally, transmission line operators aim to maximize the load on a particular circuit while minimizing the annealing (softening) of the circuit’s conductor. Annealing causes a decrease in the conductor’s strength and performance, necessitating the eventual replacement of this component. Because of the difficulty associated with taking a line out of service, and the large expense associated with the replacement of a circuit’s conductor, the operator clearly needs to balance the need for increased load flow with the economic risk associated with the premature replacement of the component, and the loss of service life or the safety risk associated with providing inadequate clearances. This section reviews issues related to the effects of hightemperature operation, including annealing, calculation

of sag and tension, thermal and creep elongation, and connectors and conductor hardware at high temperature. 2.4.2

Annealing of Aluminum and Copper

The American Society for Testing and Materials (ASTM) standards and the International Engineering Consortium (IEC) standards specify the minimum tensile strength of aluminum and copper wires, which is the stress at which the wire breaks. For aluminum and copper wires, the tensile strength of the materials decreases with time if operated at temperatures above 75°C, while the tensile strength of galvanized, aluminum-clad, or copper-clad steel wires remains constant at temperatures below 300°C. Thus, the extended exposure of conductors made up largely of aluminum or copper wires to temperatures above 75oC can eventually lead to tensile failures during high ice and/or wind loading events. Table 2.4-1 shows experimental results for a test conducted by Troia (Troia 2000). The high-temperature simulation used an ACSR conductor “Raven” with a 6/1 stranding ratio. In this study, four sets of conductors and connectors, and three sample loops, were operated at a temperature of 100°C, and cycled for 125, 250, and 500 cycles, respectively. The fourth set of samples was continued to 1000 current cycles at the 100°C temperature rise. A second group of four sets of sample test loops were operated at 175 ° C, and the current cycle counts were 125, 250, 500, and 1000. Upon completion, a Rockwell H scale was used to measure the hardness of each sample, and as expected, the average hardness was determined to be directly proportional to the temperature and duration of heating. Conductors heated to 100 ° C exhibited a decrease in hardness of up to 22% after 1000 cycles, and conductors heated to 175 ° C showed a decrease in hardness of up to 92.5% after only 250 cycles. Thus, annealing of the conductor was extensive at the higher operating temperature, and hardness readings could not be measured for conductors having been cycled 500 or 1000 cycles. Clearly, the results of this and other studies indicate that the prolonged operation of high-voltage conductors including ACSR at very high temperatures reduces the

Table 2.4-1 Hardness Resultsa Conductor

ACSR (6/1) ‘Raven’

Cycle Temp Average Hardness % Difference Temp Average Hardness % Difference 0

-

33

-

-

37.3

-

125

100

23.6

28.5

175

15.9

57.4

250

100

19.4

41.2

175

2.8

92.5

500

100

20.8

37.0

175

0b

-

1000

100

22.6

31.5

175

0b

-

a. Rockwell H scale, 1/8 in. ball, 60 kgs. b. Material hardness too soft for accurate readings on Rockwell H scale.

2-23


mechanical strength, integrity, and performance of the overhead system. It is also clear that the damage to the aluminum is of a cumulative nature and that the prolonged high temperature operation will significantly reduce the expected service life of the delivery system. Figure 2.4-1 shows the influence of prolonged hightemperature operation on the tensile strength of aluminum conductor. The graph shown has been developed based on test data of 1350-H19 “EC” hard drawn aluminum wires. In general, tensile strength reduction of aluminum wires at temperatures of less than 90 o C is considered negligible, and the effect of prolonged operation at this temperature will have very little effect on the service life of the aluminum conductor. At 100 oC, the


tensile strength of the wire is reduced by 10% after 5000 hours, equivalent to a little more than a half a year, and at 125oC, the tensile strength of the aluminum conductor is reduced 10% after 250 hours, a little more than 10 days of continuous operation. The effects of the hightemperature operation on the aluminum conductor are irreversible, and the damages experienced by the conductor are cumulative. Aluminum anneals at a slower rate than copper wire when exposed to identical conditions. Even though the use of copper conductors has significantly decreased over the years, a large number of low- to medium-voltage lines with copper conductors are still operated. The issues associated with the prolonged operation of these wires at very high temperatures are similar to the issues encountered with aluminum conductors. For example, Figure 2.4-2 shows the reduction in tensile strength with time and temperature for a sample of 0.081 in. (0.2 cm) diameter hard drawn copper wire. Since there are 8760 hours in a year, the logarithmic diagram clearly shows that the sustained operation of the copper wire at 65oC yields no measurable reduction in the tensile strength, while the sustained operation of a copper wire at 100 o C yields a 10% reduction in the tensile strength in 600 hours (25 days). More critically, the operation of the same wire at a temperature of 125oC for less than 40 hours reduces the wire tensile strength by 10%. The remaining strength of AAC, AAAC, ACAR, and ACSR conductor wires can be estimated with the following predictor equations. The use of these equations is acceptable even in the case in which several emergencyrating episodes have occurred.

Figure 2.4-1 Annealing of 1350-H19 hard-drawn aluminum wire.

2-24

Figure 2.4-2 Annealing of 0.081–in. diameter hard-drawn copper wire (Southwire).



Definition of Terms:

Predictor Equations: (English)

RS1350 = Residual aluminum (1350 Alloy) strength as a percentage of initial strength [%].

AAC:

RS6201 = Residual 6201 Alloy strength as a percentage of initial strength [%]. RSCOM = Residual strength of composite conductor as a percentage of initial strength [%]. T

= Temperature [°C].

t

= Elapsed time [hours].

d

= Strand diameter [mm, in.].

A1350

= Area of aluminum (1350 Alloy) strands [sq mm, sq in.].

A6201

= Area of 6201 alloy strands [sq mm, sq in.].

AT = Total area [sq mm, sq in.]. STR1350= Calculated initial strength of the aluminum (1350 Alloy) strands [N, lbs]. STRST = Calculated initial strength of the steel core [N, lbs]. STRT

= Calculated initial strength of the conductor [N, lbs].

Predictor Equations: (Metric) AAC: ⎛ 2.54 ⎞ − (0.001 T - 0.095 )⎜⎜ ⎟⎟

⎝ d ⎠ RS1350 = (- 0.24 T + 134 ) t 2.4-1 If (-0.24T + 134) > 100, use 100 for this term.

AAAC: ⎛ 2.54 ⎞ − (0.0012 T - 0.118 )⎜ ⎟

⎝ d ⎠ RS 6201 = (- 0.52 T + 176 ) t If (-0.52T + 176) > 100, use 100 for this term.

2.4-2

ACAR: RSCOM

⎛A = (RS1350 )⎜⎜ 1350 ⎝ AT

⎛A ⎞ ⎞ ⎟⎟ + (RS6201 )⎜⎜ 6201 ⎟⎟ ⎝ AT ⎠ ⎠

⎛ STR1350 RSCOM = (RS1350 )⎜⎜ ⎝ STRT ACSR: ACSR:

⎛ STRST ⎞ ⎟⎟ + (109 )⎜⎜ ⎝ STRT ⎠

RSCOM = (134 - 0.24 ) t (0.241 - 0.00254T ) d

RSCOM = (134 - 0.24 ) t −(0.001T - 0.095 ) 2.4-6 If (-0.24T + 134) > 100, use 100 for this term. AAAC: 0.1 d

2.4-7 RSCOM = (- 0.52T + 176 ) t − (0.0012T - 0.118 ) If (-0.52T + 176) > 100, use 100 for this term. ACAR: 0.1 d

⎛A RSCOM = (RS1350 )⎜⎜ 1350 ⎝ AT ACSR:

⎛A ⎞ ⎞ ⎟⎟ + (RS 6201 )⎜⎜ 6201 ⎟⎟ ⎝ AT ⎠ ⎠

⎛ STR1350 RSCOM = (RS1350 )⎜⎜ ⎝ STRT

⎛ STRST ⎞ ⎟⎟ + (109 )⎜⎜ ⎝ STRT ⎠

2.4-8

⎞ ⎟⎟ ⎠

2.4-9

As previously shown, when applying these equations, the cumulative strength reduction for multiple exposures at the same conductor temperature is additive; however, this is not true for multiple exposures at different conductor temperatures. To determine the cumulative strength reduction for a series of high-temperature exposures at different temperatures and times, each of the exposures must be expressed in equivalent time at the highest temperature experienced by the conductor before finding the equivalent time. The following examples illustrate a possible scenario that an ACSR and AAC conductor might experience during one year of service. Example 2.4-1: The conductor is 795 kcmil (405 mm2)ACSR “Drake”. During one year of operation, it is subjected to 7500 hours at 75°C, 1200 hours at 100°C, 50 hours at 125°C, and 10 hours at 150°C. What is the remaining strength (RS) of the conductor?

Using Equation 2.4-5, we know the following equation: 2.4-3

⎞ ⎟⎟ ⎠ 2.4-4

ACSR:

RSCOM = (134-0.24) t(0.241 - 0.00254T)

⎛ 0.1 ⎞ ⎜ ⎟ ⎝ d ⎠

and, if (134 – 0.24T) >100, use 100; if (0.241- 0.00254T) > 0, use 0.

0.1

2.4-5

a) 7500 hours at 75°C 0.1

0.241 - 0.00254T ) d RSCOM = (134-0.24 ) t (

= (134 - (0.24 x 75)) x (7500)

⎛ 0.1 ⎞ -(0.241 0.00254T)⎜ ⎟ ⎝ 1.108 ⎠

= 100%

7500 hours at 75°C has 100% remaining, which equals 0 minutes at 150°C. 2-25



b) 1200 hours at 100°C ⎛ 0.1 ⎞ -(0.241 - 0.00254T)⎜⎝ 1.108 ⎟⎠

= (134 - (0.24 x 100)) x (1200) = 99.17%

RS1350

= (134 - 0.24 T) t

-(0.001 T - 0.095)⎛⎜ 0.1 ⎞⎟ ⎝ d ⎠

= (134 - (0.24 x 75)) x (7500) -(0.001(75) - 0.095)

⎛ 0.1 ⎞ ⎜ ⎟ ⎝ 1.026 ⎠

= 98.3%

1200 hours at 100°C has 99% remaining, which equals 20 minutes at 150°C. c) 50 hours at 125°C

7500 hours at 75°C has 98.3% remaining, which equals 1 hour at 150°C. b) 1200 hours at 100°C

= (134 - (0.24 x 125)) x (50)-(0.241 -

⎛ 0.1 ⎞ 0.00254T) ⎝⎜ 1.108 ⎠⎟

= (134 - (0.24 x 100)) x (1200) -((0.001 x 100) - 0.095) = 87.4%

= 99.17%

50 hours at 125°C has 99% remaining, which equals 2 hours at 150°C.

⎛ 0.1 ⎞ ⎜ ⎟ ⎝ 1.026 ⎠

1200 hours at 100°C has 87.4% remaining, which equals 125 hours at 150°C.

d) 10 hours at 150°C c) 50 hours at 125°C ⎛ 0.1 ⎞

= (134 - (0.24 x 150)) x (10) = 95.19%

-(0.241 - 0.00254T) ⎜⎝ 1.108 ⎟⎠

= (134 - (0.24 x 125)) x (50) -((0.001 x 100) - 0.095) = 91.95%

⎛ 0.1 ⎞ ⎜ ⎟ ⎝ 1.026 ⎠

10 hours at 150°C has 95% remaining. To calculate the total loss of conductor strength, the sum of the equivalent times (hours) at 150°C is found. In this example, the sum is:

50 hours at 125°C has 92% remaining, which equals 15 hours at 150°C. d) 10 hours at 150°C

D

0 + 0.3 + 2 + 10 = 12.3 hours at 150 C. RSCOM = (134 - 0.24T) t -(0.241 -

⎛ 0.1 ⎞ 0.00254T) ⎜⎝ d ⎟⎠

= (134 - (0.24 x 150)) x (12.3)-(0.241 - (0.00254 x 150))

⎛ 0.1 ⎞ ⎜ ⎟ ⎝ 1.108 ⎠

= 95% The remaining strength for the in-service conductor is 95%. Example 2.4-2 : The conductor is 37 kcmil (19 mm 2 ) AAC “Arbutus”. During one year of operation, it is subjected to 7500 hours at 75°C, 1200 hours at 100°C, 50 hours at 125°C, and 10 hours at 150°C. What is the remaining strength (RS) of the conductor?

Using Equation 2.4-6, AAC: RSCOM = (134-0.24 ) t

and, if (134 – 0.24T) >100, use 100. a) 7500 hours at 75°C

2-26

0.1

− ( 0.001T - 0.095 ) d

= (134 - (0.24 x 150)) x (10) -((0.001 x 100) - 0.095) = 92.8%

⎛ 0.1 ⎞ ⎜ ⎟ ⎝ 1.026 ⎠

10 hours at 150°C has 93% remaining. To calculate the total loss of conductor strength, the sum of the equivalent times at 150°C is found. In this example, the sum is:

1 + 125 + 15 + 10 = 151 hours at 150D C. RS1350 = (134 - 0.24 T) t -(0.001 T - 0.095)

⎛ 0.1 ⎞ ⎜ ⎟ ⎝ d ⎠

-(0.001(150) - 0.095) ⎛⎜

= (134 - (0.24 x 150)) x (151) = 86.9%

0.1 ⎞ ⎟ ⎝ 1.026 ⎠

The remaining strength for the in-service conductor is 87%. As expected, the example calculations predict that the continuous high-temperature operation will cause the tensile strength of the AAC conductor to deteriorate faster than in the case of the ACSR conductor. In Figure 2.4-1, the graph showing the loss of strength for


individual strands of aluminum indicates that after 150 hours the remaining strength of the hard-drawn aluminum wire is 82%. When compared to the remaining strength value calculated using the predictor equations, the AAC conductor appears to be 5% stronger than predicted by using the data of the individual aluminum strands. Much of this difference in the prediction of the strength loss in the AAC conductor can be attributed to differences in behavior between the stranded conductor and an individual strand of aluminum and to differences in the nominal and actual dimensions of the manufactured product. Similarly, using strand data, the prediction equations show the ACSR conductor to be approximately 13% stronger than the tensile strength predicted by using the individual aluminum strand data itself. The difference in the remaining tensile strength can be directly attributed to the presence of the steel reinforcing strands which are significantly stronger than a comparably sized aluminum strand and are also not affected by temperatures below 300°C. 2.4.3

Sag Tension Models for ACSR Conductors

The traditional sag and tension model used throughout the industry is the model developed and promoted by the Alcoa-Fujikura LLC (Alcoa) (Alcoa 2003). The Alcoa sag and tension prediction model and methods assume that the magnitude of the compression stresses resulting from the manufacturing process are negligible and therefore do not affect the behavior of the conductor regardless of the operating temperature. Therefore, the model ignores the effects of aluminum compression. The Alcoa sag and tension model focuses on the coefficient of ther mal expansion phenomenon, which accounts for the fact that the aluminum strands expand at nearly twice the rate of the steel strands for the same increase in temperature. Consequently, as the temperature of the conductor increases significantly, the aluminum strands expand more rapidly than the steel strands. This shifts a continuously increasing percentage of the catenary tension onto by the steel strands (i.e., the aluminum “unloads” its share of the original tension). At some point (i.e., commonly called the “knee point”) the tension in the aluminum strands approaches a value of zero. At this time, the steel strands of the conductor carry all of the catenary tension of the composite wire. Based on this premise, and once the knee point temperature has been exceeded, the sag of the ACSR conductor is proportional to the rate of thermal expansion of the steel strands. It should be noted that the Alcoa sag and tension prediction model was developed in the early part of the last century when the stranding of the most commonly used ACSR conductors was six aluminum


strands to one steel strand. Nevertheless, the sags and tensions predicted by the Alcoa model generally correlate very well for most conductors operated at temperatures not exceeding 75°C to 100°C. Today, medium-to-large ACSR conductors may have as many as four layers of aluminum strands surrounding a multistranded steel core. Based on the construction methods used to manufacture these multilayered conductors, it is very likely that a significant number of aluminum strands are capable of supporting limited compression forces (as a result of the confinement provided by underlying and overlaying layers) and that the resulting conductor harbors noticeable built-in stresses. The EPRI technical report Conductor and Associated Hardware Impacts during High Temperature Operations – Issues and Problems, published in December 1997 by Shan and Douglass (EPRI, TR-109044) concluded that it is more likely that such multilayered conductors follow a sag and tension model originally proposed by Nigol (Nigol and Barrett 1980). The Nigol sag and tension model, as shown in Figure 2.4-3, assumes that the aluminum strands do not change from tension to compression until a fixed limiting value is reached. In Nigol’s sag and tension model, as the aluminum changes from tensile to compression stresses, the elastic modulus is assumed not to change. Nigol hypothesizes the existence of compression stresses in the aluminum below the “birdcaging” temperature but assumes that the outer layer of aluminum strands remains in tension. Therefore, Nigol assumes that the tension in the outer layer strands denies the inner layer to expand radially and buckle outward. Nigol concludes that, since the inner layer is in compression and the outer layer is in tension, and since the outer layer presses radially inwards against the expanding inner layer, the aluminum strands of the inner layer are pressed against the steel cores and birdcaging is effectively negated. Consequently, based on this hypothesis, Nigol concluded that the elastic modulus remains unchanged even though the net aluminum stresses change from tension to compression. Thus, Nigol’s sag-tension model assumes that, as the conductor temperature increases towards the birdcaging temperature, the tensions in the outer layers of aluminum strands and the corresponding inward directed radial forces decrease. At the same time, Nigol’s model assumes that there is an increase in the radial forces of the outer layer and also an increased axial compression in the strands of the inner layers. Nigol, therefore, concludes that at the time when the birdcaging temperature is reached, the inner and outer radial forces are

2-27


balanced, and the compressive stresses that are created reach their limiting value. Barrett’s sag and tension prediction model (Barrett et al. 1982) departs from Nigol’s model at this point. Barrett hypothesizes that at the birdcaging temperature, the radial forces within each of the aluminum strand layers balance. Based on Barrett’s hypothesis, the aluminum strands of a layer move radially outward as the temperature rises, resulting in a different elastic modulus to be used for the aluminum strands. Therefore Barrett describes the use of two compression moduli—the first value to be used at temperatures below the “knee point” and the second to be used at temperatures above the birdcaging temperature. Contrary to Nigol and Barrett, Rawlins (Rawlins 1998) proposes that there are no compression stresses above the knee point, but rather promotes the idea of large built-in tensile stresses that are the result of the manufacturing process. In Rawlins’s sag and tension prediction model, the point at which the aluminum stresses become tensile is also the point when there is a change in the elastic modulus. Therefore, Rawlins proposes that these stresses cause permanent elongations when compared to the other sag and tension models at the same level of tension. Figure 2.4-3 shows graphical representations of the four hypotheses explaining the behavior of high temperature conductors. 2.4.4


the aluminum strands are capable of greatly contributing to the sag of conductors at high operating temperatures. A simplified illustration of the influence of compression stresses in the aluminum strands at high temperatures is illustrated in Figure 2.4-4. The first sketch (Sketch 1) shows a length of the conductor at ambient temperature where the lengths of all of the aluminum and steel strands are equal. The second sketch (Sketch 2) shows an instance of the behavior of the conductor once the conductor length is heated to a temperature above ambient conditions. Because of the differences in the coefficients of thermal expansion of the aluminum and the steel strands (discounting for now issues such as stranding, manufacturing, etc), the lengths of the aluminum and steel strands will differ by an amount proportional to the temperature difference and the difference in the coefficients of thermal expansion. Of course, this scenario assumes that each type of material would be free to expand and not restricted in any manner. Similarly, the third sketch (Sketch 3) shows the behavior of the same length of conductor heated to a temperature significantly above ambient conditions, with the difference that the two materials are restricted from expanding independently of each other. As a result of the differences in the coefficients of thermal expansion, the proportion of the stresses carried by each type of material will change.

Axial Compressive Stresses

Work performed previously by Nigol and Barrett (Barrett 1982) clearly showed that compression stresses in

Finally, the fourth sketch (Sketch 4) shows the conductor in the case at which the compression in the aluminum strands is balanced by a tensile load in the steel core (i.e., the phenomenon most commonly referred to as “aluminum compression”). As the conductor reaches the birdcaging temperature (i.e., the point at which the aluminum strands expand outward to compensate for the increase in length), the aluminum strands move outward, yielding to the inherent compression stress induced by the constrained thermal expansion. At this

Figure 2.4-3 Sag-tension models. Figure 2.4-4 Manufacturing effects of ACSR conductor.

2-28


point (i.e., the point in the loading at which birdcaging is first observed), the tensile stress in the steel core far exceeds the value of the compression stress in the aluminum strands. 2.4.5

Built–In Stresses

When multistranded conductors are manufactured using a combination of steel and aluminum wires, the temperatures of the individual wire strands during the manufacturing process may vary, especially that of the steel core when compared to the aluminum strands. Contrary to the manufacturing of these multimaterial conductors, the same problem is not encountered in the manufacturing of All Aluminum Conductors (AAC), since they are constructed from the same homogeneous material. For ACSR conductors, the variance in the temperatures of the different types of stranding materials contributes to the composite behavior of the conductor. Therefore, when the conductor is placed under load, the variance in the temperature during manufacturing is likely to impact the sag and tension characteristics of the conductor. Unfortunately, quantitative values useful in estimating these manufacturing effects are neither provided by the manufacturer nor otherwise published. For example, if one assumes that a cold steel core is stranded with hot aluminum wires around the outside, the resulting conductor’s steel core will be slightly longer than the outer aluminum layers once the conductor is allowed to reach thermal equilibrium. As a result of the temperature differences, the commonly named knee point (i.e., the point at which the temperature of the complete length and cross-section has increased to a level at which the stresses in the aluminum strands approach zero) will shift relative to the knee point of a conductor constructed with steel and aluminum strands at the same temperature. 2.4.6


of the conductor is not exceeded and that the suggested minimum clearances are maintained. In this subsection the mechanical and thermal properties acquired in the EPRI Conductor High Temperature Project experiments are presented, and the calculated sags and tensions are compared to values predicted using traditional sag and tension prediction data, methods, and tools. For clarity, these comparisons have been separated into two parts; the first addresses sags of level spans, the second addresses sags for inclined spans. To illustrate the use of the results and to demonstrate the differences in the predicted sags and tensions, three ACSR conductors of varying stranding ratios (low, medium, and high aluminum- to-steel stranding ratios) have been analyzed at different temperatures. The conductor sag analyses and comparisons were made at room temperature (23ºC), at a temperature of 120ºC, and at a temperature of 150ºC. Also, sags computed at level spans are compared to values at an inclined span of 15° and 30°. The underlying principles behind sag tension calculations for both level and inclined spans are outlined in the following subsections. Sag and Tension of Level Spans The shape of a catenary of a conductor is a function of the conductor’s weight per unit length, w, the horizontal component of tension, H, the span length, S, and the conductor sag, D. Figure 2.4-5 shows an illustration relating all of these parameters for a level conductor span. The actual conductor length, L, constitutes the stretched length of conductor (Trash et al. 1994).

Sag Tension Calculations

Bare overhead conductors are flexible and uniform in weight. These characteristics allow conductors to assume a catenary shape when suspended between support points. The shape of the catenary assumed by the conductor changes continuously as a result of climatic changes such as ambient temperature, operating conditions such as the amount of current being transferred, service life, and weather-related loads such as wind, snow, and ice. Because of the threat to human life and property, it is critical to ensure adequate horizontal and vertical clearances under all circumstances. Therefore the line designer is challenged to consider all weather and electrical loading cases to ensure that the breaking strength

Figure 2.4-5 Catenary sag model – level span.

2-29



The exact catenary equation representing the height of the conductor, y(x), at its lowest point along the span is given by the following equation: y( x ) =

H wx [cosh( ) − 1] w H

2.4-10

For level conductor spans, the low point is in the center and the total sag, D, is found by substituting x = S/2 in Equation 2.4-10. The resulting hyperbolic catenary relation for sag then becomes: D=

H ws [cosh( ) − 1] 2H w

2.4-11

The horizontal component of tension, H, is located at the point in the span where the conductor slope is horizontal, or at the midpoint for level spans. The conductor tension, T, is found at the ends of the spans at the point of attachment and is calculated using the following equation. T = H + wD

⎞ ⎛ Sw ⎞ ⎟ sinh ⎜ 2H ⎟ ⎠ ⎝ ⎠

2.4-13

Therefore, in order to calculate the correct sag, it is necessary to separate the effects of conductor elongation due to tensile loading as well as thermal loading. This process requires an iterative procedure in which the mathematical formulas describing the conductor elongation caused by the temperature change are solved simultaneously with the tension and conductor length relationship. To calculate the change in length due to temperature loading, the following equation is used: REF

2-30

⎡⎣1 + α AS (T − Tr Re f ) ⎤⎦

= coefficient of linear thermal elongation for the AL/SW strands.

LT

= final length of the conductor.

LT REF

= reference length of the conductor.

(T − Tr Re f )

= change in temperature.

The NESC (National Electric Safety Code 1993) recommends limits on the tension of conductors based on a percentage of their Rated Breaking Strength (RBS). For example, the tension limits of an ACSR may be 60% under maximum ice and wind loading, 35% upon installation at 60ºF, and 25% final unloaded after maximum loading has occurred at 60ºF. Therefore, if the initial tension in a span is known along with the initial conductor length, the total elongation resulting from the tensile load is calculated as follows:

2.4-12

It should be noted that while the above equations describe the behavior of ideal (with perfectly elastic stress and strain characteristics) concentric-lay stranded conductors, actual conductors such as ACSR conductors exhibit nonlinear behavior when loaded from an initial tension to some final value due to ice, wind, or temperature loading. Permanent elongation from creep and heavy loading also affects the resulting sag. Also, hightemperature operations result in thermal elongation of the steel and aluminum strands, thus affecting sag.

LT = LT

α AS

LH = LH

Rearranging the hyperbolic catenary equation for a level span, along with the substitution of x = S /2 for level spans corresponds to a conductor length of: ⎛ 2H L=⎜ ⎝ w

where:

2.4-14

REF

⎡ H − H REF ⎤ ⎢1 + ⎥ Ec A ⎦ ⎣

2.4-15

where: LH

REF

= length of conductor under horizontal reference tension.

LH

= length of conductor under horizontal tension.

H

= horizontal tension.

H REF = length of conductor under horizontal reference tension. Ec

A

= modulus of elasticity of the conductor (psi). = cross-sectional area, in2.

It should be noted that the modulus E c in Equation 2.4-15 is the modulus of the steel and aluminum strands determined by the stress and strain relationship of the composite conductor. Since this relationship for a bimetallic construction of the conductor is quite complex, the relationship of ACSR conductors is typically described by a third or fourth order polynomial. In addition, the thermal and permanent elongation drastically affects the mechanical behavior of ACSR conductors at high temperatures, and this further complicates the analysis. Therefore, since ACSR conductors are nonhomogenous, the stress and strain characteristics are separated into their steel and aluminum components as shown in Figure 2.4-6. Numerical methods are used to calculate the resulting sags and tensions, with the aid



Figure 2.4-6 Decomposed ACSR “Tern” conductor at 120°C.

of software programs such as Alcoa Fujikura’s Sag10 package (Alcoa 2003). 2.4.7

The same equation used to represent the height of the conductor, for a level span is valid for inclined spans and is given by the following equation (Trash el al. 1994):

Sag and Tension of Inclined Spans

For inclined spans, the length of the conductor between supports is divided into two separate sections for consideration. One is to the right of the lowest point of the conductor, and one is to the left (see Figure 2.4-7).

y( x ) =

H⎛ wx ⎞ cosh( ) − 1⎟ w ⎜⎝ H ⎠

2.4-16

In each part of the span, the sag is dependent upon the vertical distance between support points and can be described by the following equations:

h ⎞ ⎛ DR = D ⎜ 1 − ⎟ ⎝ 4D ⎠

2

h ⎞ ⎛ DL = D ⎜ 1 + ⎟ ⎝ 4D ⎠

2

2.4-17

2.4-18

The maximum tension is

TR = H + wDR

2.4-19

TL = H + wDL

2.4-20

Figure 2.4-7 Catenary sag model—inclined span.

2-31


2.4.8

Calculation of Conductor High-Temperature Sag and Tension

Simplified Calculations Simplified calculations are used for demonstration using a hand calculator. While most sag and tension calculations are typically performed with an analysis software, the use of the simplified calculation clearly demonstrates the process and provides the reader some insight into how sags and tensions occur for overhead lines. Example 2.4-3: What is the sag (D) and slack for a 1000-ft level span of 795 kcmil (405 mm 2 ) ACSR “Drake” conductor at ambient temperature (25ºC, 77ºF). The weight per unit length is 1.094 lbs/ft (1.6 kg/m), the horizontal tension component, H, is 25% of the RBS.

H = 0.25 x 31,500 lbs = 7875 lbs (35,196 N)


At 50ºC, the length of the conductor is 1001.28 ft (305.2 m). At 150ºC, the length of the conductor is 1003.21 ft (305.8 m). Example 2.4-5: What is the sag of the conductor at the elevated temperature levels?

The following equation is rearranged to estimate the resulting sag, which only considers the change due to thermal effects, and ignoring any changes that are due to the changes in tension.

L=S+

hence

D(122 ) =

Use Equation 2.4.11,

H ws wS 2 D = [cosh( ) − 1] ≈ w 2H 8H wS 2 1.094 (1000 ) D= = = 17.37 ft ( 5.29 m ) 8H (8) 7875 2

The sag for this level span is 17.37 ft (5.3 m). The following equation is used to calculate the length of the conductor:

3S ( L − S ) 8D 2 becomes D = 3S 8

D(302 ) =

3 (1000 )(1.28) 8 3 (1000 )( 3.21) 8

= 21.9 ft ( 6.68 m ) = 34.7 ft (10.58 m )

Example 2.4-6: What is the tension of the conductor when subjected to the two temperatures?

Rearrange the following equation to obtain the resultant tension of the conductor.

D=

wS 2 wS 2 becomes H = 8H 8D

wS 2 1.094 (1000 ) H(122 ) = = = 6244 lbs (27,875 N) 8D 8 ( 21.9 ) 2

8D ⎛ 2H ⎞ ⎛ Sw ⎞ sinh ⎜ L=⎜ ≈S+ ⎟ ⎟ 3S ⎝ w ⎠ ⎝ 2H ⎠

2

8 (17.37 ) 8D 2 = 1000 + = 1000.80 ft ( 305.05 m ) 3S 3 (1000 ) 2

L=S+

The conductor slack is the length minus the span length, 0.80 ft (0.24 m). Example 2.4-4: What happens to the conductor length if the temperature increases from ambient to 50ºC (122ºF)? What about if it increases to 150ºC (302ºF)? The coefficient of linear thermal expansion is 10.7 x 10-6/ºF.

LT = LT

REF

⎡⎣1 + α AS (T − TREF ) ⎤⎦

L(122 ) = 1000.80 ⎡⎣1 + 10.7 × 10 −6 (122 − 77 ) ⎤⎦ = 1001.28 ft (305.2 m) L(302 ) = 1000.80 ⎡⎣1 + 10.7 × 10 −6 ( 302 − 77 ) ⎤⎦ = 1003.21 ft (305.8 m)

2-32

wS 2 1.094 (1000 ) H(302) = = = 3941lbs (17,594N) 8D 8 ( 34.7 ) 2

These values assume that the conductor has an infinite modulus of elasticity. Actually, the elastic modulus of the conductor is finite, and changes in the conductor tension do affect the length of the conductor. Therefore, these equations estimate sags that are greater than has been observed in the field. Estimating the actual change in sag due thermal effects is complex, because one needs to look at the combined thermal and elastic effects of conductors. The initial loads of concentrically stranded ACSR conductors result in elongation behavior that is different from that caused by loading several years later. Software such as Alcoa’s Sag10 program use numerical methods to estimate the resulting sags.



The following example uses an AAC, and the effects of the elevated temperature levels are estimated.

hence

D(122 ) =

Example 2.4-7: What is the sag (D) and slack for a 1000 ft. (305 m) level span of AAC “Arbutus” conductor at ambient temperature (25ºC, 77ºF). The weight per unit length is 0.746 lbs/ft (1.09 kg/m), the horizontal tension component, H, is 25% of the RBS.

H = 0.25 x 13,900 lbs = 3475 lbs. (15,513 N) wS 2 0.746 (1000 ) = = 26.8 ft ( 8.18 m ) 8H (8) 3475

D(302 ) =

3 (1000 )( 2.48) 8 3 (1000 )( 4.79 ) 8

= 30.5 ft ( 9.3 m ) = 69.2 ft ( 21.1 m )

Example 2.4-10: What is the tension of the conductor when subjected to the two temperatures?

2

D=

The sag for this level span is 26.8 ft (8.18 m). The following equation is used to calculate the length of the conductor: 8 ( 26.8) 8D2 = 1000 + = 1001.9 ft ( 305.38 m ) 3S 3 (1000 ) 2

L=S+

Rearrange the following equation to obtain the resultant tension of the conductor.

D=

wS 2 wS 2 becomes H = 8H 8D

wS 2 0.746 (1000 ) H(122 ) = = = 3057 lbs (13,647 N) 8D 8 ( 30.5 ) 2

The conductor slack is the length minus the span length, 1.9 ft (0.58 m). Example 2.4-8: What happens to the conductor length if the temperature increases from ambient to 50ºC (122ºF)? What about if it increases to 150ºC (302ºF)? The coefficient of linear thermal expansion is 12.8 x 10-6/ºF.

LT = LT

REF

⎡⎣1 + α AS (T − TREF ) ⎤⎦

L(122 ) = 1001.9 ⎡⎣1 + 12.8 × 10 −6 (122 − 77 ) ⎤⎦ = 1002.48 ft (305.56 m) L(302 ) = 1001.9 ⎡⎣1 + 12.8 × 10

−6

(302 − 77 )⎤⎦

= 1004.79 ft (306.26 m) At 50ºC, the length of the conductor is 1002.48 ft (305.56 m). At 150ºC, the length of the conductor is 1004.79 ft (306.26 m). Example 2.4-9: What is the sag at the elevated temperature levels?

The following equation is rearranged to estimate the resulting sag, which only considers the change due to thermal effects, and ignoring any changes that are due to the changes in tension.

D=

3S ( L − S ) 8

wS 2 0.746 (1000 ) = = 1348 lbs (6,018 N) 8D 8 ( 69.2 ) 2

H(302 ) =

These high readings reflect the thermal elongation assuming the strands have an infinite modulus of elasticity. Fortunately, the modulus is finite, and the changes in the tension levels do affect the conductor length. These equations are a useful way to get a rough idea of how an ACSR conductor behaves when compared to an AAC conductor. At 50ºC, the AAC elongates about 28% more than the ACSR, and at 150ºC, the AAC elongates approximately 50% more than the ACSR. Using Alcoa Fujikura’s Sag10 Software Software programs can be useful to obtain more accurate results, since they use an iterative procedure to obtain solutions to complex problems such as the sag and tension calculation of a conductor. This iterative process is commonly referred to as the “binary chop” technique, and it separates the thermal as well as plastic and elastic effects resulting from changes in the conductor’s tension.

Once the results of the iterative calculations have converged, the results reflect the conductor length that accounts for the elastic effects of an increased load as well as the thermal elongation effects. Since H, and H REF correspond to the first-, second-, third-, and fourth-order composite stress and strain curves that describe the initial and final conductor modulus, it is typically convenient to rearrange the equations in terms of strain elongation to permit the direct substitution of values into the polynomial equations.

2-33


2.4.9

Results of High-Temperature Sag Tension Calculations

Three different ACSR conductors were selected to demonstrate the high-temperature behavior of conductors and the calculation of the sag and tension. The ACSR conductors have varying steel-to-aluminum ratios, hence the effects of the construction of the conductor on the sag and tension are demonstrated. The conductors selected for the examples are ACSR “Drake,” ACSR “Mallard,” and ACSR “Tern.” All of these ACSR conductors selected for the demonstration are commonly used by electric utilities. ACSR Mallard is constructed using 30 aluminum strands and 19 steel core strands. The ratio of the aluminum’s cross-sectional area to the conductor’s total crosssectional area for the ACSR Mallard conductor is 0.814, classifying this conductor as a wire with a “high” steel-to-aluminum ratio. Similarly, ACSR Drake is constructed using 26 aluminum strands and 7 steel strands. The ratio of the aluminum’s cross-sectional area to the ACSR Drake conductor’s total cross-sectional area is 0.860, classifying this conductor as a wire with a “medium” steel-to-aluminum ratio. Finally, ACSR Tern is constructed using 45 aluminum strands and 7 steel strands. The ratio of the aluminum’s cross sectional area to the ACSR Tern conductor’s total cross-sectional area is 0.935, classifying this conductor as a wire with a “low” steel-to-aluminum ratio. In support of the analysis and the illustration of the high-temperature behavior of standard ACSR conductors, stress and strain data acquired in the EPRI Conductor High Temperature Operation Project were used. The data used for the prediction of high-temperature sags included the stress and strain curves and coefficients of thermal elongation. In order to illustrate the differences in the results, sag analyses were performed for a level conductor span as well as for inclined spans of 15° and 30°. In each case, sags were calculated for each type of conductor using two different approaches at each of the selected conductor temperatures. The resulting sags are reported at the initial and final condition at each temperature. In addition, the span length was varied, and the sag analyses were performed for 500 ft, 1000 ft, and 1500 ft span lengths. Again, the results were reported at the initial and final condition at each temperature. In the first approach, sags were calculated using Alcoa Fujikura’s Sag10 sag tension analysis program using the provided stress and strain charts included in the soft-

2-34


ware. Values are reported for initial and final conditions, respectively. In the second approach, sags were calculated using Alcoa Fujikura’s Sag10 sag tension analysis program and data obtained in the EPRI Conductor High Temperature Operation Project. Values are reported for initial and final conditions, respectively. Tables 2.4-2 through 2.4-10 provide a summary and comparison of derived sags at each operating temperature. For ACSR Drake with the 500 ft (152 m) span, the results of the comparison show that final sags calculated using EPRI High Temperature Conductor data are less than 1ft (0.3 m) greater than comparable values calculated using Alcoa Fujikura’s Sag10 data. For the 15°inclined span, the differences in the final sag were also less than 1 ft (0.3 m). Similar results were obtained for the 30° incline, which resulted in increased final sags that were less than 1 ft (0.3 m). For ACSR Drake with the 1000 ft (305 m) span, the results of the comparison show that final sags calculated using EPRI High Temperature Conductor data generally differ by about 2 ft (0.61 m) at ambient, but was about 1 ft (0.3 m) higher for elevated temperatures when compared to Alcoa Fujikura’s Sag10 data. For the 15° inclined span, the difference in the final sags was less than 1 ft (0.3 m). Similar results were obtained in the case of the 30° incline, which resulted in increased final sags that were minimal. For ACSR Drake with the 1500 ft (457 m) span, the results of the comparison show that final sags calculated using EPRI High Temperature Conductor data was up to 3 ft (0.9 m) at ambient, and 1 ft (0.3 m) at the elevated temperatures when compared to Alcoa Fujikura’s Sag10 data. For the 15° inclined span, the difference in the final sags was less than a foot (0.3 m). Similar results were obtained for the 30° incline, which resulted in increased final sags that are less than 1 ft (0.3 m). For ACSR Tern with the 500 ft (152 m) span, the results of the comparison show that final sags calculated using EPRI High Temperature Conductor data are generally less by about half a foot (0.15 m) when compared to Alcoa Fujikura’s Sag10 data. For the 15° inclined span, the difference in the final sags was negligible, and similar results were obtained for the 30° incline. Good correlation of the data occurred for the 1000 ft (305 m) and 1500 ft (457 m) span, and the sag values were less than 1 ft (0.3 m) when compared to Alcoa data. In most cases, the predicted sag was less than expected by the Alcoa database curves.



For ACSR Mallard with the 500 ft (152 m) span, the results of the comparison show that final sags calculated using EPRI High Temperature Conductor data are generally 1 ft (0.3 m) higher than comparable values calculated using Alcoa Fujikura’s Sag10 data. For the 15° inclined span, the difference in the final sags was between 0 ft and 1.5 ft (0.46 m). For the 30° incline, the difference in the final sags was between 0 and 1.6 ft (0.49 m).

For ACSR Mallard with the 1500 ft (457 m) span, the results of the comparison show that final sags calculated using EPRI High Temperature Conductor data is an additional 4 ft (1.2 m) at ambient temperature and is about 2.5 ft (0.76 m) at elevated temperatures when compared to values calculated using Alcoa Fujikura’s Sag10 data. For the 15° inclined span, the difference in the final sags was negligible at ambient, and as high at 3 ft (0.9 m) and approached 4 ft (1.2 m) for elevated temperature levels. Similar results were obtained for the 30° incline.

For ACSR Mallard with the 1000 ft (305 m) span, the results of the comparison show that final sags calculated using EPRI High Temperature Conductor data are 3 ft (0.9 m) at ambient temperatures and about 2 ft (0.61 m) at elevated temperatures, when compared to values calculated using Alcoa Fujikura’s Sag 10 data. For the 15° inclined span, the difference in the final sags was negligible at ambient temperature but 2.5 ft (0.76 m) at elevated temperatures. For the 30° incline, the difference in the final sags was negligible at ambient temperature but up to 2.8 ft (0.85 m) at elevated temperatures.

Table 2.4-2 ACSR Drake, Span Length = 500 ft Alcoa Fujikura Sag 10 Software with Alcoa Data Conductor Temperature

Level

15%

30%

Initial Sag (ft)

Final Sag (ft)

Initial Sag (ft)

Final Sag (ft)

Initial Sag (ft)

Final Sag(ft)

23 Deg

3.26

4.35

3.26

3.37

3.26

3.76

120 Deg

8.61

8.61

8.61

8.30

8.61

9.26

150 Deg

9.21

9.61

9.21

9.52

9.21

10.62

Alcoa Fujikura Sag 10 Software with EPRI Data Conductor Temperature

Level

15%

30%

Initial Sag (ft)

Final Sag (ft)

Initial Sag (ft)

Final Sag (ft)

Initial Sag (ft)

Final Sag(ft)

23 Deg

3.26

5.23

3.26

3.37

3.26

3.76

120 Deg

8.64

9.26

8.64

8.93

8.64

9.96

150 Deg

9.81

10.29

9.81

10.14

9.81

11.31

Comparison: Alcoa to EPRI Conductor Temperature

Level

15%

30%

Difference (ft)

Difference (ft)

Difference (ft)

Difference (ft)

Difference (ft)

Difference (ft)

23 Deg

0

0.88

0.00

0

0

0.88

120 Deg

0.61

0.65

0.63

0.70

0.61

0.65

150 Deg

0.60

0.68

0.62

0.69

0.60

0.68

2-35




Level Initial Sag (ft)

15% Final Sag (ft)

Initial Sag (ft)

30% Final Sag (ft)

Initial Sag (ft)

Final Sag(ft)

23 Deg

13.05

16.27

13.05

13.05

13.05

15.05

120 Deg

22.48

25.32

22.48

23.22

22.48

25.89

150 Deg

25.62

26.94

25.62

26.45

25.62

29.49



15% Final Sag (ft)

Initial Sag (ft)

30% Final Sag (ft)

Initial Sag (ft)

Final Sag(ft)

23 Deg

13.05

18.32

13.05

13.5

13.05

15.05

120 Deg

23.05

26.23

23.05

23.81

23.05

26.55

150 Deg

26.20

27.87

26.20

27.05

26.20

30.16

Difference (ft)

Difference (ft)


Level Difference (ft)

15%

Difference (ft)

Difference (ft)

30% Difference (ft)

23 Deg

0

2.05

0

0

0

0

120 Deg

0.57

0.91

0.57

0.59

0.57

0.66

150 Deg

0.58

0.93

0.58

0.60

0.58

0.67


Level

15%

30%

Initial Sag (ft)

Final Sag (ft)

Initial Sag (ft)

Final Sag (ft)

Initial Sag (ft)

Final Sag(ft)

23 Deg

29.39

34.65

29.39

30.38

29.39

33.88

120 Deg

42.39

47.81

42.39

43.74

42.39

48.77

150 Deg

46.40

49.93

46.40

47.84

46.40

53.34


Level

15%

30%

Initial Sag (ft)

Final Sag (ft)

Initial Sag (ft)

Final Sag (ft)

Initial Sag (ft)

Final Sag(ft)

23 Deg

29.39

37.61

29.39

30.38

29.39

33.88

120 Deg

43.04

48.83

43.04

44.41

43.04

49.51

150 Deg

47.10

50.97

47.10

48.56

47.10

54.14


2-36

Level

15%

30%

Difference (ft)

Difference (ft)

Difference (ft)

Difference (ft)

Difference (ft)

Difference (ft)

23 Deg

0

2.96

0

0

0

0

120 Deg

0.65

1.02

0.65

0.67

0.65

0.74

150 Deg

0.70

1.04

0.70

0.72

0.70

0.80



Table 2.4-5 ACSR Tern, Span Length = 500 ft Alcoa Fujikura Sag 10 Software with Alcoa Data Conductor Temperature

Level

15%

30%

Initial Sag (ft)

Final Sag (ft)

Initial Sag (ft)

Final Sag (ft)

Initial Sag (ft)

Final Sag(ft)

23 Deg

3.81

5.67

3.81

3.94

3.81

4.39

120 Deg

10.90

12.89

10.90

11.27

10.90

12.56

150 Deg

13.11

13.73

13.11

13.53

13.11

15.09


Level

15%

30%

Initial Sag (ft)

Final Sag (ft)

Initial Sag (ft)

Final Sag (ft)

Initial Sag (ft)

Final Sag(ft)

23 Deg

3.81

5.74

3.81

3.93

3.81

4.39

120 Deg

10.76

12.45

10.76

11.12

10.76

12.40

150 Deg

13.00

13.29

13.00

13.42

13.00

14.96


Level

15%

30%

Difference (ft)

Difference (ft)

Difference (ft)

Difference (ft)

Difference (ft)

Difference (ft)

23 Deg

0

0.07

0

-0.01

0

0

120 Deg

-0.14

-0.44

-0.14

-0.15

-0.14

-0.16

150 Deg

-0.11

-0.44

-0.11

-0.11

-0.11

-0.13


Level

15%

30%

Initial Sag (ft)

Final Sag (ft)

Initial Sag (ft)

Final Sag (ft)

Initial Sag (ft)

Final Sag(ft)

23 Deg

15.24

19.84

15.24

15.76

15.24

17.58

120 Deg

27.30

34.46

27.30

28.17

27.30

31.41

150 Deg

30.84

35.78

30.84

31.80

30.84

35.45


Level

15%

30%

Initial Sag (ft)

Final Sag (ft)

Initial Sag (ft)

Final Sag (ft)

Initial Sag (ft)

Final Sag(ft)

23 Deg

15.24

19.98

15.24

15.76

15.24

17.58

120 Deg

27.17

33.7

27.17

28.04

27.17

31.27

150 Deg

30.67

35.04

30.67

31.63

30.67

35.26


Level

15%

30%

Difference (ft)

Difference (ft)

Difference (ft)

Difference (ft)

Difference (ft)

Difference (ft)

23 Deg

0

0.14

0

0

0

0

120 Deg

-0.13

-0.76

-0.13

-0.13

-0.13

-0.14

150 Deg

-0.17

-0.74

-0.17

-0.17

-0.17

-0.19

2-37




Level

15%

30%

Initial Sag (ft)

Final Sag (ft)

Initial Sag (ft)

Final Sag (ft)

Initial Sag (ft)

Final Sag(ft)

23 Deg

34.34

41.10

34.34

35.47

34.34

39.55

120 Deg

49.79

62.49

49.79

51.31

49.79

57.20

150 Deg

54.26

64.30

54.26

55.88

54.26

62.28


Level

15%

30%

Initial Sag (ft)

Final Sag (ft)

Initial Sag (ft)

Final Sag (ft)

Initial Sag (ft)

Final Sag(ft)

23 Deg

34.34

41.27

34.34

35.47

34.34

39.55

120 Deg

49.69

61.51

49.69

51.21

49.69

57.08

150 Deg

54.13

63.26

54.13

55.73

54.13

62.12


Level

15%

30%

Difference (ft)

Difference (ft)

Difference (ft)

Difference (ft)

Difference (ft)

Difference (ft)

0

0.17

0

0

0

0

120 Deg

-0.10

-0.98

-0.10

-0.10

-0.10

-0.12

150 Deg

-0.13

-1.04

-0.13

-0.15

-0.13

-0.16

23 Deg

Table 2.4-8 ACSR Mallard, Span Length = 500 ft Alcoa Fujikura Sag 10 Software with Alcoa Data Conductor Temperature

Level

15%

30%

Initial Sag (ft)

Final Sag (ft)

Initial Sag (ft)

Final Sag (ft)

Initial Sag (ft)

Final Sag(ft)

23 Deg

3.02

4.27

3.02

3.12

3.02

3.48

120 Deg

6.21

7.43

6.21

6.42

6.21

7.16

150 Deg

7.77

8.48

7.77

8.03

7.77

8.95


23 Deg

Level

15%

30%

Initial Sag (ft)

Final Sag (ft)

Initial Sag (ft)

Final Sag (ft)

Initial Sag (ft)

Final Sag(ft)

3.02

5.45

3.02

3.12

3.02

3.48

120 Deg

7.63

8.49

7.63

7.89

7.63

8.80

150 Deg

8.67

9.57

8.67

8.96

8.67

10.00


15%

30%

Difference (ft)

Difference (ft)

Difference (ft)

Difference (ft)

Difference (ft)

0

1.18

0

0

0

0

120 Deg

1.42

1.06

1.42

1.47

1.42

1.64

150 Deg

0.90

1.09

0.90

0.93

0.90

1.05

23 Deg

2-38

Level Difference (ft)



Table 2.4-9 ACSR Mallard, Span Length =1000 ft Alcoa Fujikura Sag 10 Software with Alcoa Data Conductor Temperature

Level

15%

30%

Initial Sag (ft)

Final Sag (ft)

Initial Sag (ft)

Final Sag (ft)

Initial Sag (ft)

Final Sag(ft)

23 Deg

12.08

15.82

12.08

12.50

12.08

13.94

120 Deg

19.54

22.59

19.54

20.20

19.54

22.52

150 Deg

22.11

24.33

22.11

22.85

22.11

25.48


Level

15%

30%

Initial Sag (ft)

Final Sag (ft)

Initial Sag (ft)

Final Sag (ft)

Initial Sag (ft)

Final Sag(ft)

23 Deg

12.08

18.58

12.08

12.50

12.08

13.94

120 Deg

21.99

24.46

21.99

22.72

21.99

25.34

150 Deg

24.51

26.20

24.51

25.31

24.51

28.22


Level

15%

30%

Difference (ft)

Difference (ft)

Difference (ft)

Difference (ft)

Difference (ft)

Difference (ft)

23 Deg

0

2.76

0

0

0

0

120 Deg

2.45

1.87

2.45

2.52

2.45

2.82

150 Deg

2.40

1.87

2.40

2.46

2.40

2.74

Table 2.4-10 ACSR Mallard, Span Length = 1500 ft Alcoa Fujikura Sag 10 Software with Alcoa Data Conductor Temperature


15% Final Sag (ft)

Initial Sag (ft)

30% Final Sag (ft)

Initial Sag (ft)

Final Sag(ft)

23 Deg

27.21

33.36

27.21

28.13

27.21

31.37

120 Deg

38.20

43.22

38.20

39.45

38.20

43.98

150 Deg

41.62

45.51

41.62

42.95

41.62

47.89


Level

15%

30%

Initial Sag (ft)

Final Sag (ft)

Initial Sag (ft)

Final Sag (ft)

Initial Sag (ft)

Final Sag(ft)

23 Deg

27.21

37.38

27.21

28.13

27.21

31.37

120 Deg

40.74

45.76

40.74

42.05

40.74

46.89

150 Deg

45.07

48.03

45.07

46.48

45.07

51.82


Level

15%

30%

Difference (ft)

Difference (ft)

Difference (ft)

Difference (ft)

Difference (ft)

Difference (ft)

23 Deg

0

4.02

0

0

0

0

120 Deg

2.54

2.54

2.54

2.60

2.54

2.91

150 Deg

3.45

2.52

3.45

3.53

3.45

3.93

2-39



2.4.10 Effects of Wind Speed on Thermal Ratings

High-temperature operations are greatly affected by local wind conditions. This is discussed in Section 2.3 for its effect on clearances. Below, its effect on conductor strength is the focus. The following will demonstrate the effect of wind on the performance of the conductor. For the comparison, Power Technologies’ Ratekit was used. Ratekit is a software tool capable of evaluating the effects of wind speed and operating temperature independently. In the discussion, all conductor conditions are assumed steady state. Also, the angle of the wind relative to the conductor is 90°, the span is at sea level, and the time of year is summer. The coefficient of emissivity is 0.50, the coefficient of solar absorptivity is 0.50, the conductor resistance at 25ºC is 0.1200 ohms/mile (0.075 ohms/km), and the conductor resistance at 75ºC is 0.1442 ohms/mile (0.090 ohms/m). Atmospheric conditions are clear, and the orientation of the conductor relative to the north is 0°. The ambient temperature is 25°C , the ruling span is 1000 ft (305 m), and the conductors used in the comparisons are ACSR Drake and AAC Arbutus. The operating temperatures are 120°C and 150°C , and the wind speeds used are 0 ft/sec, 2 ft/sec (0.61 m/sec), and 4 ft/sec (1.2 m/sec). Table 2.4-11 shows the remaining strength Table 2.4-11 ACSR Drake Current (A)

Wind Speed (ft/sec)

Temperature (°C)

Remaining Strength (%)a

1180

0

150

2

110

4 1000

Initial Sag (ft)

Final Sag (ft)

98.64

36.1

39.6

100

32.3

36.1

85.7

100

29.8

33.8

0

120

100

33.3

36.9

2

85.8

100

29.8

33.8

4

68.5

100

28.0

32.1

a. The remaining strength is after 100-hours of high operating temperatures. Table 2.4-12 AAC Arbutus Temperature (°C)

Remaining Strength (%)a

0

150

2

108.5

4

Current (A)

Wind Speed (ft/sec)

1130

960

Initial Sag (ft)

Final Sag (ft)

70.12

47.4

49.0

92.11

43.5

45.2

84.6

100

41.2

43.0

0

120

85.89

44.6

46.3

2

84.9

100

41.2

43.0

4

68.1

100

39.5

41.3

a. The remaining strength is calculated when the conductor is exposed to the high temperature for 100 hours.

2-40

and sags for the ACSR Drake conductor, and Table 2.412 summarizes the results obtained for the AAC Arbutus. At 1180 A and 0 ft/sec wind, the operating temperature of the ACSR Drake conductor is 150ºC. If subjected to this high operating temperature for 100 hours, the remaining strength of the ACSR Drake conductor decreases by 1.4% to 98.64% of the rated tensile strength. If the weather conditions are favorable and the wind speed is 2 ft/sec (0.61 m/sec), the operating temperature of the ACSR Drake conductor is 110ºC, and the tensile strength of the conductor remains unaffected. If the wind speed is 4 ft/sec (1.22 m/sec), the temperature of the ACSR Drake conductor with 1180 A of current is nearly 86ºC, and the strength of the conductor remains unaffected. Similarly, the sag (final) of the ACSR conductor at 1180 A, and 0 ft/sec wind is 39.6 ft (12.1 m), while the sag of the ACSR Drake decreases by nearly 3.5 ft (1.1 m) if the wind speed increases from 0 ft/sec to 2 ft/sec. If the wind speed increases to 4 ft/sec (1.2 m/sec), the sag of the ACSR Drake conductor is 33.8 ft/sec (10.3 m/sec), nearly 6 ft (1.8 m) less than in the case where the wind is 0 ft/sec. If the ACSR Drake carries 1000 A and the wind speed is 0 ft/sec, the operating temperature of the conductor is 120ºC, resulting in no loss of tensile strength if operated for 100 hours. If the wind speed increases to 2 ft/sec (0.61 m/sec), the operating temperature decreases 86ºC and the sag decreases by approximately 2 ft (0.61 m). If the wind speed increases to 4 ft (1.2 m), the temperature decreases to 70ºC and the sag decreases an additional 2 ft (0.61 m). The temperature of an AAC Arbutus conductor carrying a current of 1130 A at a wind speed of 0 ft/sec is 150ºC. If the duration of this operation is 100 hours, the tensile strength of the conductor decreases by nearly 30% to 70.12% of the rated tensile strength. However, if the wind speed is 2 ft/sec (0.61 m/sec), the operating temperature of the AAC Arbutus conductor is 108ºC, and the operation at this condition for a period of 100 hours reduces the tensile strength of the conductor by only 9% instead of 30% at a wind speed of 0 ft/sec. The remaining strength at these conditions is 92.1% of the rated tensile strength, an acceptable value. At a wind speed of 4 ft/sec (1.2 m/sec), an AAC Arbutus conductor carrying a current of 1130 A will operate at a temperature of 85ºC, resulting in no loss of the tensile strength of the conductor. Also, a wind speed of 2 ft/sec (0.61 m/sec) reduces the sag by nearly 4 ft (1.2 m) compared to the sag calculated in the no wind scenario, and the sag is reduced an additional 2 ft (0.61 m) if the wind speed increases to 4 ft/sec (1.2 m/sec).



AAC Arbutus carrying a current of 960 A at a wind speed of 0 ft/sec operates at a temperature of 120ºC, resulting in a loss of 14% of the tensile strength if operated continuously for a period of 100 hours. The remaining tensile strength is reduced to 86% of the rated tensile strength of the conductor. If the wind speed increases to 2 ft/sec (0.61 m/sec), the sag of the conductor decreases by 3 ft (0.9 m), while an increase in the wind speed will decrease the sag by nearly 5 ft (1.5 m) when compared to the no wind case. 2.4.11 Thermal Elongation

Thermal elongation is a metallurgical phenomenon where the material increases in length in proportion to an increase in temperature. The rate of linear thermal expansion for the composite ACSR conductor is less than that of conductors that are made entirely of aluminum because the steel strands in the ACSR elongate at approximately half the rate of aluminum. The theoretical composite coefficient of linear thermal expansion (CTE) of a nonhomogenous conductor, such as the ACSR Drake may be found from the following equations: ⎛ E AL ⎞⎛ AAL ⎟⎜ ⎝ E AS ⎠⎝ ATOTAL

∂ AS = ∂ AL ⎜

⎞ ⎛ EST ⎞ ⎛ AST ⎞ ⎟ + ∂ ST ⎜ ⎟⎜ ⎟ ⎠ ⎝ E AS ⎠ ⎝ ATOTAL ⎠

⎛ 10 x106 ⎞ aAS = 12.8x10 −6 ⎜ 6 ⎟ ⎝ 12.8x10 ⎠ ⎛ 30x106 ⎞ +6.4 x10 −6 ⎜ 6 ⎟ ⎝ 12.8x10 ⎠ = 10.7 x10 −6 / °F

⎛ 0.6247 ⎞ ⎜ 0.7264 ⎟ ⎝ ⎠ ⎛ 0.1017 ⎞ ⎜ 0.7264 ⎟ ⎝ ⎠

A comparison of three different ACSR conductors of varying aluminum-to-steel ratios is used to demonstrate the effect of the steel reinforcing on the composite conductor behavior and coefficient of linear expansion. Table 2.4-13 summarizes calculated (ideal) and measured coefficients of linear thermal expansion. The measured coefficient of linear expansion of the ACSR Tern conductor (low steel-to-aluminum ratio) is 10.9% larger than the calculated value. The measured coefficient of linear expansion of the ACSR Drake conductor (medium steel-to-aluminum ratio) is approximately 6% higher than the calculated value and the measured coefficient of the ACSR Mallard (high steel-to-aluminum ratio) is only marginally larger than the calculated value. As the steel-to-aluminum ratio increases, the coefficient of linear expansion of the composite conductor approaches a limiting value equal to the coefficient of steel alone.

2.4-21

⎛ A ⎞ ⎛ A ⎞ E AS =E AL ⎜ AL ⎟ + EST ⎜ ST ⎟ ⎝ ATOTAL ⎠ ⎝ ATOTAL ⎠ 2.4-22 where EAL = modulus of elasticity of aluminum, psi. = modulus of elasticity of steel, psi. EST = modulus of elasticity of aluminum-steel EAS composite, psi. AAL = area of aluminum strands, square units. = area of steel strands, square units. AST ATOTAL = total cross sectional area, square units. αAL = aluminum coefficient of linear thermal expansion, per °F. αST = steel coefficient of thermal elongation, per °F. αAS = composite aluminum-steel coefficient of thermal elongation, per °F. Example 2.4-10: Using elastic moduli of 10 and 30 million psi (68,966 MPA and 206,897 Mpa) for aluminum and steel, find the elastic modulus for ACSR Drake is:

⎛ 0.6247 ⎞ 6 ⎛ 0.1017 ⎞ E AS = 10 x106 ⎜ ⎟ + 30 x10 ⎜ 0.7264 ⎟ ⎝ 0.7264 ⎠ ⎝ ⎠ 6 10 = 12.8x10 psi (8.83 x 10 Pa)

(

)

(

)

Note that the results of the EPRI High Temperature Conductor Project identifies the conductor’s knee point, and that the coefficient of linear expansion does not typically address the effect of the knee point on the sag and tension calculation. A typical set of test data is shown in Figure 2.4-8. The knee point is shown at approximately 120ºC. However, to accurately predict sags and tensions at high temperature, the effects of the knee point need to be considered and is discussed in more detail. The conditions under which calculations using a simple composite modulus and coefficient of linear thermal expansion fail may be illustrated by considering the tension distribution between steel and aluminum under normal and high temperature conditions. The preceding equations for composite modulus and CTE are derived based on the assumption that the aluminum and steel Table 2.4-13 Coefficient of Thermal Elongation for ACSR Conductors Measured Calculated ACSR Coefficient of Coefficient of Conductor (below 212°F, Thermal Elon- Thermal Elongation (CTE) gation (CTE) or 100°C) Tern 45/7

and the coefficient of linear thermal expansion is:

Drake 26/7 Mallard 30/19

Percent Difference

11.7 x 10-6

13.0 x 10-6

10.9

10-6

11.4 x 10-6

6.09

10.2 x 10-6

10.1 x 10-6

0.64

10.7 x

2-41



strands are of the same length. Based on this assumption, the total conductor tension (HAS) is equal to the sum of the component tensions, and the elongation of the steel and aluminum is equal: H AS = H AL + H ST HST H AL = AST ⋅ EST AAL ⋅ E AL

Figure 2.4-8 is 12.84 x 10-6 /ºC, while the corresponding value in Figure 2.4-9 is 13.74 x 10-6 /ºC, a difference of less than 7%. 2.4.12 Creep Elongation

2.4-23

2.4-24

For example, an ACSR Drake conductor installed in a 600 ft (183 m) span at an initial tension of 9450 lbs (42,188 N) carries 3124 lbs (13,946 N) of the tension in the steel core with the remainder of the tension being carried by the aluminum strands. Therefore, the tension carried by the steel is roughly 33% of the total tension. If the ACSR Drake conductor is heated to a temperature of 100oC, the sag of the conductor increases, and the total tension decreases to 4780 lbs (21,339 N), but the tension carried by the steel core increases from 3124 lbs (13,946 N) to 3305 lbs (14,754 N), or nearly 70% of the total tension. As the operating temperature of the conductor increases further, the tension in the aluminum eventually decreases to zero while the tension carried by the steel increases further. At some temperature, commonly referred to as the knee point temperature, the linear expansion of the conductor continues, but the stresses in the aluminum strands change from tension to compression (as shown in Figures 2.4-8 and 2.4-9). The knee point temperature of an ACSR conductor is directly proportional to the steel-to-aluminum ratio and is lower for ACSR conductors with high ratios and higher for conductors with low steel to aluminum ratios.

Once a conductor has been installed to an initial tension, it can elongate further. Such elongation results from three phenomena—permanent elongation due to high-tension levels resulting from ice and wind loads, creep elongation under everyday tension levels, and creep elongation due to thermal overloads. The creep resulting from thermal loading is discussed below. High-Temperature Creep Elongation The definition of “normal” creep is the accumulative nonelastic elongation of a conductor under low tension, over an extended period of time at modest operating temperatures. Normal operating temperatures are generally agreed upon as temperatures below 75°C. In any

Figure 2.4-8 ACSR Drake (26/7) composite thermal elongation, (30% of RBS Pre-Stressing, 10% of RBS Applied Tension, Manufacturer 2).

Conductors made by different manufacturers exhibit different knee-point temperatures because of differences in the manufacturing practices, processes, and machinery. For example, Figure 2.4-8 indicates that the ACSR Drake has a knee point at about 120ºC, while the data in Figure 2.4-8 suggests that the ACSR Drake has a knee point of only 70ºC. Disregarding experimental differences, built-in stresses, which are the result of manufacturing methods and tools, are the primary cause for this difference. In Figure 2.4-8, the coefficient of thermal expansion is 17.38 x 10-6 /ºC prior to the knee point, and the corresponding value in Figure 2.4-9 is 17.53 x 10-6 /°C, a difference of less than 1%. While the corresponding coefficient beyond the knee point is also fairly consistent, the temperature at which the knee point has been observed differs by nearly 50ºC or nearly 70%. The coefficient of thermal expansion beyond the knee point in

2-42

Figure 2.4-9 ACSR Drake (26/7) composite thermal elongation, (30% of RTS Pre-Stressing, 10% of RTS Applied Tension, Manufacturer 1).


case, a conductor under tension experiences a nonelastic elongation over a period of time. Time is usually measured in years. The magnitude and rate of creep are a function of the conductor's composition, stranding, line tension, and operating temperature. Conductors exhibit creep under everyday tension levels even if the tension level never exceeds normal operating conditions. Creep can be determined by long-term laboratory creep tests, and the results of the tests are used to generate charts that document the relationship of creep versus time. On the stress-strain graphs of conductors, creep curves are often shown for 6-month, 1-year, and 10-year time periods. Figure 2.4-10 shows a typical creep curve (experimental results) for an ACSR Drake conductor at room temperature. Generally, the creep elongation in aluminum conductors is quite predictable, it is a function of time and temperature, and the relationship is exponential. Thus, knowing the initial conditions of the conductor, the permanent elongation due to creep at everyday tension can be found for any period of time after the initial installation. Note that the creep elongation of copper and steel strands is minimal, and that the effects can essentially be ignored. High-temperature creep occurs when a conductor is operated for extended periods of time at operating temperatures in excess of approximately 75°C. Creep constitutes an irreversible, nonelastic elongation occurring in response to the molecular realignment in the conductor’s base material. Figure 2.4-10 shows the effects of creep on the conductor strain at an operating temperature of 120°C. Because aluminum exhibits a significantly higher rate of creep elongation than steel, the sag and tension behavior of all-aluminum type conductors such as AAC, AAAC, and ACAR is much more susceptible to high-temperature creep. Conversely, copper and steel wire strands supported aluminum conductors (Cu, ACSR, and AACSR) exhibit lower rates of creep, and the sag and tension behavior of these conductors is less affected by the high-temperature operation. Aluminum Conductor Steel Supported (ACSS) conductor, a conductor constructed using fully annealed aluminum strands and steel strands for the strength member, exhibits negligible creep rates since all of the tension is carried by the steel strength member, which is essentially not affected by creep. Creep, and the associated rate of creep, are directly proportional to the type of conductor, the steel-to-aluminum stranding ratio, the material characteristics of the conductor, and the tension and operating temperature. For example, using strands that are drawn from continuous-cast rod instead of hot-rolled rod reduces the creep


elongation and the associated long-term sag and tension behavior of the conductor. Other important parameters required in the determination of the rate of creep and the cumulative effect include the conductor stress or strain, the operating temperature, the elapsed time, and for ACAR and ACSR type conductors, the ratio of the constitutive components. Figures 2.4-10 and 2.4-11 show experimentally derived creep elongation results for ACSR Drake at room temperature and at 120°C. In both experiments, the majority of the creep elongation occurred during the initial 100 hours, a settling phase, so to speak. Note that at ambient room temperature conditions (23°C), the final creep elongation after 1000-hours was 0.01%, while the final creep elongation measured at the increased operating temperature was 0.03%. Thus, an ACSR conductor operated at a high temperature will reach its “final” sag

Figure 2.4-10 ACSR Drake composite creep at 23°C, Manufacturer 1.

Figure 2.4-11 ACSR Drake composite creep at 120°C, Manufacturer 1.

2-43



approximately two to three times faster than a conductor operated at temperatures of 75°C or below. Creep Predictor Equations Harvey (Harvey 1969) developed mathematical models and associated equations that can be used to estimate the magnitude of creep elongation. The models and equations were empirically derived, and are able to predict the creep elongation of a conductor at room temperature, as well as at an elevated temperature. The required definitions, constants, and formulas are listed (see Tables 4-14 and 4-15), along with an example.

Definition of Terms: εc = Primary creep strain (units/unit) ε = Strain - increase in length/original (units/unit) ΣεT = Increase in conductor strain due to elevated temperature operations (units/unit) σ = Stress - tension/area (N/mm2, lbs/in2) α = Coefficient of thermal expansion (units/unit/C) t = Elapsed time (hours) T = Conductor temperature (C) ΔT = Temperature change value (C) AEC = Area of aluminum strands (sq. mm., sq. in.) AST = Area of steel strands (sq. mm., sq. in.) AT = Total conductor area (sq. mm., sq. in.) %RS = Tension as a percentage of the rated strength (%) Table 2.4-14 Formula Constants (Metric Units) K1

AAC:ε c = K σ 1.3 t 0.16 AAAC:ε c = G σ

1.3

t

2.4-25

0.16

2.4-26

ACAR:ε c = (0.19 + 1.36 A EC / A T ) (T

1.4

σ

1.3

t

AAC:ε c = K σ 1.3 t 0.16 AAAC:ε c = G σ

1.3

t

2.4-28

0.16

2.4-29

ACAR:ε c = (0.0003 + 0.0021 A EC / A T ) (T

1.4

σ 1.3 t 0.16 ) 2.4-30

All-Aluminum Conductors (Elevated Temperature, Metric) AAC:ε c = M T1.4 σ 1.3 t

0.16

2.4-31

AAAC: ε c = 0.0077 T

σ

1.4

1.3

t

0.16

2.4-32

ACAR: ε c = (0.0019 +0.012 A EC / A T ) (T

1.4

σ

61 Strands

1.36

1.29

1.23

1.16

AAAC: ε c = 0.000012 T ACAR: ε c =

0.77

0.77

0.71

0.0142

0.0136

0.0129

M2

0.0090

0.0090

0.0084

0.0077

G

0.71

0.65

0.77

0.61

Note: K1, K3, M1, and M3 are for wire bar rolled rod and K2, K4, M2, and M4 are for continuous cast (rolled) rod. Table 2.4-15 Formula Constants (English Units)

1.4

19 Strands

37 Strands

61 Strands

K3

0.0021

0.0020

0.0019

0.0018

K4

0.0013

0.0012

0.0012

0.0011

M3

0.000023

0.000022

0.000021

0.000020

M4

0.000014

0.000014

0.000013

0.000012

G

0.0011

0.0010

0.0012

0.00094

Note: K1, K3, M1, and M3 are for wire bar rolled rod and K2, K4, M2, and M4 are for continuous cast (rolled) rod.

2.4-34

σ

1.3

t

0.16

2.4-35

(0.000003 +0.000019 A EC / A T ) (T1.4 σ 1.3 t

0.16

2.4-36

Steel Reinforced Conductors (Room Temperature, English) Aluminum strands drawn from hot-rolled rod: ACSR: ε c = 2.4 (%RS)1.3 t

7 Strands

t 0.16 )

All-Aluminum Conductors (Elevated Temperature, English)

37 Strands

0.84

1.3

2.4-33

19 Strands

0.0148

)

All-Aluminum Conductors (Room Temperature, English)

7 Strands

M1

0.16

2.4-27

AAC: ε c = M T1.4 σ 1.3 t 0.16

K2

2-44

Predictor Equations: All-Aluminum Conductors (Room Temperature, Metric)

0.16

2.4-37

Aluminum strands drawn from continuous cast rod: ACSR: ε c = 1.1 (%RS)1.3 t

0.16

2.4-38

Steel Reinforced Conductors (Elevated Temperature, English) Only for conductors with less than 7.5% steel by area:

)


ACSR: ε c = 2.4 (%RS) T t


Using Equation 2.4-37, the ambient temperature creep is:

0.16

2.4-39

Elevated creep in conductors with steel to aluminum ratios of greater than 7.5% can be ignored.

Temperature Change Value The equivalent temperature change value is a calculated temperature that approximates the net increase in the micro-strain due to elevated temperature creep above and beyond general creep. ∑ ε T = α ΔT or ΔT = ∑ ε T /α ∑ ε T = ε @high - ε @ambient

2.4-40 2.4-41

ε@ambient is the strain in the conductor due to room temperature creep only, and ε@high is the strain in the conductor attributed to the elevated temperature creep.

Method for Using the Predictor Equations The process of calculating the predicted elevated temperature creep is straightforward and can be accomplished using sags and tensions derived from graphical charts, long-hand calculations, or computer software predictions. The following procedure must be followed: 1. Use the standard graphical charting, long-hand calculations, or computer sag and tension methods to predict the sags and tensions without elevated creep for the given situation. 2. Compute the creep of the conductor at ambient temperature. 3. Compute the creep of the conductor at the first elevated temperature. 4. Compute the number of hours that would be required to accumulate an equivalent amount of conductor creep at the second elevated temperature. 5. Repeat steps 3 and 4 for each elevated temperature. 6. Calculate the value of the equivalent temperature change by subtracting the predicted creep elongation at the everyday temperature from the creep elongation at the elevated temperature. 7. Calculate the final sag of the conductor following elevated temperature creep by adding this temperature change value to the temperatures used in the standard sag and tension calculation.

ε c = 2.4 (%RS)1.3 t 0.16 where %RS is the Remaining Strength, and t is the time (hours) a)

Conductor creep produced for 20 hours at 60°F (16°C)

ε c = 2.4 x 0.25 1.3 x 20 0.16 ε c = 0.64 micro-in/in (1 in. = 2.54 cm) 20 hours at 60°F produces a creep of 0.64 micro-in./in. or the equivalent of operating the conductor for 0 hours at 212°F. Using Equation 2.4-39, the elevated temperature creep is:

ε c = 2.4 (%RS) T t 0.16 b) Conductor creep produced for 7500 hours at 167°F (75 C)

ε c = 2.4 x 0.25 x 167 x (7500) 0.16 ε c = 417.7 micro-in./in. 7500 hours at 167°F produces a creep of 417.7 microin./in. or the equivalent of operating the conductor for 1690 hours at 212°F (100°C).

c) Conductor creep produced for 1240 hours at 212°F (100 C)

ε c = 2.4 x 0.25 x 212 x (1240) 0.16 ε c = 397.6 micro-in./in. To calculate the total elongation due to creep, the sum of the equivalent times (hours) at 212°F (100 ° C ) is determined. In this example, the sum is:

0 + 1690 + 1240 = 2930 hours at 212°F (100°C).

ε c = 2.4 (%RS) T t 0.16 ε c = 2.4 x.25 x 212 x 2930 0.16 ε c = 456 micro-in./in. The temperature change value is calculated using Equation 2.4-40. ΔT = ∑ ε T /α

where Example 2.4-11 : A 795 kcmil (405 mm 2 )ACSR Tern conductor is subjected to 20 hours at 60°F (16°C), 7500 hours at 167°F (75 ° C ) and 1240 hours at 212°F (100°C). What is the sag and tension if creep is a factor? Use a ruling span equal to 1000 ft (305 m). Use Alcoa’s Sag10 program to directly calculate the result and compare it to the results of the Creep Predictor Equations. Assume Alcoa Heavy Loading applies.

∑ ε T = ε @high - ε @ambient ΔT = (456 − 0.64) /(11.8 × 10 −6 ) = 38.75°F(3.8°C)

The final sag following elevated temperature creep is determined by adding this temperature change value to 2-45



the temperatures used in the standard sag and tension software calculations. In this example, 60 ° F (16 ° C) becomes 98.75°F (37 ° C), 90°F (32 ° C) becomes 128.75 ° F (54 ° C), 120 ° F (49 ° C) becomes 158.75 ° F (70°C), etc. Table 2.4-16 provides a summary comparison of the calculated sags including the effects of creep at each of the reference temperatures. The differences in the sags predicted by each method can be mostly attributed to the empirical nature of the predictor equations and the creep data and numerical analysis methods deployed by the Alcoa software. Regardless, the use of the predictor equations has been illustrated to convey the process required whenever dealing with the effects of elevated temperature creep for conductors. While the predicted sags vary depending on which analysis method is used, the critical issue is the significant difference in the predicted sag that is directly attributed to the high-temperature operation of the conductor. As discussed, the results obtained by using the hand calculations are in close agreement to the values obtained using the software, and the percentage difference ranged from only 2.2 to 13%. Note that the correlation improves as the temperature is increased, with a difference of only 2.2% when the operating temperature is 212°F (100°C). 2.4.13 Connectors at High Temperature

Splices and compression fittings, which join sections of conductor and other components, must provide both structural and electrical integrity. Therefore, the integrity of these components is critical to the operation of a power line, particularly as the temperature of operation increases. Connector failures can become very costly to utilities, and the cost of failure can be attributed to one of four categories. First, there is the cost associated with potential damages and injuries to the public. Second, there is a cost for loss of revenue from rerouting power. Third is the cost of repairs, which depends heavily on the labor cost for using line crews and equipment, and

Table 2.4-16 Comparison of the Predictor Equations and Alcoa’s Software Results Temperature (°F)

2-46

Predictor Equations (ft)

Alcoa’s Sag 10 Percentage Software (ft) Difference (%)

60

27.5

31.6

90

29.5

33.4

13.0 11.8

120

31.4

35.2

10.8

167

34.2

36.6

6.3

212

36.8

37.6

2.2

fourth, there is the cost associated with the loss of competitive advantage in the marketplace. Transmission line operators use two types of tension connectors: limited-tension connectors and full-tension connectors. Limited-tension connectors are primarily designed to join conductors that are under little or no mechanical tension. These connectors are typically used to splice the ends of two conductors together in a lowtension application, tap a second conductor from a continuous run conductor, or terminate the end of a conductor in a low-tension application. Typical examples of limited-tension connectors are bolted connectors, compression connectors, formed-wire connectors, wedgetype connectors, and implosive connectors. Because these connectors exhibit a limited tensile strength, the part of the connector directly in contact with the current-carrying conductor is generally smaller in area than that of its full-tension counterpart. Full-tension connectors are designed to provide mechanical strength up to, or in excess, of the rated tensile strength of the conductor at all operating temperatures and also to provide a low-resistance conductive path for the current carried by the conductor. Thus, splice connectors are used to join the ends of the conductors in spans between supports, and dead-end (also referred to as terminations) connectors are used to join conductors to the attachment hardware at the end of each tension segment, or special heavy angle, or termination structures. Generally, full-tension connections can be achieved using one- and two-piece compression connectors, formed-wire splices, implosive connectors, and wedgetype connectors, but the compression-type connector appears to be the predominant method of creating a full-tension connection on high-voltage conductors. Although the term “full tension” is commonly used to specify the tensile strength of connectors to match the tensile strength of the conductor, the connectors are typically designed to exhibit a tensile strength of at least 95% of the conductor's rated breaking strength. The main consideration for connectors when evaluating elevated conductor temperature operations is its impact on the connector’s short- and long-term performance and the effect on the service life. Certainly, the hightemperature operation of a circuit greatly increases a connector’s electrical, mechanical, and thermal stresses. If operated unchecked, these stress increases are likely to lead to the premature deterioration of the integrity of the connector and the eventual failure of this critical component. Since the prediction of such a failure is


difficult, and the consequences are great, the successful high-temperature operation of a circuit requires a careful evaluation of all of the issues involved. Connector Breakdown Process A connector facilitates the transfer of current through numerous contact points between the connector and the conductor. High current densities and high operating temperatures tend to encourage the buildup of resistive compounds at these contact points, effectively reducing the size of the contact area, or in some cases completely restricting the current flow. Generally, the resulting increase in the temperature of the connector will then allow the formation of new contact points within the component at locations where the buildup of resistive compounds is small. The continuous cycle of closing and reopening of contact points within the connector can be thought of as an “aging” process in which the connector will continue to perform well as long as there are locations where contact points can be easily established.

Once the connector has aged sufficiently so that all locati ons for easi ly establi shin g contac t poi nts are exhausted, the connector is forced to maintain contact points at locations at which resistive compounds are present in order to reach the parent metal. This increases the overall resistance of the connector, its operating temperature, and current density within the remaining contact points. At this time, the higher current densities and operating temperatures cause further buildup of resistive compounds, which in turn further increases the current density and operating temperatures, leading to the eventual thermal failure of the connector. The thermal failure will eventually lead to the electrical failure of the connector, and eventually results in the mechanical failure of the component. Figure 2.4-12 shows typical compression deadend connectors as used on transmission lines, and Figure 2.4-13 shows an infrared image of the connector indicating an impeding failure as indicated by the significant temperature differences at the surface of the component.

Figure 2.4-12 Visual image of problem deadend.


Elevated temperature operations of conductors will increase the current density and operating temperature of associated connectors. This increase in the associated thermal, electrical, and mechanical stresses will accelerate their aging process, effectively reducing service life. The amount of accelerated aging connectors experience is directly related to the magnitude and frequency of the elevated current and operating temperature operation experienced by the component. Unfortunately, the relationship between the aging of the connector and the loads served is nonlinear, and little success has been achieved in directly quantifying that relationship. EPRI is currently conducting research to assess the performance of transmission-line components when subjected to increases in operating temperatures. Preliminary results indicate that most conductor hardware appears to operate more efficiently when compared to the conductors as long as the components are installed correctly. Results show that failures occur mostly as a result of improper installation, and that many of these issues can be addressed effectively using an appropriate quality assurance strategy. Most well-designed connectors (when properly installed) are capable of operating at high current densities and high conductor temperatures while providing acceptable performance and service life. The current cycle test, an industry standard, is commonly used to evaluate these connector designs. Current cycling the connector results in the thermal expansion and contraction of the electrical contact interface and tends to break down the contact points between the connector and the conductor. Although this standard test identifies procedures and qualification criteria for connectors used under normal operating conditions, the application of this test does have its limitations. Figure 2.4-14 shows typical test results obtained from a standard heat cycling test.

Figure 2.4-13 IR image of problem deadend.

2-47



Figure 2.4-14 Mechanical load data of a “new” Hawk conductor.

Connectors should be considered as approaching failure if the operating temperature approaches or exceeds the operating temperature of the conductor. Experiments show that the operating temperature of an adequately designed and correctly installed compression connector should be approximately 10 to 30% lower than the operating temperature of the conductor. The reduced operating temperature can be directly attributed to the significantly larger cross section of the compression connector relative to the cross-sectional area of the conductor, the increase in the surface area of the compression fitting relative to the surface area of a comparable unit length of conductor, and the increase in the convection to occur at any measurable wind speed. High-Temperature Effects on Connector Joint Compound Most aluminum connectors, especially compression type, employ a viscous compound in the interface between the connector and underlying conductor. The primary purpose of the joint compound is to provide a barrier that prevents moisture and other contaminants from leaching into the joint. The ingress of moisture and other contaminants is not desirable since this will lead to the internal corrosion of the connector, which is likely to affect not only the tensile strength of the steel strength member in the case of an ACSR conductor but

2-48

also deteriorate the connector’s ability to effectively transfer the current. The repeated high-temperature operation (connector temperatures above 200°F (95 ° C)) degrades the joint interface by causing the viscosity of the joint compound to decrease significantly, leading to the eventual outflow of the joint compound or the carbonization of the joint compound, leading to a reduction in the protection provided by the corrosion inhibitor. Thus, the later scenario leaves a shrunken and hardened residue that is no longer effective as a moisture barrier. The presence of moisture and contaminants in the joint accelerates the connector’s aging process and effectively shortens the connector’s service life. Figure 2.4-15 shows an infrared image of a compression splice on which the joint compound is leaking out of the fill hole located at the center of the component. New and Existing Connectors When designing overhead power lines for high-temperature operations or contemplating the refurbishment of existing facilities, a great deal of consideration should be given to the conductor temperatures at which the connectors were tested. Prudence dictates that connectors designed for high-temperature operation should be



high-temperature operation of a particular line can be shunted to reduce their electrical loading and to prolong their service life. Shunts provide an alternate path for the current flow, thereby reducing a connector’s current density and operating temperature. The reduction in the connector’s current density retards the aging process, and extends the long-term performance and service life. Similarly, shunting of marginal connectors can be used to extend the service life and to improve the performance of components.

Figure 2.4-15 Leakage of connector joint compound.

tested and qualified for temperatures well in excess of those expected in service. When evaluating existing connectors prior to the operation of a circuit at a higher operating temperature, it is recommended to evaluate the original performance specifications of the existing connectors. A review of the standards against which the connectors were designed and tested assists in evaluating whether these components are acceptable for operation at significantly increased operating temperatures. Operating electrical connectors at temperatures above those for which they were designed can be risky, and at the least, a standard current-cycle test should be performed to evaluate the performance of each connector. Mitigation of Effects of Connector High-Temperature Operations A cost-effective and frequently used method used to increase the operating life of connectors is by using reinforcing methods such as shunts. Typically, existing connectors that are suspected of being inadequate for the

Nondestructive Methods to Measure Connectors The degradation of a connector can be observed by increases in its resistance and temperature. The increased resistance is measured with devices such as an Ohmstik, developed by SensorLink Corp. The tool takes advantage of the increased resistance by measuring the ac voltage drop across the component that is caused by the current. Typically, resistance measurement devices such as the Ohmstick can operate at currents ranging from 2 to 1400 A and can measure resistances from 5 to 2500 micro-ohms. Figure 2.4-16 shows an infrared image of a defective conductor connection and a summary of the corresponding resistance measurements. 2.4.14 Conductor Hardware

Conductor hardware, as defined in this report, refers to noncurrent carrying devices attached directly to the conductor. Conductor hardware includes components such as suspension clamps (with or without armor rods), dampers, repair sleeves and splices, spacers and spacer dampers, shackles, pins, etc. Generally hardware is manufactured from cast or forged aluminum, but there are instances where metallic hardware has been used, and the issues associated with the use of metallic hardware are discussed.

Figure 2.4-16 Resistance measurement of connector.

2-49


Metallic Conductor Hardware Metallic conductor hardware for aluminum conductors is fabricated primarily from aluminum alloys, while hardware for copper conductors is mostly fabricated from copper alloys. One of the reasons for the strict selection and use of similar metals is the recognition of the differences in the galvanic properties of these materials. When metals of different galvanic properties are permitted to react in the presence of moisture, the resulting reaction quickly deteriorates the lower ranked material, resulting in significant corrosion to an assembly. Nevertheless, galvanized ferrous hardware and components have been used extensively in the past because of the inherent high strength-to-weight ratio and the fact that the galvanized steel component is relatively inert to both aluminum and copper in a mild climate and environment.

High-Temperature Effects of Ferrous Conductor Hardware Ferrous hardware that either partially or completely surrounds a current-carrying conductor is subject to hysteresis and eddy current losses caused by the magnetic flux associated with the current flow. These eddy current losses manifest themselves in the form of significant heat gains within the hardware, and hence significantly increased operating temperatures. Thus, excessive heating of the hardware or greatly increased operating temperatures within the ferrous hardware at levels above the acceptable level of the conductor is likely to cause the annealing of any aluminum components. The excessive heating and increased temperatures conveyed by the ferrous hardware can anneal the conductor or other aluminum components, thereby reducing the tensile strength and the expected service life. While the effect of the heating is typically localized and adjacent to the ferrous component, the effect on the conductor can be detrimental and sufficiently destructive to mandate the eventual replacement. Heat gain due to hysteresis and eddy current losses in ferrous hardware is a function of the magnitude of the current in the conductor and the hardware’s thermal conductivity. Convection and radiation heat losses from the ferrous hardware are primarily a function of the hardware’s surface area and surrounding ambient conditions. Hence, the operating temperature of ferrous hardware fluctuates in response to changes in the circuit’s load and the ambient conditions. Conductor hardware is deployed in numerous configurations to support and protect the conductor, and is available in many different sizes and shapes. Smaller versions of ferrous hardware have a relatively low ratio of mass to surface area and usually operate at temperatures well below that of the conductor, regardless of cur-

2-50


rent. Conversely, larger versions of ferrous hardware have a mass-to-surface-area ratio that can result in hardware temperatures greater than the conductor’s allowable annealing temperature at higher currents. Hardware large enough to produce localized conductor temperatures of concern are usually confined to suspension and strain clamps, but can occasionally be caused by any ferrous device surrounding the conductor as long as they have a large mass-to-surface-area ratio. Published literature, which permits the calculation of the local temperature increase in a conductor’s temperature as a function of the load, is limited. The mitigation of the effects of localized heating under ferrous hardware usually involves either limiting the current rating of a line, limiting the cumulative time a conductor can operate at the elevated rating, or replacing the hardware with nonferrous hardware. Experience shows that the number of conductor and hardware configurations are extensive, requiring each utility to develop customized solutions to address this problem. Nonferrous conductor hardware does not internally generate any heat in response to a conductor’s current. Generally, nonferrous hardware operates at temperatures well below the conductor’s operating temperature because of the increased surface area and the corresponding increase in the convective cooling provided by the wind, if any. Nonmetallic Conductor Hardware Nonmetallic conductor hardware is generally limited to elastomeric compounds, which serve as compressive “bushings” within a hardware assembly. Compression bushings are typically used in spacers, spacer-dampers, and armor grip suspension clamps to provide a resilient interface between the conductor and the hardware.

Publications concerning the effects of high-temperature operations on elastomeric hardware components are limited. During and after high-temperature excursions, the elastomeric components must retain their resilient and semiconductive properties for long-term survival. Loss of such properties can result in component deterioration and/or component failure. High-Temperature Tests on ACSS Conductor Hardware Reynolds Aluminum performed high-temperature current cycle tests of ACSS conductors and associated fittings. Tests were performed on a loop of 1033.5 kcmil (527 mm2), with a 45/7 Stranding, “Ortolan” SSAC conductor with various fittings installed. In all cases, the temperatures measured at the conductor hardware were well below the conductor operating temperature. At a 200oC conductor operating temperature, the measured


full-tension splice temperatures ranged from 120o to 130oC. The operating temperature of the partial-tension splices was observed to be significantly higher, ranging from 160o to 170oC. On the contrary, the operating temperature at the suspension clamp was 84oC, and the temperature measured at the first insulator pin was 37oC. Operating temperatures at the AGS unit were 102oC on the armor rods, 46oC on the clamp surface, and 106oC beneath the neoprene sleeve. High-Temperature Tests of ACSR Conductor Hardware Detroit Edison conducted tests of ACSR conductors and hardware to determine if high-voltage power line hardware could be safely operated at temperatures up to 200oC. Tests were conducted over a temperature range from 75oC to 200oC. Hardware tested included aluminum body bolt-type strain clamps, aluminum body suspension clamps, armor rods, parallel groove clamps, line dampers, and full-tension splices. Hardware was tested with 477 kcmil (243 mm2) ACSR Hawk, 795 kcmil (405 mm2) ACSR Drake, 954 kcmil (487 mm2) ACSR Cardinal, and 1431 kcmil (730 mm2) ACSR Bobolink conductors. The aluminum strain clamp temperature ranged from 35 to 61% of the conductor operating temperature for the four conductors tested, while the suspension clamp temperature ranged from 29 to 43% of the conductor temperature. On the contrary, armor rod temperatures were 68 to 80% higher than the conductor’s temperature. High-Temperature Tests on Polymer Insulators Test results on polymer insulators indicate that most insulators are well equipped to handle high operating temperature loads. An EPRI report (EPRI 2002) describes the results of a typical conductor suspension assembly using a polymer insulator. In the test, temperatures were measured on the conductor, suspension clamp, shackle, link, insulator pin, and polymer insulator, as well as the ambient temperature. The temperatures of the test components at the maximum conductor operating temperature of 292oC (not referenced to ambient temperature) ranged from 163oC at the suspension clamp, to 88oC at the shackle, to 43oC at the link, to 32oC at the insulator pin, to 28oC at the insulator. The ambient temperature at the time of the test was measured at 17oC.

Another set of tests on polymer insulators had similar results. In these tests, temperatures were measured at the insulator end fitting near the fiberglass rod end, near the suspension fitting end, on the suspension fitting conductor keeper, on the suspension fitting body near the conductor groove, and on the conductor itself. The testing included the mechanical loading of the suspension assembly and current cycling of the conductor to a max-


imum conductor core operating temperature of 250oC (not referenced to ambient temperature). Tests were conducted on high-voltage polymer suspension insulators of five different manufacturers. The measured insulator end fitting temperature, nearest the fiberglass rod, ranged from 47o to 61oC depending on the type of polymer insulator. The end fitting temperature nearest the conductor was slightly higher, ranging from 54o to 67oC. After the thermal testing, each insulator was tested mechanically to determine the residual strength. Results showed no measurable degradation of the mechanical performance of the five polymer insulators regardless of the manufacturer. A third set of tests reinforces the same conclusions for polymer suspension insulator assembly. In each test, thermocouples were used to measure the conductor temperature, the insulator end fitting temperature, and the ambient temperature. Sufficient current was applied to the conductor to generate a nominal operating temperature of 200oC. Tests generated end-fitting temperatures ranging from 38o to 46oC at ambient temperatures ranging from 19o to 27oC. 2.5

UPRATING WITHOUT RECONDUCTORING

2.5.1

Introduction

There are two overall strategies to uprating overhead transmission lines without reconductoring: using deterministic methods or probabilistic methods. With deterministic methods, line rating calculations are done using traditional tools, such as the EPRI DYNAMP program, and assumed ambient conditions. Physical alterations to the line can be made (such as retensioning the conductors or raising their support points) to increase the maximum allowed conductor temperatures, thereby increasing the ratings. Or, the assumed ambient conditions themselves can be changed (such as assuming a higher wind speed). With probabilistic methods, actual weather data is analyzed statistically to determine the most viable assumptions and the associated risks. 2.5.2

Deterministic Methods This subsection focuses on uprating methods that avoid reconductoring, involve minimal capital investment, and do not require field monitors. Typical increases in power flow resulting from these options range from 5% to 50%, depending on the original design conditions, the present rating assumptions, and the type of structure and conductor used in the existing line. These uprating choices are particularly effective for older lines, perhaps

2-51


designed under the old 120oF (49oC) clearance temperature. Since the transmission conductors are not to be replaced, the result will be operation of the line’s existing conductors at increased temperature levels. Consequently, the conductor, its hardware, and its connectors need to be carefully inspected prior to uprating. Any questionable elements need to be replaced. In addition to a physical inspection, the line uprating process must verify that adequate electrical clearances will be maintained after the uprating is complete. Typically, this verification should consist of three steps: 1. Measurement of “everyday” sag clearance and support point locations by use of conventional survey equipment, or airborne digital imaging equipment, with the line out of service or at relatively low electrical load. 2. Calculation of maximum sag (minimum ground clearances) under electrical load equal to the proposed new thermal rating. 3. Experimental verification of electrical clearances under a combination of rated load and worst-case weather conditions through the use of sag or tension monitors. Since the maximum allowable temperature is to be increased, these steps are necessary to be certain that the additional sag does not violate minimum electrical clearance requirements and that any increased annealing of the conductor’s aluminum or copper strands does not reduce the line’s loading safety factors to an unacceptable level. Evaluating Sag Clearance Under “Everyday” Conditions As discussed in Section 2.3, new lines are designed to meet certain minimum electrical clearances under all weather conditions at electrical loads less than or equal to their thermal rating. They are also designed to limit the maximum tension under maximum ice and wind loads to the structure design values. To do this, initial unloaded conductor sags are specified such that the final sags at high temperatures and the maximum tensions under ice and/or wind loading are within these limiting values. By adjusting the initial sags to these “stringing sags” at the time of construction, minimum clearance and maximum tension limits are maintained throughout the life of the line. The “final” sags include an allowance for permanent elongation due to creep elongation of aluminum and to plastic elongation due to ice and wind loads. In addition, because of uncertainties in these calculations, new lines are typically designed with clearance buffers of at least 3 ft (1 m).

2-52


With existing lines that have been in service for 10 years or more, the measured sag may be assumed equal to “final” conditions. That is, the conductor has experienced most of the permanent elongation allowed in the original design. Unless the line is retensioned, the error in estimating final sag at the maximum design temperature is limited to questions about thermal elongation at high temperature. Also, since the structures have been located and the support point elevations determined, the initial sag buffer requirement may be less than that required for a new line. Many different techniques are available to determine the electrical clearance under everyday loadings where the conductor temperature is quite close to air temperature. These techniques range from the use of survey crews at selected spans, to flying the span by airplane or helicopter with digital recording devices. The latter provides more data than required and costs more. The former provides less data than one might wish for and costs less. Particularly with digital recording from the air, the data can be loaded directly into line profiling and design programs like PLS-CADD™ and TL-CADD™. This allows a span-by-span verification of sag and a relatively straightforward calculation of conductor sag at higher temperatures. While the accuracy of these measurements is in the range of a few inches (several centimeters), the determination of the corresponding conductor temperature at the time of measurement is less accurate. Generally, the conductor temperature is determined by use of a heat balance equation such as IEEE738 or DYNAMP with the line electrical load and local weather data. If the electrical load of the conductor is less than 0.25 A/kcmil (0.5 A/mm 2 ), then the difference between calculated conductor temperature and actual should be less than 5oC. If the electrical load is higher, then the difference can also be higher, depending on how the calculation is done and how the weather data (see Section 2.3) is determined. Raising Conductor Support Points The thermal elongation of stranded conductors is essentially the same as that of its component strands. Therefore, for an all-aluminum or copper conductor, once the sag at “final” everyday conditions is established, the sag at high temperatures can be calculated with relatively small uncertainty.

For example, consider a line section of an all-aluminum, 37 strand (Arbutus) conductor having a ruling span of 600 ft (183 m) installed to meet the following constraints: maximum tension of 50%, 33% initial unloaded



at 15°F (9.4°), and 25% final unloaded at 15°F (-9.4 °C). An equally typical SAG10 program line design sag-tension run is in Table 2.5-1.

In existing lines having longer ruling span sections, there are fewer structures per mile (km) to modify but greater sag increases required to offset increased sag at higher operating temperatures, as shown in Figure 2.5-2.

As an example, consider that the line was originally designed for a maximum conductor temperature of 120°F (49 °C) and the line structures were placed such that the minimum ground clearances are met with the ruling span final sag of 15.5 ft (4.7 m).

Retensioning Existing Conductors Rather than replacing existing conductors with new, it may be possible to increase the everyday tension of existing lines in order to reduce sag at high temperature and therefore increase the line rating. For example, consider the following case where an existing line with Mallard ACSR is to be uprated.

To operate the existing line at 167°F (75 °C), the attachment points must be raised approximately 2.2 ft (0.67 m). To operate at 212°F (100 °C), the attachment points must be raised approximately 4.2 ft (1.28 m).

Table 2.5-2, taken from the SAG10 program, shows the sag and tension (total, aluminum, and steel component tensions) for initial and final conditions for 30/19, 795 kcmil (405 mm2) ACSR (Mallard) initially sagged so as

Given rating conditions of 2 ft/sec crosswind, sun, and an air temperature of 35oC, the rating of the original line is 345 A. By raising the attachment points by 2.2 and 4.2 ft (0.67 and 1.28 m), to allow operation to 75oC and 100oC, the line’s thermal rating is increased to 775 and 1010 A, respectively. Note the large increase in thermal rating corresponding to modest increase in attachment height. Many lines built prior to 1970 originally utilized 49oC as the maximum conductor temperature for clearance estimates. With wood pole H-frame structures, increasing attachment height in order to increase the line thermal rating may be particularly attractive. Crossarm attachment points can be raised, hardware replaced, and shield wires placed on metal pole top extensions at minimal cost. Figure 2.5-1 is a photograph of a wood pole structure where the conductor attachment height has been raised.

Figure 2.5-1 Photograph of a wood pole H-frame structure with raised crossarm and pole-top extensions for shield wires.

Table 2.5-1 Sag-tension Calculations for 37 AAC (Arbutus) ALUMINUM COMPANY OF AMERICAN SAG AND TENSION DATA Conductor Arbutus

795.0 kcmil

37 Strands AAC


Dia + 1.026 in.

Wt = 0.746 lb/°F

RTS = 13900 lb

Span + 600.0 ft

Creep is a Factor


Design Points

Final

Temp (°F)

Ice (in.)

Wind (psf)

K (lB/°F)

Weight (lb/°F)

Initial

Sag (ft)

Tension (lb)

Sag (ft)

Tension (lb) 6140

15.

.25

4.00

.20

1.451

12.02

5446.

10.65

32.

.25

.00

.00

1.143

12.00

4294.

10.06

5118

0.

.00

.00

.00

.746

8.77

3833.

6.63

5067.

15.

.00

.00

.00

.746

9.67

3475.a

7.27

4621.

30.

.00

.00

.00

.746

10.58

3179.

7.98

4212.

60.

.00

.00

.00

.746

12.34

2727.

9.54

3524.

90.

.00

.00

.00

.746

13.99

2406.

11.19

3006.

120.

.00

.00

.00

.746

15.54

2167.

12.82

2624.

167.

.00

.00

.00

.746

17.78

1897.

15.24

2210.

212.

.00

.00

.00

.746

19.73

1711.

17.37

1941.

257.

.00

.00

.00

.746

21.54

1570.

19.33

1746.

302.

.00

.00

.00

.746

23.22

1457.

21.15

1598.

a. Design condition. 2-53



result from pulling the conductor to a higher everyday tension (up to 25% rather than 15% of RBS at 60 ° F [16°C]) can be offset by the addition of dampers. From Table 2.5-2, it can be seen that increasing the tension from 15% to 25% RBS will reduce the high-temperature sags at temperatures of 75oC to 150oC by about 4 ft (1.2 m). Therefore, the maximum design temperature can be increased to 150 o C or more without violating clearance limits. At the original line’s maximum allowable conductor temperature of 75oC, with an air temperature of 40oC, full summer sun, and a wind blowing perpendicular to the conductor axis at 2 ft/sec, the thermal rating was 735 A. If the retensioned line is rated at 150oC with the same weather conditions, the new thermal rating is 1345 A (83% higher).

Figure 2.5-2 Change in sag for all aluminum conductor as a function of span length.

Limitations on Retensioning Existing Conductor There are several concerns about this method of thermal uprating:

not to exceed a final unloaded tension of 15% of Mallard’s Rated Breaking Strength at 60oF (15.5oC). NESC Medium Loading conditions and conductor temperatures up to 302oF (150oC) are included, but the original line is rated at 75 o C, at which temperature electrical clearance to ground is near the NESC minimum values.

1. The maximum tension exerted on strain structures during maximum wind and ice loading has increased from 7800 to 11,300 lbs. (34.8 kN to 50.4 kN). As a result, it is likely that these structures would need to be replaced. An alternative solution may be to limit the increase in everyday tension so that the increase in tension loading of existing structures was acceptable without having to rebuild. This would, of course, reduce the allowable conductor temperature and the resulting increase in thermal rating.

Notice that the knee-point temperature, where the aluminum tension goes to zero, under final conditions, occurs at only 90oF (32oC). It is assumed that the existing conductor has been inspected, and that the increased vibration that will

Table 2.5-2 Sag-tension Calculations for 30/19, 795 kcmil ACSR (Mallard)a ALUMINUM COMPANY OF AMERICAN SAG AND TENSION DATA Conductor Mallard

795.0 kcmil

30/19 ACSR


Dia + 1.140 in.

Wt = 1.235 lb/°F

RTS = 38400 lb

Span + 600.0 ft

Creep is a Factor


Design Points Wind (psf)

15.

.25

4.00

.20

32.

.25

.00

.00

K (lb/°F)

Original Line

Sag (ft)

Tension (lb)

1.955

7.80

11283.

11.26

7823

1.667

7.68

9773.

11.39

6600 6202

Weight (lb/°F)

Sag (ft)

Tension (lb)

0.

.00

.00

.00

1.235

5.30

10495.

8.97

15.

.00

.00

.00

1.235

5.79

9600.

9.66

5760

30.

.00

.00

.00

1.235

6.34

8775.

10.35

5377

60.

.00

.00

.00

1.235

7.56

7357.

11.71

4755

90.

.00

.00

.00

1.235

8.65

6432.

12.57

4433

120.

.00

.00

.00

1.235

9.26

6010.

13.26

4204

167.

.00

.00

.00

1.235

10.27

5422.

14.33

3891

212.

.00

.00

.00

1.235

11.27

4939.

15.33

3637

257.

.00

.00

.00

1.235

12.30

4528.

16.32

3419

302.

.00

.00

.00

1.235

13.34

4178.

17.28

3230


2-54

Re-tensioned

Ice (in)

Temp (°F)


2. While the conductor in the existing line had reached its final sag condition, increasing the tension will cause additional creep elongation and must be allowed for in the uprating study (see Section 2.4). 3. The calculation of sag and tension for this Mallard ACSR ignored the problem of compression in the aluminum strands. If compression is considered, the sag at high temperature will be higher than that indicated in Table 2.5-2. This has two effects: the sag clearance of the original line may not have been adequate at 75oC, and the change in sag with temperature after retensioning will also be greater than indicated. 4. Conductors and structures that have been in place for many years will be mechanically and electrically stressed to increased levels. Unless the existing conductor, structures, hardware, and connectors are thoroughly inspected, there is a possibility that the reliability of the line will be less than that of a new line or one that was reconductored. Redefining Weather Assumptions Through a careful review of weather conditions, it may be possible to use less conservative weather assumptions for rating calculations. This increases the rating without the need for physical modification of the line. The technique is limited by the increased risk necessarily assumed by allowing higher current operation without increasing everyday clearances.

Figure 2.5-3 illustrates the difference between actual line ratings and static ratings. The rightmost bell-shaped curve represents the probability distribution of line thermal ratings calculated based upon real-time field measurements of weather data. Note that the ratings of the line typically vary over a range of more than 2:1. The


very lowest ratings correspond to still air, maximum air temperatures, and full sun. A typical static thermal rating of 800 A is shown at the left tail of the rating distribution. A less conservative static rating of about 900 A is also shown. Clearly, the higher the static rating, the more frequently the actual line rating is less than the static. The leftmost distributions are line loadings (which vary as a result of varying customer load levels and system configuration changes) appropriate to each of the static ratings. Note that in this case, the line loadings approach, but do not exceed, the static ratings, and for each loading curve, the load may occasionally exceed the dynamic rating. This happens more frequently (larger overlap area) for the higher load distribution. Unless a dynamic line rating system is in use, the operator cannot know when the actual line rating is lower than the line load and therefore is unable to avoid occasional clearance infringements if the load distribution is high enough.

Actual Line Ratings are Normally Higher than Static Ratings It can be seen from Figure 2.5-3 that most of the time the line rating is well above the static rating and that under these conditions, the line current could safely be higher than the static limit. As long as line loads only rarely approach the line rating, it has been argued that the static rating can be increased with a negligible effect on electrical safety. This approach is investigated more thoroughly in Section 2.6. The method discussed here is much less scientific and much more common. Lines are sometimes uprated simply by using less conservative weather assumptions. Concerns About Using Less Conservative Weather Conditions In a regulated business environment, under ordinary operating conditions, power equipment was lightly loaded. High electrical loadings were rare; hence, the precise determination of high-temperature behavior was not critical. Some years ago, however, as the regulation of utility business began to decrease, many older highvoltage lines have been operated at higher and higher load levels. This might lead to increased failure rates and consequent service outages unless the mathematical models used to specify load limits were refined, and critical equipment parameters verified by measurement.

Figure 2.5-3 Probability density distributions for a typical circuit load and dynamic rating.

Driven by the advent of open transmission access and deregulation of the utility business, there has been a distinct trend toward the use of less conservative rating assumptions with little or no basis in science. Field test-

2-55



ing of dynamic thermal methods offered an opportunity both to evaluate the possible increase in ratings, and to detect the frequency of occurrences where existing equipment might be damaged due to less conservative rating assumptions. The calculation of thermal ratings for overhead lines is typically based upon heat balance methods such as that found in IEEE 738-1993. Given a maximum allowable conductor temperature, the corresponding maximum allowable current (the thermal rating) is determined for “worst-case” weather conditions. Maximum allowable conductor temperatures typically range from 50° C to 150°C. Typical “worst-case” weather conditions are a wind speed of 2 ft/sec (0.61 m/sec) perpendicular to the conductor, with full solar heating and an air temperature of 30°C to 40°C. Table 2.5-3 illustrates the advantage of assuming a higher wind speed and the consequence of doing so. Use of a higher wind speed for thermal rating calculations yields an increase in the line rating, even though the maximum conductor temperature (100°C) remains the same. For example, an increase in assumed wind speed from 2 to 3 ft/sec (0.61 m/sec to 0.91 m/sec) yields an increase in the rating from 990 to 1080 A and, since the assumed conductor temperature remains the same, no line modifications are required. The major advantage of this method of uprating is clear—it is very inexpensive. Since the maximum allowable conductor temperature remains the same (100°C), the corresponding maximum sag is unchanged and no line modifications are required. The major disadvantage of this approach is also clear from the rightmost column of Table 2.5-3. This column shows the temperature attained by the conductor for still air conditions , with a line load equal to the calcuTable 2.5-3 Effect of Assumed Wind Speed on Thermal Rating for Drake 795 kcmil ACSR at 100°C, Assuming Full Sun and an Air Temperature of 40°C. Assumed Wind Speed for Line Rating Calculation

Line Rating for 795 kcmil ACSR @ 100°C

Conductor Temperature When Current = Rating and Wind Speed = 0 ft/sec (0 m/sec) (°C)

(ft/sec)

(m/sec)

(A)

0

0

750

100

2

0.61

990

130

3

0.91

1080

145

4

1.22

1160

160

2-56

lated rating shown in column 2. Historically, the joint probability of maximum loading and worst-case weather was considered a rare event. Recent field studies indicate that, in certain areas, the probability of still air may be in excess of 10%. Combined with the previously noted increase in normal and emergency line loading, the temperatures indicated in the last column of Table 2.5-3 may be a real concern, and the use of a less conservative wind assumption may impact line reliability. 2.5.3

Probabilistic Methods

The probabilistic approach uses the actual weather data and conditions prevailing on the line to determine the likelihood or probability of a certain condition occurring. Such a condition could be, for example, the conductor temperature rising above the design temperature (the maximum allowed conductor temperature). These methods have been developed to include a measure of safety of the line. This can be used as a means of comparison of practices between utilities in all countries. The pros of probabilistic methods are that the risk is better known and can be quantified and defended if necessary. The designs can be consistent from a risk point of view in that, if localized weather conditions are used for different lines in different geographical areas, the lines can have different ratings, even though their design temperature and conductor types are the same. If there is a thermal rating limitation on a line, the probabilistic approach can ensure minimal or zero capital is used to uprate the line. The line designers also have far more parameters to vary in increasing the rating of a line. They could use the load profile, surge, or traffic patterns to increase the thermal rating of lines. This is not possible in the deterministic method. The cons of the probabilistic method are that significant amounts of data are required to determine the rating. This includes weather data as a minimum. If more sophisticated methods are required, the data needs to be determined on traffic patterns, surge patterns, and load profiles etc. Regarding the weather data, the variation of the data with time as well as with area needs to be taken into account. While the ambient temperature and solar radiation may be consistent over large areas, the wind speed and direction may vary within a few meters. It is also necessary to know how the parameters will vary into the future. This is particularly important with regard to the more complicated probabilistic methods where, for example, load profile is used. It is thus necessary to be aware of these issues in the determination of ratings.


Three main probabilistic methods are available at present: 1. Absolute Method The probability of an unsafe condition occurring can be quantified in this method. The benefit is that an absolute measure of safety can be achieved. The drawback is that the nature of the parameters is extremely difficult to determine. In addition, the correlation between the parameters—for example, the weather parameters—must be determined. This could vary from country to country. 2. Exceedence Method Historical weather data is used to determine the temperature of the line conductors for a given current flow. The amount of time that the temperature exceeds the line design temperature can be determined for each current level. The utility can then decide on the current level to use based on the percentage of excursion or “exceedence.” The advantage of this method is that it is relatively easy to determine the percentages and decide on a level by which to operate. The disadvantage is that there is no way of determining the difference in safety (to the public) between, for example, the 5% and 6% exceedence levels. An adaptation of the above method is to simulate the weather data and the current flow to determine the cumulative distribution of the conductor temperature as a function of current. This curve could be used to determine the current and excursion level. 3. Modified Exceedence Method The safety of a transmission line is estimated by incorporating all relevant factors. From this method, a measure of safety can be developed whereby the practices in different countries can be compared on an objective basis. The advantage of this method is that all factors are considered. The variation of the occurrence of objects under the line—for example, a traffic pattern—can be related to the safety of a line. Designers can use a wider range of methods, not generally used before, to increase the thermal rating of the line. Examples of this are the reduction of surge magnitudes or the number of surges per year, both of which can be used to increase the current-carrying capacity of a line. By using the measure of safety, system planners and line designers are in a position to determine the consequences of decisions in a more objective, rather than a subjective, way. Similarly by using the measure in conjunction with real-time monitoring systems to determine exact conductor temperature, operators can take more objective decisions. Utilities worldwide would also be in a position to determine the safety of their lines in relation to those of other utilities.


The “Absolute Method” of Determining the Probability of an Accident Research to date has primarily been confined to attempts at determining the probability of an unsafe condition arising. This is determined by ascertaining the probability of each factor occurring and multiplying the probabilities. This is represented in Equation 2.5-1.

P(acc) = P(CT) • P(I) • P(obj) • P(surge)

2.5-1

Where: P(acc) is the probability of the accident occurring. P(CT) is the probability of a certain temperature being reached by the conductor, and is calculated from existing weather conditions, conductor types, and an assumed current. P(I) is the probability of the assumed current being reached, and is determined from the actual current being measured on a system. P(obj) is the probability of the electrical clearance being decreased by an object or person. P(surge) is the probability of a voltage surge occurring in the line and may be determined from fault records kept by the power utility as well as simulations on switching surge overvoltages on the system. If the surge occurs simultaneously with an object being under the line, the likelihood of a flashover is increased. Each of the above is considered to be determined independently. P(CT) is determined by the Monte Carlo simulation technique sampling from distributions of ambient temperature, wind speed, wind direction, and solar radiation to calculate the probability of a certain temperature being reached given a current transfer. The ambient temperature, solar radiation, wind speed, and wind direction are sampled independently to form a set of parameters from which the temperature of the conductor is determined. The problem with the above method is that it assumes no correlation between weather parameters or the current, object, and surge occurrences. This may not be correct in all cases. The correlation between the individual weather parameters, as well as the weather parameters and the surge occurrences and objects being under the line, needs to be ascertained. This problem can be partly overcome by using sets of weather parameters, nmeasured at the same time. These sets will be used to determine the P(CT). Since each set used is determined from actual recordings of ambient

2-57


temperature, solar radiation, wind speed, and wind direction taken at the same time, the correlation between the parameters is taken care of. Determination of Line Rating by the “Standard Exceedence Method” This method assumes that the design temperature of the line may be exceeded for a small percentage of time, but that the line remains safe because of the low probability of other factors, such as high current levels and switching surge voltages. The amount of time the conductor exceeds the design temperature expressed as a percentage of total time is termed the exceedence level. By determining the exceedence level, and keeping it constant, the line ratings can be determined using different weather conditions or different geographical locations. This method is simpler to use than the absolute probabilistic method described earlier and does ensure consistent risk. The standard use of this method assumes that the full load current will flow at all times. A modified exceedence method uses the load profile of the line in question to increase the thermal rating above that of the standard method.

This (standard) method uses the weather data as well as the current and conductor characteristics to determine the frequency of occurrence of each temperature range attained for a given conductor current. Alternatively the current that would result in the templating or design temperature being reached can be calculated for each set of weather conditions. The frequency of occurrence of each current range can be determined. The weather data


used can be hourly readings, although the accuracy will increase with more frequent readings. The steady-state model can be used for the determination of the conductor temperature or the current required to reach a certain temperature. With reference to Figure 2.5-4, the exceedence levels have been calculated for the same conductor (Bersfort) in two separate locations in South Africa. The solid line represents the exceedence levels experienced in Bloemfontein, a hot semi-arid climate, compared to Volksrust, a small town in a more moderate climatic region. The number of lines for Volksrust indicates the differences in the weather data from year to year. The dashed line represents the average of the years. The graph indicates an interesting fact in that the operators utilize a single rating for both sites. The risk or exceedence experienced at both sites is likely to be different for the same current. The operators are therefore operating “blind” with regard to the risk. The exceedence method has the benefit of applying a uniform risk, or probability of exceeding the design temperature, by utilizing different ratings at the different locations. Difficulty often arises in setting the exceedence limit. One approach could be to determine the exceedence limits experienced at present for various geographical areas at different times of the year. This can be achieved by plotting graphs similar to those of Figure 2.5-4. The present current limit is used to determine the exceedence level. This level can then be used to determine the

Figure 2.5-4 Graph showing the results of the use of the exceedence method.

2-58



ampacity of different conductors at different design or line design temperatures.

the current is not at the maximum level all the time. These factors vary from area to area and line to line.

Benefits of Using Standard Exceedence Method The Standard Exceedence Method has been in use by the National Grid Company (UK) for some years. Table 2.5-4 gives an example for rating its transmission system. The percentage excursion time, now called “exceedence,” corresponds to the portion of time that the conductor would exceed the stated design temperature if it were operated continuously at the corresponding current. These values of current are compared in the table with their previous ratings assigned on a deterministic basis. The exceedence to which the deterministic ratings actually corresponded, which could not be identified or acknowledged previously, are seen to vary from approximately zero to 6%, depending on the rating, season, and the design temperature.

Instead of looking to the probability of an unsafe condition arising that relates directly to safety, it has been assumed that to exceed the design temperature is unsafe. No knowledge exists of exactly how unsafe it is. The next method, although more complex, goes some way to solve this problem.

Adopting a consistent 10% exceedence throughout the year led to increases in rating from 3% to 30%. More accurate meteorological studies may allow a rating increase without increasing the exceedance. The method also allows greater consistency compared to the other approach, since the exceedence can be made constant for all seasons. Note that the ratings given in Table 2.5-4 are post-contingency values, which are used only in emergency conditions. The risk of flashover depends on the coincident risk of a maximum voltage surge occurring while worstcase cooling conditions exist in the span with the critical clearance. This risk is many orders of magnitude less than the value of exceedence chosen. In addition to this,

Modified Exceedence Method The Standard Exceedence Method assumes that the line current is constant. For lines having a reasonably predictable electrical load cycle, the load cycle shape can be used. The calculation is then referred to as the Modified Exceedence Method.

Effect of the Load Profile on Thermal Rating The effect of a load profile on thermal rating can be quite pronounced. This can be shown in the following set of graphs (Figure 2.5-5) developed for conditions prevailing in Cape Town (moderate climate with strong winds). This load profile was used to generate the exceedence and modified exceedence curves. The conductor used in this case was 196 kcmil (100 mm2), 6/1, “Hare”. Figure 2.5-6 shows the increase in the ampacity of the conductor using the load profile and local weather data. The graph shows that the ampacity can be increased, if we are using an exceedence level of 5%, for example, from 230 A to 340 A. The two graphs using the load

Table 2.5-4 Comparison of Deterministic and Probabilistic Ratings for 4% - A1/S1 - 54/7 “ZEBRA” Design Exceedence Temp %

0.1 50

Summer Previous Deterministic Rating (A)

Probabilistic Rating (A)

Previous Deterministic Rating (A)


Previous Deterministic Rating (A)


610

683

770

789

950

847

745

861

925

6

769

888

954

10

790 795

826

912 896

910

980 1019

959

3

901

994

1046

6

930

1025

1079

10 0.1 75

Winter

3

0.1 65

Spring/Autumn

955 912

906

1053 1000

981

1109 1090

1025

3

989

1071

1118

6

1020

1105

1153

10

1048

1135

1185

2-59



Figure 2.5-5 Load profile for exceedence rating example.

1. 2. 3. 4. 5. 6.

Figure 2.5-6 Results of exceedence rating probability example.

profile for HARE and HARE 95 result from different year’s data being used. This shows that in this type of evaluation it may not be necessary in Cape Town to use many years’ data to determine ampacity as each year is sufficiently variable. 2.5.4

Development of a “Measure of Safety” as a Basis for Line Rating

The above probabilistic methods—the absolute method, the standard exceedence method, and the modified exceedence method—do not make use of all the factors that affect the thermal rating of a line. The factors that affect the safety are:

2-60

Whether or not a surge exists on the line. The magnitude of the surge should one be present. Whether or not an object is present under the line. The size of the object should one be present. The position of the conductor. The probability of flashover as a function of spacing and shape.

Types of Accidents Occurring Relating to Transmission Lines Based on the research conducted to date in Eskom (South Africa), the area in which this probabilistic approach to the determination of conductor ampacity would be most beneficial is on lines above 132 kV. The objects that would result in an unsafe condition arising in this case are mainly vehicles. It should be noted that these findings may vary from country to country, and similar research may be required.

Simulations of transmission-line flashovers indicate that the correlation between the various factors make the calculation of probable safety difficult, if not impractical. It is not merely a matter of multiplying the probabilities of each of the factors together, but to include the correlation functions, which are extremely difficult to determine.



Simulation using actual weather and data for each factor that affects the safety of a line measured at the same time eliminates the need for correlation evaluation. Simulation of Unsafe Conditions The simulation combines different models to determine whether a flashover occurs to a vehicle or how close the situation was to a flashover. At Eskom this is done by means of four modules. Each of the modules simulates the behavior of the particular parameter. These modules are:

required to cause a flashover from the surge generated at the time. The more positive the mean of the difference, the safer the line. This measure is felt to be the most valid since it takes into account not only the surges generated, but also the surges generated at the time the vehicle is under the line. The designer can readily determine the probability of an accident occurring since the integral (number of incidents) of the curve below zero would represent the number of accidents expected. The distribution of the new safety measure as a function of line design temperature is shown in Table 2.5-5.

• Surge Module. This module determines the month, day, hour, minute, and second in which a surge occurs. It then determines the magnitude of the surge.

• Object Module. This simulates the size and time that a vehicle will be under the line. If the vehicle is under the line at the same time as the simulated surge, the data containing the surge time and magnitude, as well as the vehicle data, is stored.

• Position Module. The position module determines the position of the conductor at the time of the surge.

• Accident Module. Using the gap-surge relationship, it is possible to determine the surge required to create a flashover. This module determines the difference between the surge required to cause a flashover with the actual simulated surge on the line. Developing a Measure of Safety Parameters Independent of Current and Line Design Temperature

The number of surges and vehicles in each category were analyzed based on the generation of 572 “counts,” or times at which the surge and the truck were simultaneously under the line.

• • • • • • • • •

Average counts per year

12.43

Number of cars

26.4% of vehicles

Number of small trucks

49.8%

Number of large trucks

23.8%

Surges of magnitude 1.6

30.6% of surges


40.6%


17.1%


10.1%


1.4%

The probability of surges follows the expected distribution, but the probability distribution for vehicles under the line is affected by the time span that the different vehicles remain under the line. Incorporating the surges generated on the line into the measure of safety is difficult. One method investigated was to subtract the surge

It appears that the statistical description of the safety measure as listed above is a valid and reliable means of determining the safety of a transmission line since the measure is valid for any line design temperature and takes into account every parameter dealt with in determining the likelihood of an accident. Uses of the Established Measure of Safety A statistical “signature” can now be established describing the safety of a particular line. This can be used as described in the above example to increase current by line design temperature or by reducing surge magnitude.

Utilities are now able to quantify the safety of a transmission line. This will enable presentation of the rationale behind any action taken. Uprating an existing line or establishing a power transfer rating for a new line can be justified in an objective rather than a subjective way. The advantage of the above method is that the probability of an accident occurring can be determined. The safety of the line can be quantified and compared with other risks such as that of nuclear facilities. This will assist with objective discussions with regulators. The model can be used to determine the reliability of lines by comparing statistical signatures of the difference between the surge present on the line and that required to cause a flashover with the insulator string swinging due to wind. The wind data as well as the surge modules can be used in this case. Lines in similar areas with difTable 2.5-5 Probability Distributions versus Line Design Temperature Line Design Temperature oC Mean Std. Dev Max. Min. % below 0

40°C

50°C

60°C

80°C

1.58 0.84 1.95 -1.9 4.3%

1.64 0.78 3.2 -0.37 4.0%

1.89 0.70 3.09 -0.19 0.8%

2.34 0.56 3.32 0.91 0%

2-61



ferent designs can be compared, and a measure of reliability relating to conductor swing can be developed. 2.5.5

Comparison of Probabilistic Rating Methods

Table 2.5-6 summarizes the main points of each probabilistic rating method. 2.5.6

Device for Mitigating Line Sag - SLiM

A new class of line hardware, SLiM (Sagging Line Mitigator) (Figure 2.5-7), can help solve problems where there may exist excessive line sag. SLiM reduces excessive sag in transmission lines and allows transmission owners to realize higher line ratings and increases transmission system performance, reliability, and asset utilization. The

passive design of SLiM and its ruggedness allow transmission owners to treat SLiM like typical transmission line hardware such as insulator strings. Its installation procedure is a relatively simple O&M activity. SLiM reduces excess sag and allows transmission owners to realize higher line ratings, permitting them to increase asset utilization and maintain safety and reliability in a very cost-effective manner. SLiM has multiple applications for both new and existing transmission lines to address a host of challenges for transmission owners. SLiM provides transmission planners, engineers, and asset managers another tool to help them manage transmission systems in an increasingly challenging environment. The SLiM can serve as an economic alternative to conventional solutions, such as:

• Replacing the existing conductor with a premium conductor that can operate at high temperatures without increased sag.

• Reinforcing line structures and foundations for increased mechanical loading, and either reconductor with a larger conductor or bundle with the existing size conductor.

• Raising towers and improving foundations at key line locations to provide for increased clearance.

• Adding intermediate towers at key line locations to increase ground clearances.

Figure 2.5-7 The SLiM device. Table 2.5-6 Comparison of Probabilistic Rating Methods Absolute Method

Std Exceedence Method

Modified Exceedence Method

Safety Method

Establishes the absolute probaUses relative comparison of bility of an unsafe condition risk. Cannot relate to an absoarising. Can be used to compare with other industries such lute probability. as nuclear safety standards.

Uses relative comparison of risk. Cannot relate to an absolute probability.

Uses relative comparison of risk. Cannot relate to an absolute probability.

Complex method that requires Uses simulation. Little explicit equations for the proba- advanced probabilistic theory bilities of current, surges, etc. required.

Uses simulation. Little advanced probabilistic theory required.

Uses simulation. Little advanced probabilistic theory required.

Takes into account all factors that affect thermal rating of lines.

Uses weather data and load profile.

Takes into account all factors that affect thermal rating of lines.

Takes only the weather data into account.

Automatically takes care of Requires analysis of correlation weather data correlation by between weather data and using actual wind speed, solar weather data and other factors radiation, wind direction, and such as surges and load. ambient

Can be used on its own.

Can be used in isolation, but may encounter difficulties in determining the exceedence limit to use without reference to an absolute risk

Uses simulation that automatiUses simulation taking care of cally takes care of correlation if correlation if sets of weather sets of weather data and load data are used. profile data are used. Can be used in isolation, but may encounter difficulties in determining the exceedence limit to use without reference to an absolute risk

Can be used as a comparison between two lines, but needs to refer to the risk level found in the absolute method to determine a reference level.

Analysis of data is required to Data can be used directly in the Data can be used directly in the Data can be used directly in the determine the probabilistic func- method without statistical analy- method without statistical analy- method without statistical analytions. sis of the data itself. sis of the data itself. sis of the data itself.

2-62


• Installing a sag monitoring system and the infrastructure to process this information. How SLiM Works SLiM uses a shape-memory alloy actuator that is activated by the same temperature changes that cause a conductor to change sag. The device is passive, with no motors or electronic controls. As increasing temperature increases conductor length, and hence its sag, SLiM changes its geometry to decrease line length. As conductor temperature returns to normal, SLiM returns to its original shape, keeping the conductor always within acceptable sag and tension limits (see Figures 2.5-8 and 2.5-9). Some Potential Applications Here is a bulleted list of situations where a SLiM device may offer a viable solution:

• A system contingency situation can cause loading on parallel transmission lines to exceed their thermal limits. These limits are often established to maintain conductor line-to-ground clearances. Thus, the action of SLiM, which mitigates the excess sag caused by high-temperature operation, can allow for safe line operation during these contingencies. Line capacity is increased by allowing operation beyond conventional thermal limits, and expensive line modification projects may not be required.

• Many older lines were constructed to 120°F maximum conductor temperature operation. Studies have shown that SLiM can enable operation of such lines at a conductor temperature of about 200°F without compromise of line clearances or tensions. This can represent a substantial increase of rated line capacity.

• System planning may project that certain lines will become overloaded as local growth increases demand. In this instance SLiM can delay the need for either a new line or considerable line modifications while the anticipated load materializes. Installation of SLiM is a simple O&M activity and can help bridge needs.


to be as low-profile as possible. SLiM can be employed in a cost-effective fashion to minimize tower height for such installations while maintaining required ground clearances and higher power flows.

• Limitations on line ratings to maintain clearances over road or river crossings can be lifted by using SLiM while maintaining ground clearances and higher power flows.

• SLiM can be used on new line construction and allow for use of lower towers, mitigating visual impacts and community objections. SLiM Specifications

Electrical Connection The SLiM device carries the full line current, splitting the current between the actuator and the body of the device. Standard flexible connectors carry current between the transmission line and the SLiM device. The electrical connectors on the device terminate with 4-bolt NEMA paddles for easy connection to standard line hardware. Mechanical Connection The device is installed in series with the transmission line. Either end of the device is equipped with standard oval-eye end fittings. The mating attachment on the conductor is the choice of the utility. The device accepts any industry standard dead-end attachment with a 1 in. (2.54 cm) clevis pin. Options include dead-end compression fittings, preformed dead ends, and wedge dead ends. Installation The device can be installed at a dead end, or anywhere along a span using procedures similar to line-splicing techniques. During installation, a piece of conductor approximately the length of the SLiM device is removed and replaced by the device. The length of conductor to be removed as well as the number and locations of devices along a section of transmission line can be determined using line-sagging software for optimum performance.

• Line routing or line modifications near airports or other unique situations quite often require structures

Figure 2.5-8 SLiM is strong, maintenance-free, and designed to have a very long life. It is designed for easy installation using hot or cold procedures. Industry standard connectors can be used to attach SLiM to the line. Its operation is configurable to match specific line requirements, and has no negative effects on line electrical performance.

2-63



Figure 2.5-9 The major components of the SLiM device in its “Dead-End Configuration” and its “In-Line Configuration.”

Operating Parameters Tables 2.5-7 and 2.5-8 list some of SLiM’s basic parameters and operating characteristics. The standard unit is targeted primarily to 115- and 230-kV lines, but can operate in 60- and 70-kV class, as well as 345-kV class lines. Standard units can also be configured to actuate at different temperature points based on individual requirements. Table 2.5-7 Operating Parameters for Standarda SLiM Criteria

Application

Voltage Rating

230 kV and below. Higher voltages (345 and 400 kV) possible.

Target Conductor

Conductors with a breaking load 40,000 lb (180 kN)

Range of Motion

Up to 8 in. (200 mm)

Line Tension @ 110°F

Up to 5,000 lbs (22.5 kN)

Functional Temperatures

~120–212°F (50-100°C) (conductor temperature)

Mechanical Failure Load

> 49,000 lbs (218 kN) – Tested per IEC at Kinectrics

Electrical Current Capacity

> 1400 A

Short Current Rating

40 kA (rms) – Tested per IEC at Kinectrics

Development and Testing of SLiM SLiM has been through several years of extensive R&D and testing including laboratory functionality and reliability testing as well as actual field demonstration.

Functionality testing was performed at PG&E’s training facility in Livermore, California. The sag differential between the test and control spans at the maximum temperature of 100°C was 44 in. (Figure 2.5-10), which closely matched the predicted effect of SLiM. Prior to and following the full functionality testing at PG&E, SLiM and its components were extensively tested for load and current-carrying capacity, fatigue, corrosion, and repeatability of performance. SLiM was also tested at Kinectrics and was subjected to a number of fault current events ranging from 21 kA to 40 kA (rms) for a minimum of 10 cycles. After current testing, SLiM was subjected to increasing load until its break links failed, as designed, at about 49 Kips, exceeding the target range (110% of the conductor breaking load).

Total Weight

~ 85 lbs (380 N) (Production Version)

End-to-end Dimension

~ 5 ft, 3½ in. (1610 mm) open, 4 ft, 7½ in. (1410 mm) closed

End Connectors

Any standard connector with 1 in. clevis pin (utility’s choice)

Installation

“Cold” using standard procedures – or – “Live” using live-line hand procedure (similar to splicing procedure). Detail procedure available upon request.

a. Custom sizes for special applications available.

The SLiM device was installed on the bottom phase of a 69-kV transmission line, in SDG&E’s service area in Escondido, California (Figure 2.5-11), and monitoring equipment was installed directly below the test span on a 12-kV distribution pole. The field demonstration was intended to prove both ease of installation and functionality and reliability. SDG&E crews called the installation “straightforward.” SLiM has successfully completed over a year of field demonstrations.

Table 2.5-8 Example Sag Mitigation for a Drake Conductor Conductor Temperaturea

Excess Sag due to Heating

Span ft / m

Initial ºF / ºC

Final ºF / ºC

Without SLiM ft / cm

750 / 230

110 / 43

212 / 100

1000/300

110 / 43

212 / 100

Reduction ft / cm

5.2 / 158

0.2 / 6

5.0 / 152

6.0 / 183

1.9 / 58

4.1 / 125

a. Tension at 40°F considered equal to 20% of tensile strength of conductor.

2-64

Sag

With SLiM ft / cm



Figure 2.5-10 The sag differential being measured on a control span (bottom) and a test span (top).

2.6

RECONDUCTORING WITHOUT STRUCTURAL MODIFICATIONS

2.6.1

Introduction

By replacing the original line conductors, it is possible to employ modern conductors having lower resistance for the same diameter and/or having the same maximum sag as the original conductor but at greatly increased temperature. The use of certain new conductors can yield an increase in thermal capacity of as much as 100% at a cost of less than half that of a new line. This section concerns the application of commercially available conductors, but the analysis methods are applicable to new conductor types. Existing lines may be uprated using methods discussed in preceding sections of this chapter, all of which involve using the original conductor. In certain applications, it may make sense to replace the original conductor with a new one, usually having a diameter near the original and often capable of operation at higher temperatures. This section reviews the various reconductoring choices, and provides some insight into those line uprating applications where reconductoring is preferred. Given the low cost, high conductivity, and low density of aluminum, no other high conductivity material is presently used. Therefore, any “low-resistance” replacement conductor must have increased cross-sectional aluminum area, and increased wind/ice and tension loads on the existing structures. Figure 2.5-11 Field demonstration of the SLiM device at SDG&E.

Figure 2.6-1 shows how the thermal rating of an existing line may be increased by about 50% by using a replace-

2-65


ment conductor with twice the original conductor’s aluminum area. Note that this doubles the original strain structure tension loads and increases transverse wind/ice conductor loads on suspension structures by about 40%. Such large load increases would typically require structure reinforcement or replacement. “High-Temperature, Low-Sag” (HTLS) conductors, capable of continuous operation at temperatures above 100oC with stable tensile strength and creep elongation properties, are commercially available or under development. Practical temperature limits of up to 200oC have been specified for some conductors. As is also shown in Figure 2.6-1, use of an HTLS conductor (having the same diameter as the original) at 180oC also increases the line rating by 50%, but without any significant change in structure loads. Raising the structures may also be avoided if the replacement conductor has a lower thermal elongation rate than the original. EPRI is presently engaged in a project to field-test long samples (several spans) of HTLS conductors in operating lines. This project is in its early stages at the printing of this guidebook, but some preliminary observations are discussed in the following sections. Future versions of this guidebook will be updated with the latest publishable results. The use of a lower-resistance conductor has two advantages—losses are reduced, and operating temperatures remain modest. The use of HTLS conductor has the primary advantage that structure modifications are minimized. In either case, the replacement of existing conductor should improve the mechanical reliability of the line since conductor, connectors, and hardware are all new.

2-66


Sag Constraints for Reconductoring As shown in Figure 2.6-2, the original conductor’s “Initial installed sag” increases to a final “everyday” sag condition (typically at 60×F [16×C] with no ice and wind) as a result of both occasional wind/ice loading events and the “normal” creep elongation of tensioned aluminum strands over time. This everyday final sag increases further (but reversibly) due to ice/wind loading or high electrical loads. For most transmission lines, as shown, maxiTm[(Sa)1(t(i-)]327)1(8o)-13(har)18(d. Th)5(is e)17(v)32ion

Chapter 3: Underground Cables


dewatering, backfilling, and other activities. The ambient temperature recorded at the start of an in situ thermal resistivity test is an important value to record for the cable designer. In the laboratory, a soil sample is prepared to evaluate thermal dry-out characteristic– the variation in thermal resistivity of the material as a function of moisture content. The results of these tests (dry-out curves) are presented on charts that show thermal resistivities at the in situ moisture content (if known), at “critical moisture content,” and in totally dry condition (worst case). Some degree of drying beyond the native moisture levels should be expected in the presence of energized power cables, so an adjusted soil thermal resistivity that factors in the drying should be incorporated into ampacity calculations. Once the soil thermal resistivity results are known, they can be used in ampacity calculations. For the case of installed cable systems, it may be necessary to do testing outside the cable trench to get native conditions, and within the cable backfill to characterize the special thermal backfill that may have been used around the cables. If the trench is known to have a common material throughout, testing of the backfill material may only be needed at a few selected locations. Thermal Diffusivity Although thermal diffusivity is not commonly recorded (typical transient needle TPA equipment can measure this parameter) for most applications, its application is in “transient” calculations. In simple terms it can be treated as the “inertia” in the heat and mass transfer equation. The three terms—resistivity (ρ), diffusivity (α) and heat capacity (C)—are related by Equation 3.6-1.

ρ ⋅ α ⋅C = 1

3.6-1

Thermal Stability Thermal stability is a system-driven parameter and is a soil characteristic that describes how well a soil maintains a constant thermal resistivity when exposed to cable heating. The main issue is to consider if the heat leaving a cable would result in the soil being below its critical moisture content, in which case the soil would experience net drying and an increase in thermal resistivity. Smaller diameter cables with direct contact to the soil are more likely to result in thermal instability because of a larger heat flux (temperature gradient) at the cable-soil interface.

A classic example of a thermally instable material is modeling clay. The clay can be dried at room temperature over time. If the dried sample is then placed in water, it does not readily reabsorb water to return to a

3-32

malleable substance. Some soils—including soils with high clay and silt contents—have these characteristics. A common situation where this may be an issue for power cables is the use of bentonite as a grout material either in trenchless casing installations or for cable conduits; pure bentonite has high thermal resistance and is prone to drying. Bentonite is prone to shrinkage and cracking (leaving voids) if drying does occur. A better solution is to use as much sand as possible while minimizing the bentonite content, and to seal the ends of the casing or ducts so that the grout cannot dry. Moisture Migration in the Soil For any given soil or backfill, the major influence on the thermal resistivity is the moisture content. In a dry state, the pore spaces between soil particles are filled with air (thermal resistivity of about 45°C-m/W). As water (thermal resistivity of about 1.65°C-m/W) replaces air, the soil resistivity decreases substantially by as much as 3 to 7 times, as the good heat conduction paths are expanded (additional thermal “thermal bridges”). This is illustrated by the “thermal dry-out curve” (thermal resistivity vs. soil moisture content) shown in Figure 3.6-3. A soil that is better able to retain its moisture, as well as being able to efficiently re-wet when dried, will have better thermal performance characteristics. The soil water content is expressed as a percentage of the weight of water to the dry weight of soil solids, as determined by oven drying at 105°C.

The heat generated by energized cable tends to cause soil moisture to migrate away from the cable/backfill interface. In unstable backfills or soils, this drying increases the resistivity substantially, inducing further heating of the cable and thus more drying of the soil. Eventually this cycle may create a totally dry zone of the backfill around the cable, resulting in excessive heating and potential thermal runaway. In a stable backfill, the heatinduced drying raises the resistivity marginally, thus minimizing the potential for thermal runaway. Thermal stability is best illustrated by means of thermal dry-out curves (Figure 3.6-3). The “critical moisture” is defined as the moisture content below which the relatively flat nature of the thermal dry-out curve gives way to a disproportionate increase in the thermal resistivity. Above the critical moisture a soil will resist thermal drying (by means of capillary suction), whereas below this value, thermal runaway is inevitable (unless soil moisture is externally replenished, (i.e., rain). Although some native soils at high moisture content (10–25%) may exhibit fairly low thermal resistivity (0.4 to 0.6 °C-m/W), this value may increase a few fold when dry. Well-graded sands and stone-dust containing 10–



15% fines (-200 Sieve size material) make good corrective thermal backfills.

thermal resistivity, heat transfer takes place by radiation instead of conduction that is much less efficient.

Cable Route Soil Test Spacing The soil testing and sampling frequency for thermal resistivity testing along the cable route can vary depending on the area and the length of the route. In rural areas, where the use of fills is minimal and historical construction has not been significant, sampling and insitu testing every 500 m might be done. In urban areas or locations where fill materials have been used, sampling might be done every 200–500 m. Known variations in geology or other conditions might affect how often along the route testing and sampling are done. The goal of testing is to capture test results for any unique soils and potential hot spots along the cable route while categorizing where each soil type is found.

Soil Texture and Dry Density The soil texture is also critically important to thermal resistivity. The grain size distribution and grain shape are evaluated by a sieve analysis (e.g., ASTM D422, etc.) to determine the variation in particles both in backfill materials and native soils. Figure 3.6-5 shows a sieve analysis for four materials and a band of “good” granular thermal backfill.

Factors Affecting Soil Thermal Resistivity

Soil Composition The soil composition is an important characteristic affecting soil thermal resistivity. Soils are typically a conglomerate of various materials, and the ratio of these materials within a soil affects the thermal resistivity. Table 3.6-1 summarizes the dry thermal resistivity values of various components.

Because the soil components are so important in affecting the thermal resistivity, a good understanding of the geology along a cable circuit is valuable to assessing where soil testing should be performed and how much variation might be expected along a given cable route. It is important to note from Table 3.6-1 and Figure 3.6-3 that dry soils have a much higher thermal resistance than moist soils because the thermal resistivity of water (1.65 C°-m/Watt) is much lower than that of air (~45 C°-m/Watt). In addition to the air having higher

Table 3.6-1 Thermal Resistivities of Soil Components Component

Dry Thermal Resistivity C°-m/Watt

Quartz

0.12

Granite

0.30

Limestone

0.40

Sandstone

0.50

Shale (sound)

0.60

Shale (highly friable)

2.00

Mica

1.70

Ice

0.45

Water

1.65

Organics (peat, etc.)

~5.00

Petroleum Oil

~8.00

Air

~45.00

Water Content and Ground Water Level As is seen in Figure 3.6-3, soils with higher moisture content generally speaking have better thermal resistivity. Some soils naturally retain water better than others. Certain soils may not retain water well—e.g., they have a high hydraulic porosity—but are below the water table so they remain saturated even though the dry density is low and dry thermal resistivity would otherwise be high. Dry Density The dry density of a soil determines its ideal ability to conduct heat away from the cables. Factors that influence the dry density are porosity, solids content, interparticle contacts and pore size distribution. Having a well-graded material with a range of particle sizes improves the dry density and minimizes pores and voids in the material. Other Subsurface Characteristics Concerns for solutes and hysterisis apply only in areas where significant fluctuation in the water table may “wash out” fines from the backfill, making it thermally poor. For most applications, this is not a concern for cable system uprating and, in any case, would be found during soil thermal resistivity testing. Surface Characteristics and Vegetation Surface conditions have an impact on soil thermal resistivity. For example, soils below asphalt roadways generally will not gain or loose moisture readily under normal conditions. However, in the presence of cables, the drying that does occur may not be mitigated by heavy rains since the water will not be easily reabsorbed.

Surface vegetation can be significant factor affecting soil thermal resistivity. The root systems on large trees and plants will draw moisture out of the soil, drying it. Also, the decaying components of plants and their root systems will tend to increase the organic component of soils, which tends to increase the soil thermal resistivity (see Table 3.6-1). Surface cover has strong influence over earth ambient temperatures, especially at shallower depths. A difference of 4–5°C has been measured between grasses versus asphalt cover over cables. 3-33



Engineered Thermal Backfills The general goal of engineered thermal backfills (ETB) is to enhance the removal of heat away from buried cables. In most cases, the native soil materials have a higher thermal resistivity than good quality backfills and, in any case, are difficult to reconstitute in the trench with the same density as the native soil. For this reason, special backfill materials are often designed for use in a cable trench. These include well-graded sands, stone screenings, and concrete or Fluidized Thermal Backfill. In addition to having excellent thermal properties, they are engineered to meet civil requirements (strength and ease of voids-free installation) that are associated with the particular application. The criteria considered for these ETB are:

• Low thermal resistivity over the expected range of operating conditions

• Low critical moisture content and high thermal stability limits

• No adverse affects on materials used for cable conduits, cable jackets, or pipe coatings

• Easy to install • Inexpensive and locally available to the location where the materials will be used Types of engineered thermal backfills are discussed in the following sections. Granular Backfill Materials These materials should be composed of hard, wellgraded, natural or crushed mineral aggregate (limestone, granite, quartz or other similar rock). The material should be sound (porosity less than 2%) and be free of any organic material (peat, root matter, topsoil, vegetation) and foreign matter (wood, rubble, cinders). The sieve analysis should match closely to that given in 3.6-5. The maximum particle size should be no larger than 1/4in. sieve size with a fines content (material finer than #200 sieve size) of 12% to 18%.

During supply and installation of this material, quality assurance is very important. Sieve analysis on the delivered materials should be performed periodically to check and verify its compliance with the above characteristics.

Figure 3.6-5 Grain size distribution for soil samples.

3-34


Fluidized Thermal Backfill (FTB) One of the difficulties with any granular backfill is that it must be installed properly, regardless of its ideal thermal properties. Granular backfills should be installed in shallow lifts 15 cm (6 in.) at a time and well compacted to give good density. This is labor intensive, and great care must be used when working close to directly-buried cables or conduits so as not to damage either.

Leading up to and during installation, FTB delivered to the project site should conform to the respective mix design and performance specifications of low-strength and/or high-strength FTB. This should be checked with samples collected during the project. When installed by pouring into the cable trench, the material should be free flowing and without any segregation. This will help ensure that the material completely surrounds the cables, conduits, or pipes. The amount of water in the FTB mix may be adjusted to increase or decrease the flow (slump) as directed by the field engineer. If lower slump FTB is required for a particular area, it is generally better to adjust the water content at the batch plant rather than as the material goes into the trench. Air content (natural trapped) should not be higher than 2%. Mixing at the batch plant and transportation to the project site should be done in accordance with ASTM or American Concrete Institute (ACI) specifications.


If trench shoring and sheathing is being used, these should be removed immediately after the installation of FTB, unless otherwise required by the field engineer. If FTB is installed in cold conditions, care should be taken to protect the installed FTB from freezing. This applies to both low-strength and especially high-strength FTB. ASTM or ACI specifications should be followed for such installations. Sampling and testing for quality control/assurance should be performed on FTB samples taken every 250 ft along the cable trench, or every 100 cubic yards of material installed, or as directed by the field engineer. Component materials from an FTB mix design are shown in Figure 3.6-6. Grouts for Cable Conduits and Trenchless Casings For extruded or self-contained cables in ducts or the space between inner-ducts and trenchless (directional drilling, pipe jacking, etc.) casings, the air space between the cable and conduit or conduit and casing is often filled with air, which is a poor thermal conductor. Filling the duct with a thermally conductive material improves the cable ampacity by 5–10%, depending on the configuration and the type of filler. The annular space is generally small, and utilities usually want to retain the ability to remove the cables from the conduits later in the event of a failure or for upgrading. Therefore, it is not practical to fill the annular space with a solid filler material (or one

Figure 3.6-6 Component materials used in a typical Fluidized Thermal Backfill.

3-35



that becomes solid over time), so a pumpable material that will not hard set is ideal.

locations of other underground utilities that may impact cable ratings.

IEC-60287 allows that cables with grouted conduits may be treated as direct-buried cables for the purposes of ampacity. Various materials that have been considered for conduit grouts are:

The plan drawings will show a variety of factors that may be relevant to determining the cable ampacity and possible locations where uprating could be considered:

• • • • •

Bentonite and sand/bentonite slurry Sand-cement grout Flyash-cement grout Grease and viscous oil, along with other compounds Water

Factors that must be considered when selecting a grout are the total length that must be filled and the amount of annular space. For trenchless installations, the potential softening of a plastic duct at elevated temperatures— including potentially the heat generated as cement-based grouts cure—could soften ducts and cause partial collapse. The safe pumping pressure for the grout material must therefore be considered when a grout is pumped on the outside of air-filled cable conduits. The grout material typically will have a thermal resistivity of 0.4 to 1.4 C°-m/Watt, which is much lower than air (45 C°-m/Watt) at the set moisture content. A sandbentonite slurry backfill with a thermal resistivity of approximately 0.7 C°-m/Watt is easy to formulate and generally easy to install. Varying the amount of sand, bentonite and water affects the pumpability of the grout. Bentonite tends to absorb a lot of water, so this must be factored into the mix. Mixing the sand/bentonite slurry also requires special equipment (i.e., colloidal mixer). The thermal resistivities of these components are as follows:

• Sand: 0.12-0.20 C°-m/Watt—optimizes the thermal resistivity but negatively affects pumpability.

• Phase and circuit or pipe spacing among the cables being studied, which would impact mutual heating effects.

• The locations of other utilities that cross the cables, especially other transmission or distribution cable circuits that could produce mutual heating effects. Also, steam lines may be present.

• Sections of the route that parallel other utilities, including power cables. Parallel cables within a certain range may produce sufficient mutual heating to cause derating. A general guideline is, if the horizontal spacing is within 25% of the depth, mutual heating may be a factor (e.g., if the cables being studied are at 4 m depth, parallel cables or other heat sources within 1 m horizontal spacing should be examined for mutual heating effects).

• Topographical profiles may show areas where overburden has accumulated above the cable route. Profile drawings mainly indicate the cable circuit’s depth of cover below grade and usually the locations of other utilities that cross the cable circuit. Areas that are important to note on the profile drawing are:

• Entry/exit to manholes since cables frequently dip to enter a manhole

• Road crossings where the cable burial depth may be increased to accommodate the required road bedding materials

• Directional drilling locations where the burial depth is significantly greater than conventionally-trenched sections

• Water: 1.65 C°-m/Watt—optimizes the flowability but negatively affects shrinkage.

• Bentonite: 3.50 C°-m/Watt—optimizes the pumpability but negatively affects thermal resistivity. These materials are combined by a soil specialist for use by the contractor or utility during installation. 3.6.2

Review Circuit Plan and Profile

A classical approach to performing uprating on underground cable circuits is to review the circuit plan and profile drawings, preferably the “as-built” versions, which may show additional details about the locations of the buried power cables, as well as better illustrate the

3-36

3.6.3

Evaluate Daily, Seasonal, or Other Periodic Load Patterns

Load shape is generally not that important for most transmission equipment, particularly overhead lines where the thermal time constant is relatively short. With underground transmission cables, the long thermal time constant—35–150 hours—can significantly impact loading patterns for both normal and emergency ratings, particularly for short-duration emergencies. In typical normal ampacity ratings on cables, daily load cycles are modeled by rating techniques through the application of a load factor or loss factor. The load fac-


tor relates the average daily load to the peak load, usually following a relationship similar to the following: Loss Factor, p.u. = 0.3 (Loss Factor, p.u.) + 0.7 (Loss Factor, p.u.)2 This relationship is graphed in Figure 3.6-7. As mentioned earlier, the loss factor (or load factor of the losses) considers the average daily heat output relative to the peak heat output. Consider Figure 3.6-8, which shows several load shapes that all have the same peak current but substantially different load and loss factors. All of the curves in Figure 3.6-8 have the same peak current (1000 A), but substantially different loss factors. On a daily basis, the different loads shown will release different amounts of energy into the surrounding soil. This has a significant impact on conductor sizing for a desired rating or on the available current for a given conductor size. Note that the loss factor is also the perunit power delivered on a daily basis.


If the cable construction and installation conditions are held constant and the loss factor is varied, the cable ratings will vary substantially. From the standpoint of uprating, increases in loss factor over time mean that the ampacity will tend to decrease. For example, on a recent uprating study for a New England utility, the loss factor in 1959 when the circuit was built was 57% but had grown to 83% in 2001. While the utility was able to increase capacity on the circuit with some extraordinary methods, the normal book rating actually decreased with respect to time because of the increasing loss factor. Load shape may also play an important role from the standpoint of emergency ratings. If the daily load cycle is such that the load during portions of the day (typically at night) is lower than at other times of the day (typically mid-afternoon), short duration emergencies can vary greatly. This is illustrated in Figure 3.6-9, where the normal ampacity (1.0 per unit), A, is determined for a peak temperature of 90°C, and two 4-hour emergency ratings are determined:

• Emergency Rating B: The peak temperature is 105°C with a rating of 2.6 per-unit (as compared to the normal rating). This emergency starts going into a lowload period, so the pre-emergency load temperature is about 73°C.

• Emergency Rating C: The peak temperature is also 105°C with a rating of only 1.3 per-unit (as compared to the normal rating). This emergency starts going into a peak load period, so the pre-emergency temperature is about 85°C. Figure 3.6-7 Ampacity as a function of loss factor.

Figure 3.6-8 Graph of load profiles showing the same peak current with different load and loss factors.

The above example illustrates that considering the load shape for emergency ratings is important. Dynamic ratings (see Section 3.8) is a main benefit for this type of analysis in optimizing—and generally increasing—the current carrying capacity of an underground cable circuit.

Figure 3.6-9 Temperature plots and ratings as a function of rating starting time.

3-37


3.6.4

Temperature Monitoring

Using Thermocouples Temperature measurements are an important part of verifying assumptions when calculating ampacity and studying ways to improve ratings. Ideally, one would want to measure the cable conductor temperature—the hottest location in the cable system—to be sure that insulation temperature limits are not exceeded. However, because the conductor is energized, this is typically difficult to do. Instead, it is common to measure the temperature on the outer surface of the cable either on the pipe coating of a pipe-type cable or the jacket of the other cable types. For conduit installations, temperatures might be measured in the conduits.

To perform these measurements, thermocouples are often used. Thermocouples are temperature sensors based on the principle that when two dissimilar metals are joined, a predictable voltage will be generated that relates to the difference in temperature between the measuring junction and the reference junction (connection to the measuring device). The types of metals that are used depend on the application (temperature range, location, cost, etc.). There are varieties of thermocouple types (T, F, N, J, etc.). For cable-related measurements, “Type-T” thermocouples are most often used because they have a temperature range most closely matched to typical cable operating temperatures. The Type-T thermocouple has a blue outer jacket in the United States, France and the United Kingdom (up until 1993) or dark brown outer jacket in the United Kingdom (since 1993) and Germany. Inside, the thermocouple wire consists of a copper electrode (positive, +) and a constantan electrode (negative, -). Each electrode has an insulating coating that varies in color depending on the country of origin (United States is blue on the positive and red on the negative; the United Kingdom is white on the positive and blue on the negative (pre-1993) or brown on the positive and white on the negative; France is yellow on the positive and blue on the negative; and Germany is red on the positive and brown on the negative). When connecting thermocouple wire to a meter, data logger, or other measuring device, it is important to verify that the polarity is correct. Otherwise, the schematic will essentially create three thermocouple junctions in series (rather than one), which could provide misleading results. Also, the thermocouple wire or extension grade thermocouple wire must also be run from the measurement location all the way to the test instrument. A thermocouple junction is created by joining the copper and constantan wires together as shown in Figure 3.6-10. The junction can be left bare, which minimizes thermal capacitance and increases temperature mea-

3-38


surement response. However, depending on the environment, the junction may need to be coated or soldered to protect the thermocouple junction from corrosion, etc. Laboratory-grade thermocouples are typically welded together. A thermocouple has an accuracy of typically less than 1 C°. A key advantage to thermocouple temperature measurement is that the wire itself and the equipment to measure thermocouple temperatures are both relatively inexpensive and minimal training is required to use the technology. Several companies including Telog Instruments, Omega, and Fluke make data loggers that cost less than US $1000 to read and possibly record thermocouple temperatures. Battery-powered recorders can log data for 6–18 months, recording temperatures every 15 minutes for an extended period. Once suspected or known cable circuit hot spots are identified, low-cost thermocouples and data loggers may be placed at these locations and checked periodically, particularly during periods of high load. By comparing measured temperatures with those predicted using load history and the equivalent thermal circuit from ampacity calculations, it is possible to evaluate the assumptions used in ampacity calculations. From an operations standpoint, monitoring the cable temperatures gives some assurance that the cables are not exceeding their allowable temperature during typical load cycles. The main disadvantage to thermocouple measurements is that they only take a temperature measurement at one location. It is, therefore, possible to miss hot spots if they are not already identified. Also, the practical lead length limit of thermocouples is about 300 m (1000 ft), and each thermocouple requires its own pair of wires to

Figure 3.6-10 Thermocouple wires (copper and constantan with U.S. color scheme – left) and completed junction (right).


make a measurement. Therefore, it is difficult to instrument more than a few tens of locations. Distributed Fiber Optic Temperature Sensing (DFOTS) Distributed fiber optic temperature sensing (DFOTS) uses a specialized optical time-domain reflectometer (OTDR) to measure the temperature along a multimode optical fiber. The process works by taking advantage of temperature-dependent reflections (called “backscatter” based on the Raman Effect) in the fiber. The special OTDR instrument, such as York Sensors (Sensa) DTS80 or SensorTran’s Model 5000 (see Figure 3.6-11), records the magnitude of the reflection (proportional to temperature) and the time for reflections to return after sending an incident 1080 nm laser pulse into the fiber, which, when combined with the fiber’s propagation velocity, gives the distance to the measurement location. By successively sending light pulses into the fiber, the special OTDR can scan the entire fiber and obtain a temperature trace along the fiber with a spatial resolution of approximately 1 m and a temperature accuracy of 1°C. The obvious advantage of DFOTS is that a continuous end-to-end temperature measurement is possible, allowing the ampacity study to reveal all of the hot spots along the cable route. Later, these hot spots could be instrumented with thermocouples for extended temperature measurements at key locations.


buried system is impractical unless there is a conduit (communications or power) within a meter or so of the energized cables in which the fiber may be installed. An example of fiber that might be installed directly buried or in a conduit is shown in Figure 3.6-12. The fiber optic cable typically consists of four to six 50 x 125 μm fibers, each with a 900 μm tight buffer (only 1 or 2 fibers are needed, but some may be damaged during installation so spares are desirable), Kevlar strength members to improve pulling strength (usually only 3000N, 675 lb), and a fire-retardant PVC jacket. Some XLPE cable manufacturers are embedding optical fibers under the jacket of the cable to facilitate temperature measurements (Figure 3.6-13). Since this is physically closer to the conductor—ultimately where we would like to know the temperature—this has some advantages. A disadvantage of DTS equipment is the cost of the electronics to measurement the fiber temperature, which may be upwards of US $60,000. Also, the equipment is

Depending on the configuration of the fiber (number of splices, etc.) and the temperature measurement mode (single or double ended), a fiber length of 5–10 km may be scanned. Equipment is also available that works with single-mode fiber and can measure up to 30 km. However, this equipment suffers from both lower spatial resolution (4–10 m) and lower accuracy (2–3°C). All fiber test loops are limited by the losses in the system, so fusion splicing is the preferred method for joining fibers. Fiber used for DTS measurements is typically installed in a parallel conduit or directly buried alongside an existing cable or pipe. Retrofitting a fiber on a direct-

Figure 3.6-11 Distributed temperature sensing equipment.

Figure 3.6-12 Optical fiber cable used for DTS measurements.

Figure 3.6-13 XLPE cable with integrated optical fiber under the jacket. 3-39


not well suited for operation in the field on an extended period of time, which makes “spot” measurements or extended measurements in manholes or stations difficult. Most of the equipment has an operating range of 10–35°C, which is fairly limited in particularly warm or cool climates. 3.6.5

Ampacity Audit

An “ampacity audit” involves investigating ampacity for a cable circuit by applying the various techniques described in this chapter. The basic concepts include performing a soil thermal survey to determine soil characteristics and ambient temperatures, evaluating load history, and then calculating ampacity. If AEIC guidelines are being followed on a circuit that previously had used assumed soil parameters, the 10°C increase in conductor temperature by itself generally allows a 20% increase in ampacity.


constructed using an alcohol-water or ammonia-water mixture in a partially filled copper tube. A partial vacuum is drawn on the tube to adjust the vapor pressure to the operating temperature range for the particular application. The heat pipe is then installed at an angle with the low point installed near the heat source (cable, steam main, etc.). Heat from the source is absorbed by the liquid alcohol-water or ammonia-water solution, causing a phase change to vapor, which rises, carrying the heat away. The gaseous vapor then condenses back to a liquid away from the hot spot and then drains back to the hot spot location. This continuous process removes heat from the location. The number and installation geometry of the heat pipes are typically designed by a specialist. An example of a heat pipe installation to mitigate the effects of crossing cable circuits is shown in Figure 3.6-14.

The ampacity audit is geared towards verifying the ampacity by whatever means are available and assessing which locations along the route limit the overall circuit ampacity. This might possibly include obtaining a DFOTS temperature trace for the route to find hot spots, or looking at route plan and profiles to find limiting installation conditions. These “hot spots” would then be investigated further to see how they might be mitigated. 3.6.6

Remediation of “Hot Spots”

Remediation of hot spots is sometimes possible if the scope of the hot spot is limited. If the hot spot is the result of overburden, or increased burial depth, it might be possible to remove some of the overburden above the cables. This reduces the thermal resistance to heat leaving the cable and may improve ampacity. Poor soil thermal resistivity can often lead to hot spots, particularly if a low quality thermal backfill was used – or not backfill at all. A hot spot may be eliminated or partially mitigated by excavating around the cables and installing a good quality thermal backfill. This will improve the heat transfer characteristics away from the cable, lowering the operating temperature for a given load condition. Heat Pipes In extreme cases, usually where one circuit experiences a hot spot from mutual heating of another circuit, the installation of heat pipes can help. The heat pipe is a passive device that takes advantage of the heat of vaporization to remove heat from a location. A heat pipe is

3-40

Figure 3.6-14 Heat pipes being installed to mitigate a hot spot where a steam main crosses a pipe-type cable.

3.6.7

Active Uprating

The following methods are mostly applicable to pipetype cables, although there are applications that could extend to extruded or self-contained cables.


Fluid Filling Gas-filled pipe-type cables may be uprated slightly by replacing the dry nitrogen gas with a dielectric liquid such as polybutene or alkylbenzene. Since a liquid is a more efficient heat transfer media than a gas, fluid-filling alone provides a small ampacity improvement (~23%). However, this allows for additional uprating methods to be applied. Fluid Circulation Fluid circulation is a relevant uprating technique when a short section, relative to the overall circuit length, is limiting the pipe-cable rating. By circulating the dielectric liquid within the cable pipe, the heat generated in the hot section will be transferred to other portions of the route, mitigating the hot temperatures at that location. One requirement for this to be implemented is to have a fluid return pipe or a parallel cable pipe that will permit a continuous circulation path as shown in Figure 3.6-15. Flow rates may be up to 800 liter/min (200 gpm), but slow circulation with only 20 liter/min (5 gpm) may be used for small hot spots or where the fluid viscosity limits the flow rate.

If no fluid return pipe or parallel cable pipe is present, fluid oscillation may be used. In this configuration, fluid is moved through the pipe at 4–40 liter/min (1–10 gpm) and cycled between the 4,000–11,000 liter (1000–3000 gallon) fluid reservoirs at either end of the pipe circuit. Major considerations for fluid circulation are the free area in the pipe and the viscosity of the dielectric liquid used in the pipe. As a result, the pressure rise when pumping dielectric fluid through a pipe could be too excessive for practical uses. If the flow rate is limited to a value below what is necessary to mitigate a hot spot, circulation may not be possible to mitigate a hot spot; the utility might consider changing to a lower viscosity dielectric liquid or re-examining pressure rise limitations.


The basic principle of fluid circulation is based on work done by CIGRÉ and discussed in Electra (CIGRÉ 1979). The approach is to evaluate sections of the fluid circulation route that have basically the same characteristics and then use boundary conditions to match the flow rate from one section to the next. Dielectric liquid (or water in parallel circulation/cooling tubes) is relatively noncompressible, although the density varies with temperature around the circulation loops. To consider this, the dielectric fluid characteristics—density and specific heat—are adjusted for each section that is being modeled. As fluid circulates through the pipes, the temperature of the fluid leaving one section is assumed to be the temperature entering the next section, satisfying the boundary conditions. To model each section, the “un-cooled” (temperature that would result absent of any cooling or circulation movement in the pipes) temperature is calculated based on circuit loading, the cable construction, and installation conditions at each section. Then, heat absorbed or removed would cause increases or decreases in the dielectric fluid temperature as it moves through the pipes. The temperature change with respect to distance is of the form shown in Equation 3.6-2. T ( x ) = TUN −COOLED − K ⋅ A ⋅ exp( P ⋅ x )

3.6-2

In the equation, x is the distance, K is a value proportional to the maximum change in temperature possible for a section of infinitively long length, A is a value relating the mutual heating affects among the pipes (either cabled or fluid return), and P is a value characterizing the rate of temperature change as air moves along the pipe section. There is one exponential term for each pipe in which fluid is circulating.

Figure 3.6-15 Example pipe cable dielectric fluid circulation loop with heat exchangers.

3-41



The “un-cooled” temperature is the steady-state temperature of the dielectric liquid inside the cable pipe that would result if the loading remained fixed on the energized cables and no fluid circulation was in place. As the flow rate is reduced, the value of K approaches zero. As the flow rate increases, the value of K approaches the difference between the inlet temperature of the dielectric liquid and the uncooled temperature for a given section. Changes in dielectric liquid temperature as it passes through the cable pipes provide an indication of the heat being removed in each section based on the mass flow through the section as defined by Equation 3.6-3. •

m = ρ ⋅ A ⋅υ

3.6-3

from the cable pipe, passed through a heat exchanger to remove heat, and then reintroduced to the cable pipe. This has the potential of increasing the ampacity by 50– 70%, although the cost and maintenance of these active systems can be high. Considerations for Active Uprating With fluid circulation or forced cooling in pipe-type cables, there are some cautions associated with using these uprating methods. Pressures along the hydraulic loop may become excessive as a result of hydrostatic head pressure, fluid flow restrictions near joints, and cross-over plumbing between feeders and fluid return pipes. The high pressures could cause the termination housing to fracture, potentially resulting in a cable failure, dielectric fluid leak, and fire.

Where: •

m is the mass flow rate in kg/sec. ρ is the density in kg/m3. A is the free area within the pipe in m2. υ is the velocity in m/sec. The heat removed, Watts, in a given section can then be found from Equation 3.6-4. •

q = m⋅ CP ⋅ (TOUT − TIN )

3.6-4

Where: CP is the specific heat in kJ/kg-°C. TOUT and TIN represent the outlet and inlet temperatures, respectively, of the dielectric liquid in a given section. By knowing the net heat absorbed or lost in a given section and the length of that section, it is possible to evaluate the net heat removed (or gained) in a given section. For a forced-cooled system (described next), the net heat gained by the system will assist with sizing the forced-cooling plant and heat exchangers. Fluid circulation could be applied to extruded dielectric or self-contained liquid-filled cables by installing parallel water cooling pipes next to the cables and then circulating water through those pipes. Although technically feasible, this is not often done. In addition, some utilities such as National Grid in the United Kingdom circulate the dielectric liquid in the fluid channel of self-contained liquid-filled cables. Again, this is relatively rare. Forced Cooling (Water or Oil) Forced cooling is an extension of fluid circulation. The main difference is that, rather than just moving heat around from “hot spots” to “cold spots” in the cable route, the dielectric liquid (or water in the case of water cooling of extruded or self-contained cables) is diverted

3-42

Pressure drop along long circulation loops must be considered. The degree of snaking of the cable phases within the pipe can affect the fluid flow and pressure drop, potentially limiting the flow rate. The pressure drop as a function of length can found by evaluating the Darcy-Weisbach equation, as shown in Equation 3.6-5. dP ν ⋅V 2 = f 2 ⋅ Dh dL

3.6-5

Where: f is the friction factor, empirically determined based upon the Reynolds Number cable-topipe inner diameter ratio. γ is the density, kg/m3. V is the flow velocity, m/sec. Dh is the hydrostatic diameter, m. The pumping plant, in particular the fluid circulation pump, must be able to accommodate the circulation pressure. The density and viscosity of the dielectric liquid will impact the allowable pressure drop, in addition to the free area within the pipe and the degree of cable snaking. On long circulation loops, multiple loops may be needed with intermediate fluid circulation stations to limit the pressure drop. Complex control systems, particularly in the event of a cable failure, must also be developed to manage the various cooling loops and to stop fluid circulation in the event of a fault. Fluid circulation is often considered for the buried pipe sections. However, when forced cooling is used, the riser sections—lengths of pipe between the trifurcator and termination—may become limiting and could require specialized plumbing to allow circulation in these areas. Diffusion chambers may also be necessary to avoid damaging the outer layers of insulation. A factor to consider for uprating older pipe circuits, where the riser


section may be limiting, is that installation of a diffusion chamber on a riser that is not so equipped can be difficult. This is because working “close in” on the riser pipe would be difficult with the cable already in place, and removing and installing a new termination to put in the diffusion chamber may be impractical. 3.6.8

Shield/Sheath Bonding Scheme

As discussed to some extent in Section 3.4, there are three methods for grounding the shield/sheath on singleconductor (extruded dielectric, self-contained fluidfilled) cable systems: multipoint bonding, single-point bonding and cross-bonding. Multipoint bonding involves tying the shield/sheath connections together and to local ground at both terminals and usually at intermediate manholes, resulting in a path for induced circulating currents but with minimal induced voltages. Single-point bonding involves grounding the shield/sheaths at only one location along a given section, preventing circulating currents but leaving the other end un-grounded where a standing voltage will appear. Cross-bonding involves dividing the cable sections into groups of three minor sections that are close to the same length and transposing sheath connections at the one-third and two-third locations, thereby eliminating net circulating currents and minimizing induced voltages. Generally, single-conductor transmission cables are designed with cross-bonding or single-point bonding to minimize shield/sheath circulating currents in the presence of relatively high phase currents. The one exception to this common practice is submarine cable installations, where multipoint bonding of the sheath is almost mandatory because of the long installation lengths and typically wide phase spacing. Contrary to transmission practice, most distribution circuits are multipoint bonded where the utility transformer and customer service panel are both grounded for safety and so the neutral can carry imbalance currents. The circulating currents in multipoint bonded systems generate additional I2R losses (heat) in the shield/sheath that impacts ampacity. Multipoint bonding systems generally have about 2030% lower ampacity than single-point bonded or crossbonded systems constructed with similar cable sizes. If the ampacity audit reveals that a circuit has lower ampacity than desired and happens to be multipoint bonded, the shield/sheath connections might be reconfigured for sectionalized single-point bonding or crossbonding to eliminate the circulating current and gain a significant improvement in ampacity. The reconfiguration may require changing out some or all joints since


the joints must have shield interrupts to provide for single-point bonding or to facilitate transposing the sheath connections for cross-bonding. If a system that was previously multipoint bonded is being reconfigured for single-point bonding, a ground continuity conductor should be installed to provide a low impedance path for fault current; the shield breaks will otherwise block the flow of fault current. Also, single-phase or three-phase link boxes or cross-bonding boxes will be needed. If uprating using a reconfigured sheath bonding scheme is being considered, and utility practice is typically with multipoint bonding systems, care should be used to clearly mark all manholes where standing voltages may appear. A shield that is not grounded locally, but is connected to ground at the adjacent manhole, may experience a significant voltage rise with respect to local ground during nearby system fault conditions from a combination of induced voltages and system potential shifts. This is not a phenomenon peculiar to single-point grounded arrangements, as any shielded cable is susceptible when the shield is connected to a remote ground yet remains ungrounded locally. The remedy for this situation is to provide secure, temporary shield grounding as appropriate. This has always been a recommended practice. This is particularly important when working on a de-energized single-point bonded circuit that parallels an energized circuit, since the parallel circuit can induce a voltage. Also, single-point bonded or cross-bonded cable systems require periodic maintenance to check the jacket integrity and ensure that there are no unexpected current circulation paths. Fault location efforts may also be complicated by single-point bonded or cross-bonded sheaths, possibly requiring that the bonding connections be reconfigured during cable fault location. Jacket fault location in duct bank installations is difficult unless the ducts are under the water table. Although not technically necessary, many cross-bonded cable systems are installed with a parallel ground continuity conductor. Induced currents in this parallel conductor can generate enough I ^ 2 x R losses to produce mutual heating that can affect ampacity of the phase conductors. 3.7


3.7.1

Introduction

In contrast to uprating, which is generally defined as improving the capacity of existing equipment, upgrading considers using available infrastructure to economically put in new cables, replacing existing conductors. This section discusses some of these issues.

3-43



A basic assumption for this section is that the cable system is either pipe-type or a duct installation. Reconductoring a direct buried cable is impractical and really should be considered a new installation, along with the installation of a parallel circuit when there is no existing infrastructure (pipe or conduits). Neither of these cases is covered by this chapter. One possible scenario might be reconductoring one of two parallel cable circuits. The condition of the older circuit should be evaluated to see if loss of life or higher operating temperatures might affect reliable performance. The upgrading topics in this guidebook would apply to the scenario, although the details of evaluating the impact on the older circuit or other connected equipment are beyond the scope of this chapter. 3.7.2

Larger Conductor Sizes

The main issue with considering a larger conductor size is whether the cable will fit within the same conduit or pipe. Paper-insulated insulation thicknesses are fairly standardized based upon voltage class, but the designer might consider using a larger conductor size combined with a switch from conventional Kraft paper insulation to laminated paper polypropylene paper (PPP) insulation, which has a higher dielectric strength and, therefore, a lower insulation wall thickness. With pipe-type cables, the issue is to maintain sufficient clearance in the cable pipe. The traditional guideline for new pipe installations is to have at least 12.5 mm (0.5 in.) of clearance in the pipe, as determined by Equation 3.7-1. However, with older pipes, where upgrading would more often be considered—either pipes that have cables to be replaced or old but unused empty pipes that might have new cables installed—a minimum clearance of 25 mm (1 in.) is often considered prudent to allow for the possibility that overburden or settling may have increased the ovality of the pipe that possibly could affect a successful installation. C=

D 1 ⎛ d ⎞ − 1.366d + ( D − d ) 1 − ⎜ ⎟ 2 2 ⎝ D−d ⎠

diameter of the conduit and the outer diameter of the cable. Again, it is typical to have 12.5–25 mm (0.5– 1.0 in.) of clearance in the conduits. If cables are not already in the conduits, a mandrel through the conduits should be used to check the maximum size cable that can pass through the pipe or conduit. For extruded cables in particular, the construction of the metallic moisture barrier and metallic shield could be adjusted to allow for a larger cable. As an example, Commonwealth Edison (now ComEd, An Exelon Company) removed 138-kV paper-insulated cables from ducts to be replaced by cross-linked polyethylene cables. If the typical 3.2 mm (0.125 in.) lead sheath moisture barrier and full-wall 138-kV insulation 21.6 mm (0.85 in.) were used, it would have meant the standard XLPE cable design could not fit in the existing conduits. Instead, the installation included a reduced insulation wall (16.5 mm, 0.65 in.), a copper laminate tape with copper shield wires, and a reduced jacket wall (as compared to typical industry practice for that size cable), greatly reducing the outer cable diameter and allowing the cable system to fit in the conduits. The relative effect of reconductoring on ampacity is discussed in Section 3.4. 3.7.3

Cupric Oxide Strand Coating

Some cable manufacturers have investigated using cupric oxide coated strands to make conductors. By coating the strands with cupric oxide, each strand has a slightly increased resistance (in the radial direction) to each adjacent strand. This improves the skin and proximity effect factors of the conductor—reportedly down to 0.3 for both values—over conventional copper stranded insulations. This reduction in ac incremental losses significantly improves the ac to dc resistance ratio and ampacity. To illustrate, the pipe-type cable example

2

3.7-1

Where: D is the inner diameter of the cable pipe. d is the diameter of the cable over the insulation, plus 1.5 times the height of a skidwire, all values in inches. Figure 3.7-1 shows the clearance in a pipe-type cable. For extruded or self-contained cables where normally a single phase would be installed in each conduit, the clearance is simply the difference between the inner

3-44

Figure 3.7-1 Clearance in a pipe-type cable.


in Appendix 3.1 would show an increase in ampacity by almost 3% if a cupric oxide strand coated conductor were used. 3.7.4

Voltage Upgrading

Voltage uprating, possibly combined with an increase in conductor size, would significantly improve the power transfer limits. As an example, an 8-in. cable pipe that is typically used for 138-kV cables with 11.2 mm (0.44 in.) of Kraft paper insulation might be reconductored with 11.4 mm (0.45 in.) of PPP insulation, allowing an increase to 230-kV cable with virtually no change in the outer cable diameter and a 67% increase in power transfer. Additional improvements in capacity might be possible if a larger conductor size can also be used. Section 3.2 lists typical insulation thicknesses for the various cable constructions and insulation materials.


• Sumitomo: 100 m of 66-kV cable with 1000 A. • Southwire: 30 m of 12.5-kV cable with 2600 A (operated in parallel to an overhead line on Southwire's property).

• NKT: 30 m of 30-kV cable with 3000 A (utility substation).

• Condumex: 5 m of 2000 A (Condumex test facility). • Nexans / American Superconductor / LIPA: 610 m circuit 138-kV cable with 2510 A is being developed for a new installation on Long Island.

The main issue with voltage upgrading is that, in addition to possibly significant costs in new cables, several pieces of substation equipment must also be replaced to accommodate the new voltage level. This is sometimes not so significant if the higher voltage level being considered for voltage upgrading already exists within both terminals. Otherwise, the cost and effort generally make voltage upgrading infeasible. 3.7.5

Superconducting Cables

At the time this chapter is being prepared, superconducting cables are largely in the research stage. Limited sections of cable have been installed in controlled settings (e.g., parallel to a 100% redundant overhead line, in a “laboratory” setting, or in a nonessential capacity underground). Several high-temperature superconducting (HTS) cable projects have been demonstrated largely with U.S. Department of Energy funding, using either warm or cold dielectric technology (Figure 3.7-2). As the names imply, the “warm dielectric” cable uses insulation that is at or above room temperature to support the energized line-to-ground voltage, while “cold dielectric” cable utilizes cryogenic (liquid nitrogen ~80°K) insulating medium. Examples of recent research in superconducting cables are summarized below: 1996-1999

• Pirelli/EPRI: 50 m of 115-kV cable with 2000 A. • Sumitomo/TEPCO: 30 m of 66-kV cable with 1000 A. 2000-2002

• Pirelli/Detroit Edison: 130 m of 24-kV with 2500 A (system could not be energized because of a vacuum leak in the cryostat).

Figure 3.7-2 Examples of superconducting cables (courtesy of American Superconductor Inc.).

3-45


While favorable results have been observed, the available technology is not yet practical for typical transmission voltages, and the operating lengths have not been increased sufficiently to allow “transmission” at what have typically been considered medium-voltage levels (e.g., transferring bulk power at high-current/low-voltage). At this point, superconducting cables do not yet offer a commercially viable means for uprating existing transmission circuits, though this is likely to change within the next decade.


tion aging and “acceptable loss of life” has not often been considered for underground cable ampacity. The main benefit to dynamic ratings is the ability to track the cables’ temperatures with time and changing load conditions and then base emergency ratings on the actual, rather than assumed, pre-emergency temperatures. The benefits of this type of evaluation were illustrated in Section 3.6.3 and Figure 3.6-9. 3.8.2

3.8


3.8.1

Background

As discussed in Section 3.3.1, the thermal time constants of underground transmission lines are significantly longer than those of overhead lines and power transformers. This is a result of the thermal inertia (or heat capacitance) of the earth that surrounds the cables. As a result of this thermal inertia, the dynamic rating of underground transmission lines significantly exceeds their steady-state ratings, provided that there are significant variations in the line loading. Conversely, the dynamic rating of underground transmission lines is not much higher than their steady-state ratings if the lines are consistently loaded near their steady-state ratings. The term “dynamic rating” means the present rating of a line, taking into account its load history and real-time measurement of parameters (mainly ambient earth temperature). In actuality, the “normal” ampacity of a circuit does not change, except for changing ambient temperature, since it is generally based on an assumed daily loss factor and installation conditions. Therefore, a “dynamic” normal rating remains relatively constant unless some decision about future loading is evaluated. Predicting future loading patterns is difficult since unplanned system changes may affect loading patterns, but the use of predicted load patterns, usually based on utility SCADA systems, does allow for some future load estimations (usually limited to 24 hours). Tracking the cable conductor temperature is the main goal of dynamic ratings, since this is ultimately what limits the power transfer on the circuit. For paper-insulated cables, tracking the conductor temperature also permits an assessment of insulation aging and ultimately the life of the cable system. EPRI funded a detailed investigation of paper-insulated pipe-type cables in the 1990s. Transformer ratings have been based on a variety of factors including the insulation aging and loss-of-life criteria. However, application of insula-

3-46

EPRI Dynamic Ratings on Cables

Development of the EPRI Dynamic Thermal Circuit Rating (DTCR) system was started in 1991 with advanced models for overhead transmission lines, power transformers, and underground cables. The cable model used in DTCR was initially based largely on the underground cable ampacity program “Alternative Cable Evaluation (ACE)” in the EPRI Underground Transmission Workstation (UTW) that was started in 1990. ACE was an off-line ampacity program that would determine normal and emergency ratings based on userspecified input data. The ratings generated by ACE were similar to what many utility engineers refer to as “book ratings” in that they were static ratings based on assumptions (usually worst-case) and then tabulated for reference by engineers and operators. As the utility industry changed dramatically during the 1990s, toward achieving higher profits, there was increased pressure to get more capacity from existing equipment while minimizing new construction whenever possible. To this end, DTCR was developed to take realtime data from “off the shelf ” monitoring hardware, and determine optimal ratings (not worst-case) for the conditions at the time the ratings were performed. Although this required some philosophical changes at utilities to consider circuit ratings as moving, changing entities rather than fixed parameters, the overall benefit was to demonstrate a greater capacity in transmission assets, including underground transmission cables. The general theory behind DTCR is that, probabilistically, there are relatively rare circumstances where the worst-case rating conditions occur at the same time that the greatest possible circuit loading is required or desired. As a result, by evaluating the ratings on a realtime basis using actual, rather than worst-case conditions, the real-time rating is much higher and the allowable power transfer is greater. This is illustrated graphically in Figure 3.8-1. In Figure 3.8-1, there is a relatively small region (rating regime) where the dynamic rating distribution overlaps the loading, indicating that at most times, the dynamic



Figure 3.8-1 Probabilistic view of dynamic ratings and actual circuit loads.

rating is greater than the “book” ampacity. DTCR allows the circuit to operate closer to the limit by performing a real-time rating evaluation using measured (rather than conservative or worst-case estimates) parameters. Cable Models One approach to dynamic ratings on cables—that used in the Underground Cable Module in DTCR—is based on the paper by Neher and McGrath (1957), and on the International Electrotechnical Commission (IEC) Publications 287 and 853 (International Electrotechnical Commission 1982, 1989). These same calculation methods are used in off-line rating tools such as EPRI’s UTWorkstation ACE program.

The numerical technique used in DTCR to track conductor temperatures is an “additive wave method,” whereby the temperature response to a constant heat input is tracked into the future. For cables, DTCR looks at “small” intervals (< 0.5 hours), over which the load can be treated as constant. The temperature response to the load with respect to time is a function of the heat input to the cable (either positive for increasing load or negative for decreasing load). Each time the load changes, a new temperature response “wave” is launched. As the load changes from interval to interval, the total temperature response at a given time is the summation of all the previous temperature response functions from each change in heat from the cable (as a function of load and the change in resistance with temperature). This basic concept is described in a paper by Neher (Neher 1963) and illustrated in Figure 3.8-3 with an arbitrary load. The numerical calculations are based on equations from IEC-287 and IEC-853 and make use of attainment fac-

tors for changes in heat output from the cables. The cable temperature changes with respect to time and changing load based on the thermal response of the cable and environment. The cable or pipe temperature response is defined by Equation 3.8-1.

θCable (t ) = Wi ⎡⎣ RA (1 − exp( −at ) ) + RB (1 − exp( −bt ) ) ⎤⎦ 3.8-1

Where: Wi is the heat output from the cable. RA, RB is the thermal resistance at steady state. a, b are time constants representing how the temperature changes with respect to time for a given heat input. For the temperature response of the environment, there are two models in DTCR: one that assumes all circuits/cables carry identical currents, and a second where two circuits may carry unequal loading. Equal Loading For the case of two three-phase circuits of extruded or self-contained cable, all six (6) cables are assumed to carry the same load even if the circuits are electrically disconnected. The temperature rise above ambient from ac loading is described by Equation 3.8-2, utilizing exponential integrals, for the cable that is identified to be the hottest cable in the trench.

⎡ ⎛ D2 ⎞ ⎛ L2 ⎞ ⎢ −Ei ⎜ − earth ⎟ + Ei ⎜⎜ − ⎟⎟ ⎜ 16δ t ⎟ ⎝ δt ⎠ ⎝ ⎠ ρs ⎢ θ HottestCable (t ) = Wi ⎢ ⎛ rj 2 ⎞ ⎛ r ' j2 4π ⎢ 6 ⎜ ⎟ ⎜− + − − + Ei Ei ⎢ ⎜ 4δ t ⎟ ⎜ 4δ t ⎢⎣ j = 2 ⎝ ⎠ ⎝

∑

⎤ ⎥ ⎥ ⎥ ⎞⎥ ⎟⎥ ⎟⎥ ⎠⎦ 3.8-2

3-47



Where: is the heat generated by each cable. Wi Ei is an exponential integral. Dearth is the earth diameter for the cable or conduit. L is the burial depth for the “hottest” cable among the group. is the actual distance between the hottest rj cable and adjacent cables. is the distance between the hottest cable and r’j the image of adjacent cables. The watts generated by each cable, Wi, are identical for all cables in the group. Unequal Loading For the case of two circuits with unequal loading, the heat output from the second circuit is defined separately from the first circuit. The mutual heating effects with respect to time are then evaluated as shown in Equation 3.8-3.

⎡ ⎛ D2 ⎞ ⎛ L2 ⎞ ⎢ − Ei ⎜ − earth ⎟ + Ei ⎜⎜ − ⎟⎟ ⎜ ⎟ ⎝ δt ⎠ ⎝ 16δ t ⎠ ρs ⎢ θ Pr imaryCable1 (t ) = Wi1 ⎢ ⎛ rj 2 ⎞ ⎛ r' 2 4π ⎢ 3 ⎟ + Ei ⎜ − j ⎢ + − Ei ⎜ − ⎜ 4δ t ⎟ ⎜ 4δ t ⎝ ⎠ ⎝ ⎣⎢ j = 2

∑

+Wi 2

⎤ ⎥ ⎥ ⎥ ⎞⎥ ⎟⎥ ⎟⎥ ⎠⎦

⎛ r2 ⎞ ⎛ r ' 2 ⎞⎤ ρs ⎡ 6 ⎢ − Ei ⎜ − j ⎟ + Ei ⎜ − j ⎟ ⎥ ⎜ 4δ t ⎟ ⎜ 4δ t ⎟ ⎥ 4π ⎢ j = 4 ⎣

∑

⎝

⎠

⎝

⎠⎦

3.8-3

Where: Wi1 , Wi2 are, respectively, the heat generated by each cable in circuit 1 and circuit 2. Cable Dynamic Rating Model The combined effects of the two temperature response functions gives the complete temperature response of the cable conductor to a given cable heat output. When there is changing load, typical of most transmission circuits, the accumulated temperature responses for each change in load will give the conductor temperature with respect to time. The general procedure and flow of the DTCR cable model are illustrated in Figure 3.8-2.

Graphically, the changing load is illustrated in Figure 3.8-3, where the top graph shows an arbitrary load pattern, with loads that are both increasing and decreasing over time. The bottom graph shows the individual temperature response waves to each change in load (fine lines) and the summation of all the temperature response waves (dark line). Also shown in the graph is the addition of the dielectric temperature rise, which remains constant with respect to time as long as the lineto-ground voltage remains constant (this is an assumption). As compared to other modules (overhead lines and power transformers) within DTCR, the cable model requires extensive computations since the long earth thermal time constant requires “looking back” hundreds of hours in the loading history. As a result, ratings are normally not performed more often than once every 15 minutes or so. Fortunately, the long thermal time

Figure 3.8-2 General flow of information in DTCR cable model. (“STE” means “Short Time Emergency” rating, and “LTE” means “Long Time Emergency” rating.)

3-48


constant also means that there are limited temperature changes over that time. Because of the considerable heat storage capacity of underground cables, the operating power levels prior to a contingency loading have a large effect on the actual thermal behavior during emergency loading events. EPRI’s DTCR technology allows continuous monitoring and establishment of such power equipment’s actual pre-contingency thermal state. As a result, load shedding during emergencies can often be avoided and capital investment in new equipment postponed. 3.8.3

Benefit of Dynamic Ratings

The thermal rating of underground cables is traditionally calculated using worst-case seasonal loads and soil temperatures. Underground cable thermal parameters are based on manufacturer’s data, installation assump-


tions, and industry standards. Rating calculations are typically performed “off-line” using worst-case assumptions to derive seasonal limits (maximum soil temperature, worst-case loss factors). With dynamic ratings, actual soil temperatures and load data are used in place of worst-case approximations, allowing higher operating limits under most conditions and more accurate thermal modeling under all conditions. Other than cable parameters and configuration, dynamic thermal rating calculations for underground cable require soil characteristics and temperature. The equipment parameters can be verified by comparing calculated to measured equipment temperatures, which in the case of high-voltage underground cable is the earth interface temperature, or a more general comparison between a measured temperature and calculated temperature in a location near the power cables. The measured temperature from a thermocouple or DFOTS can be compared to the dynamic rating system-calculated temperature, as described in Section 3.4.7. DTCR Circuit Ratings The DTCR software allows the user to calculate realtime equipment temperatures, multiple thermal ratings, and “remaining-time” (or “Time to Temperature Overload,” TTO) during emergency loadings, given real-time load and ambient ground temperature for underground cable circuits. “Circuit” ratings, rather than “equipment” ratings, are possible by modeling all of the power equipment on a given circuit (e.g., series-connected transformers, overhead lines, cables, etc.), or in the case of cables, each unique installation section along a given route, and then letting DTCR calculate ratings for all equipment and locations on a circuit. Then, DTCR selects the lowest rating for each category (normal, LTE, STE) and reports these values as circuit ratings. Utility Implementation of Dynamic Ratings Some dynamic rating systems interface directly with monitoring hardware. This has some disadvantages:

• The hardware is probably redundant to monitoring already done by the utility.

• The hardware is sometimes very specialized, meaning that the original vendor must be recalled for maintenance and repairs, usually at a high cost.

• Telemetry for any monitoring outside of a substation is often complex, expensive, and prone to interruption. Figure 3.8-3 “Additive Wave” model for temperature tracking in underground cables.

• The computer system used to perform rating calculations, by virtue of the direct connection to the moni-

3-49



time input data file on the dynamic rating system computer through use of “Network Access calls” or other operational programs.

toring hardware, must be located in the field where weather and security are difficult to manage.

• Any changes to the hardware usually require a

• The real-time input data on the dynamic rating sys-

new custom-designed interface to collect the monitored data.

tem is read from the ASCII file created by a SCADA Network Access call.

• There is an issue of getting calculation results from

• A specific “SCADA” input file containing real-time

the remote location back to the utility’s operations center, where it can be used by engineers and operators to optimize circuit capability.

temperatures and ratings is continually updated by the dynamic rating system and made available to the utility SCADA/EMS system. This allows dissemination of the calculation results to anywhere within the utility.

For these reasons, dynamic rating systems may be interfaced to the utility SCADA system so that the SCADA system can handle all of the utility-specific telemetry issues, and the dynamic rating system can concentrate on just the rating and temperature calculations. Some favorable characteristics are as follows:

All calculations can now be performed in an engineering office or operations center environment (rather than in a substation) without the need for special monitoring device communication links. Utility operations programmers need only develop simple SCADA Network Access calls to write ASCII input data files to the dynamic rating computer, rather than spending a lot of time writing equipment-specific interface programs. Figure 3.8-4 shows the general layout of EPRI’s dynamic rating system (DTCR), which utilizes this approach.

• The preferred mode of operation is one wherein remote monitors provide data to the SCADA/EMS database using utility-specific communication links, and the dynamic rating system obtains its real-time data from that database rather than directly from the remote monitors.

• The utility SCADA/EMS system must transfer realtime monitor data from the database to a simple real-

Monitor

PC in Engineering Office or Operations Center

Modem Cell or Land Line

Monitor

Wire or Fiberoptic (RS232)

Modem

Direct Monitor Input

Monitor

Input Data File*

Direct Connect Communications Program

Input Data File*

Radio Link Communications Program

wireless

Network Access Call

Telephone Communications Program

Input Data File* Input Data File*

* File with most recent realtime data appended.

DTCR Software Product User Interface

File Handler

Real-Time Historical Data File (mmddyy.###)

File

DTCR Calculation Algorithms

Real-Time Output File (ratings, temps., etc.)

Real-Time SCADA Output File (ratings, temps, etc.)*

Network Access Call

SCADA/EMS Database Output to Engineering or Operations Center

DTCR Functional Diagram

Figure 3.8-4 Schematic overview of DTCR’s location within the utility architecture.

3-50


3.8.4

Required Monitoring

Underground cable dynamic rating systems require various monitored parameters. Some of the parameters that could be evaluated are summarized as follows: Ambient Soil Temperature The ambient temperature is a fundamental parameter to be monitored since it directly affects the allowable temperature rise from ac loading. Soil temperature monitoring should be located where it is representative of the ambient conditions imposed on the cable system. Usually, this means being at least 10 m (30 ft) away from an energized cable circuit at typical installation depths. A thermocouple tree—a series of thermocouples installed at various depths at the same location—is ideally suited for this type of monitoring, since it gives a range of temperatures that may be used for the variation in burial depth encountered along the circuit. Load The load is also an important parameter to know, even if doing quasi-dynamic ratings (described in Section 3.8.4). The load serves two purposes. First, it allows the conductor temperature to be calculated as a function of load. Second, it allows a correlation between any measured temperatures and the circuit load (see Section 3.4.7). This is important for verifying ampacity capability. Soil Thermal Resistivity Real-time monitoring of soil thermal resistivity is not common, mostly because the soil thermal resistivity does not change rapidly. Some utilities permanently install a thermal probe so that additional thermal resistivity measurements can be made to account for seasonal variations or weather effects.

As discussed in Section 3.6, thermal resistivity is a very important parameter, since earth components of thermal resistance represent more than half of the total thermal resistance to heat leaving the cable. Pipe-Type Cable Monitoring Some parameters are uniquely important to pipe-type cable dynamic ratings, particularly those that utilize fluid circulation or forced cooling. Inlet and outlet pressure to a cooling loop, fluid flow rates through the cooling loop, inlet dielectric liquid temperature, and cooling system outlet temperature all may be monitored to evaluate the performance of a pipe-type cable system with active forced cooling. The capability of the cooling plant to remove heat from the dielectric liquid is very important, since this ultimately dictates how much forced cooling can be applied to the pipe-type system.


3.8.5

Quasi-Dynamic (Real-Time) Ratings

“Quasi-dynamic ratings” utilize many of the principles of real-time ratings except they may not be done on a continuous basis. For example, a utility may have a cable circuit that is only heavily loaded two months of the year. On that basis, the cost to implement a dynamic rating system may not be justified, but the ratings during that two-month window are still critical. Quasi-dynamic ratings might be applied by monitoring load and temperatures for a period of time and then calculating what the conductor temperature might be as a result of that load. From this, the temperature of the cable conductor at rated temperature can be extrapolated for rating purposes. For example, the earth interface temperature of a cable system may be monitored with thermocouples for several months until a period of high loading occurs. At that time, the utility may download measured temperatures from a thermocouple data logger and compare measured to calculated temperatures to evaluate the assumptions used for rating models, both real-time and off-line ratings. Quasi dynamic ratings may also apply to reviewing historical load profiles using dynamic rating algorithms. The load history on a circuit for a year or two—perhaps covering high-load periods during summer months— could be run through a dynamic rating tool to evaluate peak loading periods and study loss-of-life criteria (on paper cables). 3.9


Section 3.9 describes uprating projects recently conducted at utilities. It is hoped that these case studies help to illustrate the general application of uprating techniques described in this chapter. 3.9.1

CenterPoint Energy

Description of Circuit and Summary of Rating Constraints and Utility Goals A 138-kV HPFF underground transmission line was constructed in 1969 from CenterPoint Energy’s Polk substation (located at the intersection of Polk and La Branch Streets in Houston, Texas) to CenterPoint’s Garrott Substation (located at the intersection of Garrott Street and Blodgett). The total length of this 138-kV underground transmission line is approximately 2.37 miles (12,500 ft). A 2500-kcmil, compact segmental copper, 138-kV HPFF cable with 505 mils of insulating tapes was used to construct the Polk – Garrott transmission line.

3-51


In March 2001, a loop feed to a new CenterPoint substation, Midtown Substation, was constructed by tapping into the existing Polk to Garrott underground transmission line. This loop feed to the Midtown Substation (located on La Branch Street between Taum and Drew Streets) segregated the Polk to Garrott underground transmission line into two parts with the lengths of 0.96 and 1.41 miles. CenterPoint wanted to evaluate the power transfer capabilities of the Polk-MidtownGarrott and Polk-Downtown 138-kV underground transmission lines in light of these changes and to optimize the current-carrying capacity of the circuits. The ampacity audit was based on an evaluation of recent and historical data including:

• Long-term load current, ambient soil temperatures, and cable pipe temperatures during summer operating conditions

• Distributed fiber optic temperature sensing (DFOTS) measurements performed on the circuits in February 2002 for hot spot identification

• As-built plan and profile drawings for the two cable circuits

• Cable manufacturing data CenterPoint Energy also wanted to evaluate the condition of the thirty-two-year-old Polk-Garrott HPFF cables in coordination with the ampacity analysis. Consequently, two investigations were performed for this purpose. First, Detroit Edison (DECo) performed dissolved gas analysis (DGA) and laboratory testing of cable paper tape samples obtained during construction of the loop feed to the new Midtown Substation. Power Delivery Consultants (PDC) also performed cable dissipation factor measurements at rated voltage using EPRI-developed instrumentation. A previous EPRI project (Transmission Cable Life Evaluation and Management) indicated that cable tape physical property measurements, DGA, and dissipation factor measurements are the best diagnostic tests to determine cable loss-of-life. The primary focus of the DTCR project was to examine the ratings on the Polk-Midtown-Garrott circuit. This circuit consists of two segments: 5,060 ft from Polk to Midtown Substation, and 7,440 ft from Midtown Substation to Garrott Substation. DTS measurements showed that the hotspot for the Polk-Midtown-Garrott underground line is a crossing with the Polk-Downtown 138-kV underground transmission line at the intersection of Polk and La Branch (just outside of the Polk Substation). The cable used for the Polk to Downtown 138-kV line is identical to the Polk to Garrott line. The depth of cover over the Polk-Midtown-Garrott line is approximately 11 ft-2 in. at the hot spot location, and 3-52


the vertical clearance to the Polk-Downtown line (above it) is approximately 3 ft. CenterPoint placed a thermocouple on the Polk to Garrott cable pipe near the intersection. Initially, the thermocouple temperature was monitored with a data logger, but this thermocouple is now connected directly to CenterPoint's SCADA system. A thermocouple was also placed on the PolkDowntown circuit at the location of the crossing and connected to SCADA. In 2000, CenterPoint Energy (Houston Lighting & Power) began this investigation (completed in December 2002 – EPRI Report 1007539) to increase the circuit capacity on the high-pressure fluid-filled (HPFF) pipetype cable connecting the Polk and Garrott Substations. Various studies were performed to evaluate uprating possibilities for this circuit, including the application of distributed fiber optic temperature sensing (DFOTS). Results of DFOTS revealed that a hot spot existed where another pipe-type cable (CenterPoint’s Polk-Downtown circuit) crossed over the Polk-Garrott circuit. Although an overall increase in ampacity was found for the general cable circuit, a net decrease in ampacity resulted from the modeling of the mutual heating of the two cable circuits where they cross. This was anticipated prior to beginning the project, so DTCR was implemented on the Polk-Garrott circuit in an effort to optimize available circuit capacity. The principal goal of the project was to investigate an optimized circuit rating in light of the interference temperature effects detected by DFOTS and experienced by the crossing pipes. A secondary objective was to demonstrate that, under normal loading patterns, the maximum normal temperature (85°C) of the conductor would infrequently be exceeded. Results of Uprating and Benefits to Utility The following conclusions may be reached from reviewing the application of DTCR at CenterPoint:

• The DTCR modifications and subsequent data analysis showed that CenterPoint Energy’s Polk-Midtown-Garrott and Polk-Downtown pipe-cable circuits can benefit from dynamic ratings. DTCR’s predicted load pattern assumes a typical 24-hour loss factor cycle consistent with static ratings. However, the emergency loading is a function of pre-load conditions, and DTCR accurately calculates the conductor pre-load temperature based on historical loading patterns. Also, DTCR uses the present loading to predict time to temperature overload (TTO).

• While a detailed ampacity study indicated there was effectively a reduction in the established book rating of 3.4%, applying DTCR allowed for a net increase in the normal rating of 20.7%, based on considering a


“dynamic” rating using summer 2000 load data for a “quasi-real-time” dynamic rating analysis.

• In summary, the real-time dynamic ratings of the


the harbor section. An additional goal was to consider means for increasing ampacity on the circuit.

Polk-Midtown-Garrott and Polk-Downtown underground transmission lines are expected to be significantly higher than the static ratings that were calculated under a separate project, assuming there is similar load pattern variability to that observed during the summer 2000.

Power Delivery Consultants, Inc. (PDC) was contracted in 2001 to perform a very detailed evaluation of the Bridgeport Harbor portion of UI’s 1710 and 1730 lines using sophisticated modeling and state-of-the-art technology to gather information about the installation and environment. The evaluation included several technologies:

The following conclusions are a result of the cable condition assessment testing performed on the Polk-Garrott 138 kV underground transmission line.

• Gyroscopic testing on the empty cable pipe to

• DGA testing of pipe fluid samples and laboratory

• Hydroscopic surveying of the harbor bottom to eval-

testing of a cable sample indicated that Polk-Garrott 138-kV cable offers an exceedingly long life, which is characteristic of HPFF cables.

uate the degree of siltation over the cable pipes since they were installed in 1961 and, ultimately, to determine the cable depth of cover.

• Results of the dissipation factor measurements con-

• Distributed temperature sensing (DTS) using EPRI’s

firmed that the Polk-Garrott 138-kV HPFF cables do not show any signs of insulation deterioration after more than 30 years of operation.

DTS equipment and fiber optic cable installed in the spare cable pipe

3.9.2

United Illuminating Company

Description of Circuit and Summary of Rating Constraints and Utility Goals In 1989, United Illuminating Company (UI) performed an engineering evaluation on the ampacity of the existing 1.4-mile-long UI 115-kV high-pressure gas-filled cable Circuits 1710 and 1730, which connect UI’s Pequonnock Substation to the Seaview Tap in Bridgeport, Connecticut, where the lines transition to overhead conductors. A 1600-ft section under Bridgeport Harbor, where the cables were buried approximately 25 ft under high-resistivity sediments, appeared to limit the overall circuit rating. UI’s construction records indicated that the cable configuration under the harbor consists of three pipes in a 5-ft trench, with a spare (empty) pipe centered between the two cabled pipes.

Results of the 1989 thermal tests showed that soil resistivity ranged widely, from 90º to 250º C-cm/Watt. This range of values produced a degree of uncertainty in the ratings. In addition, the degree of siltation and the actual pipe positions since the cable pipes were installed in 1961 was unknown. Because of the uncertainty of the pipes’ locations, 1989 soil tests were done at least 50 ft away from the expected pipe position to avoid possibly damaging the pipes with the soil-coring equipment. The uncertainty of some parameters from the 1989 study, the limiting of the entire circuit’s ampacity by the harbor section, combined with UI’s interest in increasing the total power transfer on the circuit, precipitated UI in undertaking a more thorough ampacity evaluation of

develop accurate cable pipe plan and profile information for the harbor crossing.

• Continuous thermocouple temperature monitoring using installed thermocouples and data loggers

• Updated soil sample testing to characterize the soils at the depths of interest

• Forced air ventilation to characterize possible uprating by removing heat from the cabled pipes An EPRI report (1007534) documents the results of these evaluations and a detailed ampacity study to determine the actual capacity of UI’s 1710 and 1730 lines under both normal and emergency ampacity conditions, and describes possible approaches for increasing the ampacity on the lines. In 2002, UI implemented two of the recommendations of the ampacity study:

• Applied forced-air cooling on the parallel cable pipe. • Implemented DTCR to monitor conductor temperature and evaluate real-time temperatures on the circuit as the result of circuit loading. Results of Uprating and Benefits to Utility The initial ampacity study resulted in several recommendations to mitigate the rating limits on UI’s cable circuits. These are summarized in Table 3.9-1. Two of the options, forced air cooling on a parallel empty cable pipe and dynamic ratings, were later implemented.

The forced-air cooling equipment is shown in Figure 3.9-1. The actual cost to install the forced-air cooling equipment was substantially higher than the initial esti-

3-53



Table 3.9-1 Summary of United Illuminating Pipe Cable Uprating Methods Forced Air Cooling Location

Reconditioning

Harbor only Harbor only

Fluid Filling

Circulation

Forced Cooling

Reconductoring

XLPE

Water Cooling

Dynamic Rating

Circuit

Circuit

Circuit

Circuit

Circuit

Harbor only

Circuit

Maximum estimated increase

4.0%a

5.6%b

<3.0%

7.8%

25–50%

18.0%

c

5.6%d

e

Additional maintenance

Minimal

None

Moderate

Moderate

High

None

None

Moderate

None

Environmental Concerns

Low

None

High

High

High

None

None

Moderate

None

Estimated Cost

$100k

$1.2M

$1.5M

$200kf

$1.5Mg

$3M

c

$500kd

$200k

a. b. c. d. e. f. g.

Based on testing in September-October 2001; small additional increase possible. Land rating becomes limiting. Not recommended for pipe-type retrofit with conventional technology. Not recommended; air-cooling could achieve same result. Rating improvements by dynamic ratings vary depending on circumstances. Increase in cost minimal after fluid filling. Assumes fluid filling already done.

mate, largely due to some complications associated with the civil works of the installation. The following conclusions and recommendations were reached based upon implementing DTCR on United Illuminating Company’s 1710/1730 circuits:

• DTCR shows that the maximum normal operating temperature of paper-insulated pipe-type cables (e.g., 85°C) is rarely exceeded, even though there are frequent occasions when the actual circuit loading exceeds the normal book ratings.

• The combined effects of circuit loading on 1710 and mutual heating from circuit loading on 1730 sometimes result in the conductor temperature on the 1730 circuit exceeding its maximum normal temperature.

As was indicated in an earlier study, this results from the typically increased load levels on the 1710 and 1730 circuits, the increased daily loss factors, and the fact that loads on the 1730 circuit are increasingly approaching the loads on the 1710 lines.

• UI may want to consider performing a long-term loss-of-life evaluation on the 1710 and 1730 circuits to see how the calculated operating temperatures on the circuits have influenced accumulated loss-of-life. Despite the occasional incursions above rated temperature, the evaluation would likely show that during a typical calendar year, the below 85°C operating temperatures for most of that time indicate that less than a calendar year of life has been consumed. This would provide increased confidence to UI that this occasional high-temperature operation should not adversely affect the future operation of the circuit. If pursued, this additional work would apply paperinsulated pipe cable aging characteristics developed during EPRI work on accelerated aging at Waltz Mill.

• From the standpoint of evaluating normal ratings, the book ratings were previously found to be 743 A (on the 1710 circuit). Real-time ratings show a range of improvements (10–25%) depending on the conditions (Table 3.9-2).

• If the 1710 and 1730 circuits are ever decommis-

Figure 3.9-1 Blower assembly for forced-air cooling on pipe-type cable circuits. 3-54

sioned, an evaluation of the paper insulation aging should be performed to determine if the typically higher operating temperatures on the 1710 cables show increased aging over the 1730 cables, since both circuits are made of similar vintage cable and have had similar in-service lives.



3.10

Table 3.9-2 Comparison of Normal “Book” Rating to RealTime and Dynamic Ratings Rating Type

Minimum

Normal Book (Previous Study)

Maximum

Tables 3.10-1 and 3.10-2 summarize the major improvements in ampacity that may be realized by the various uprating and upgrading techniques described in this chapter. The specific costs for each depend largely on the unique aspects of each installation or project, but qualitative costs, along with many other factors, are listed in the tables for reference.

743A

Real-Time Normal

621A

817A

Dynamic Normal (100% Loss Factor)

0A (722A)

877A

Dynamic Normal (with Cyclic Rating Factor)

0A (774A)

929A


• Further work on DTCR may be warranted to provide for a cyclic rating factor on emergency ratings of longer than 24 hours to fully take advantage of the “dynamic normal rating” concept.

The case studies in Section 3.9 give an indication of specific costs for one of the uprating projects.

Table 3.10-1 Summary of Uprating and Upgrading Techniques Applicable to All Cable Types Measure Soil Rho, Heat Pipes, Mitigate Hot Spots

Evaluation Criteria Rating Incremental Increasea

20%

Reliability

High

Lead Time Cost

Real Time Monitoring Thermocouples (Temp.)

Dist. Fiber Optic (Temp.)

Dynamic Ratings

Replace Conductors

Voltage Upgrading

10-20%

3-20%

66-80%

High

High

High

N.A.b High

High

Maintenance

Low

Low

Low

Low

Low

Increased, but Low

Losses

None

None

None

Low

Low

Increased, but Low

Installation

2 mos.

3 mos.c

3 mos.

2 mos.

14 mos.

24 mos.

Operating

None

Real Time

Real Time

Real Time

None

None

Installationd

Low

Low-Med

Low-Med

Low

High

High

Operating

None

Low

Low

Low

Med.-High

Med.-Highe

a. Incremental increase in ampacity over previous options. b. Monitoring the cable circuit alone, does not provide for rating improvements. Real-time monitoring, with the monitored parameters fed into rating calculations provides for optimum ampacities. c. If not done during the original installation of the cable system. d. Including material costs. e. Generally, higher voltage equipment requires more extensive and expensive maintenance. Table 3.10-2 Summary of Uprating Techniques Predominantly for Pipe-Type Cables Evaluation Criteria

Rating Incremental Increase

Cost

2%

Circulation

Forced Cooling

Slow

Rapid

Passive Heat Exchanger

21%

8%

16%

Forced-Air Heat Exchanger Refrigerated Cooling 31%

16%

Reliability

High

Medium

Medium

Medium

Low

Low

Maintenance

Medium

Medium

Medium

Medium

High

High

Losses Lead Time

Fluid Filling

None

Low

Medium

Medium

High

High

Installation

10 mos.

2 mos.

2 mos.

2 mos.

3 mos.

6 mos.

Operating

N.A.

Lowa

Lowa

Lowa

Lowa

Lowa

Installation

High

Low

Low

Medium

High

High

Operating

Low

Low

Medium

Medium

Medium

High

a. Typically less than 24 hours.

3-55


REFERENCES

The following references were used for this chapter and may be useful to the reader for additional background on the topics discussed. Anders, G. J. 1997. Rating of Electric Power Cables, IEEE Press/McGraw Hill. Bascom, III, E. C., D. A. Douglass, G. C. Thomann, and T. Aabo. 1996. “Hybrid Transmission: Aggressive Use of Underground Cable Sections with Overhead Lines.” CIGRÉ 21/22-10. Bascom, III, E. C. and J. A. Williams. 2002. “Taking Your Cable’s Temperature.” Transactions of the T&D World Expo. 7-9 May. Indianapolis, Indiana. Bascom, III, E. C. and J. A. Williams. 2002. Ampacity Evaluation and Distributed Fiber Optic Testing on PipeType Cables Under Bridgeport Harbor. Electric Power Research Institute Publication 1007534. December. Bascom, III, E. C. and J. H. Cooper. 2002. Condition and Power Transfer Assessment of CenterPoint Energy’s Polk-Garrott Pipe-Type Cable Circuit. Electric Power Research Institute Publication 1007539. December. Bascom, III, E.C. 2003. “Underground Cable Uprating and Upgrading Tutorial.” Transactions of IEEE PES Transmission & Distribution Conference. Paper 03TD0362 (Panel Session). Dallas, Texas. 7-12 September. Bascom, III, E. C., J. A. Williams, M. A. Pasha, S. M. Rahman, and W. Zenger. 2003. “Ampacity Evaluation of High-Pressure Gas-Filled (HPGF) Pipe-Type Cables Under Bridgeport Harbor.” Transactions of IEEE PES Transmission & Distribution Conference. Paper 03TD0093. Dallas, Texas. 7-12 September. CIGRÉ 1979. “The Calculation of Continuous Ratings of Forced-Cooled Cable.” Working Group 21.08. Study Committee 21. Electra. No. 66. pp. 59-84. October. CIGRÉ. 1987. “The Calculation of Continuous Rating for Forced-Cooled High-Pressure Oil-Filled Pipe-Type Cables.” Working Group 21.08. Study Committee 21. Electra. No. 113. pp. 97-120. El-Kady, M. A. and D. J. Horrocks. 1995. “Extended Values of Geometric Factor of External Thermal Resistance of Cables in Duct Banks.” IEEE Transactions on Power Apparatus and Systems. Vol. PAS-104.

3-56


EPRI. 1982. High Ampacity Terminations. EL-2233. January. EPRI. 1985. Volume 1: Calculating AC/DC Resistance Ratios for High-Pressure Oil-Filled Cable Designs Designer's Guide. EL-3977. EPRI. 1985. Volume 2: Calculating AC/DC Resistance Ratios for High-Pressure Oil-Filled Cable Designs Details of Mathematical Derivations. EL-3977. EPRI. 1992. Underground Transmission Systems Reference Book. TR-101670. EPRI. 1997. Thermal Properties Manual for Underground Power Transmission. TR108919. November. EPRI. 1998. Transmission Cable Life Evaluation and Management. TR-111712. September. EPRI. 2002. Increased Power Flow Guidebook – Overhead Transmission Lines. 1001817. December. Holman, J. P. 1997. Heat Transfer. 8th Edition. McGraw-Hill. New York. IEEE. 1988. “IEEE Guide for Application of SheathBonding Methods for Single- Conductor Cables and the Calculation of Induced Voltages and Currents in Cable Sheaths.” 575-1988. Iizuka, K. 1974. Power Cable Technology Hand Book. DenkiShoin, Tokyo. pp. 80. International Electrotechnical Commission. 1982. IEC287. “Calculation of the Continuous Current Rating of Cables (100% Load Factor).” International Electrotechnical Commission. International Electrotechnical Commission. 1989. IEC853-2. “Calculation of the Cyclic and Emergency Current Rating of Cables.” International Electrotechnical Commission. 1st Edition. Neher, J. H. and M. H. McGrath. 1957. “The Calculation of the Temperature Rise and Load Capability of Cable Systems.” Paper 57-660. AIEE Insulated Conductors Committee. June. Neher, J. H. 1963. “The Transient Temperature Rise of Buried Cable Systems.” Paper 63-917. IEEE Insulated Conductors Committee. June.



Parmar, D. and J. Steinmanis. 2003. “Underground Cables Need a Proper Burial.” Transmission & Distribution World. April. pp. 44-51.

Williams, J. A., E. C. Bascom III, B. Horgan, and T. Aabo. 1991. “Field Test Program and Results to Verify HPFF Cable Rating.” IEEE Transactions.

Purnhagen, D. W. 1984. “Designer’s Handbook for Forced-Cooled High-Pressure Oil-Filled Pipe-Type Cable Systems.” Electric Power Research Institute. EL3624. Project 7801-5. July.

Williams, J. A. and J. H. Cooper. 1998. “Distributed Fiber Optic Temperature Monitoring and Ampacity Analysis for XLPE Transmission Cables.” Electric Power Research Institute. TR-110630. June.

Stevenson, Jr., W. D. 1982. Elements of Power System Analysis, 4th Edition. McGraw-Hill. New York.

Williams, J. A. 2000. “Application of Fiber-Optic Temperature Monitoring to Solid Dielectric Cable.” Electric Power Research Institute. Publication 1000469. November.

Williams, J. A., T. R. Grave, and E. Kallaur. 1986. “Uprating of High Pressure Gas-Filled Feeders by Fluid Filling and Rapid Circulation.” IEEE Conference. Anaheim, CA. September 15-19.

3-57


APPENDIX 3.1

PIPE-TYPE AMPACITY EXAMPLE


The cable configuration is as shown in Figure A3.1-1.

This appendix contains a sample calculation of pipetype cable ampacity using the procedures outlined in this chapter and detailed in the references.

Figure A3.1-1 Cable configuration for pipe-type ampacity example.

3-58



Pipe-Type Cable Ampacity Worked Example Cables are 345kV HPFF cables with 2500kcmil segmental copper conductors, 905 mils kraft paper insulation, 0.1x0.2, 2x3in. lay stainless steel skid wires in an 10-inch cable pipe, 2 circuits, 0.62 loss factor. Cable Data: A := 2500 ρ conductor := 0.017241

Conductor area, CI ohm -meters

Electrical resistivity, copper conductor

ks := 0.39

Conductor skin effect factor, in oil

kp := 0.46

Conductor proximitty effect factor, in oil, cradled

Dc := 1.824

Diam eter of the segm ental conductor, inches

Tc := 85

Maximum normal conductor operating tem perature, °C

tcs := 0.005

Thickness of conductor semiconducting shield, inches

ti := 0.905

Insulation wall thickness, inches

tan δ := 0.0023

Values for Paper Dielectric constant of the insulation Insulation Dissipation factor of the insulation, numeric

ρ insulation := 6.00

Thermal resistivity of the insulation, C°-m/Watt

tis := 0.005

Thickness of insulation shield tapes, inches

SIC := 3.5

ρ shield := 0.7

ohm -meters

Skid W ire Size/Type

0.1in. x 0.2in., 2 x 3in. lay

ρ skidwire := 0.7

ohm -meters

f := 60

Hz

Electrical resistivity of stainless steel shield tapes

Electrical resistivity of stainless steel skidwire

LF = 0.62

Daily (24-hour) loss factor, per unit (entered below)

n := 3

Num ber of cables within pipe or conduit

N := 2 Pipe Data: Pipe is HPFF ODpipe := 10.75

Pipe outside diameter, inches

IDpipe := 10.25

Pipe inner diameter, inches

t coating := 0.07

Pipe coating (Som astic) thickness, inches

ρ coating := 3.5

Thermal resistivity of the pipe coating, C°-m/w

3-59


Installation Data: x1:= −15 burial1 := 42


x2 := 15

Horizontal location of pipe center, inches

burial2 := 42

Burial depth to pipe center, inches

Ta := 25

Ambient earth temperature, °C

f := 60

Power frequency, Hz

E := 345000× 1.05

System maximum line to line voltage, volts

ρ native := 0.9

Thermal resistivity of the native earth, C°-m/w

ρ backfill := 0.5

Thermal resistivity of the duct concrete, C°-m/w

Width cbf := 53

Height cbf := 29

Width and height of backfill, inches

Center_Depth cbf := 39

Value for center-line depth of cbf is arbitrary

Calculate Cable Geometry: Dcs := Dc + 2tcs

Diameter over the conductor shield, inches

Dinsulation := Dcs + 2ti

Diameter over the insulation, inches

Dis := Dinsulation + 2tis

Diameter over the insulation shield, inches

Dskidwire := Dis + 1.5 × 0.1

Diameter over 0.1" skid wires, inches

Dearth := ODpipe + 2t coating Clearance :=

IDpipe 2

− 1.366Dskidwire +

(IDpipe − Dskidwire) ⎡ 2

Dskidwire ⎞⎤ ⎛ ⎢1 − ⎜ ID ⎟⎥ ⎣ ⎝ pipe − Dskidwire ⎠⎦

0.5

Clearance in pipes, inches Dcs = 1.834 Dinsulation = 3.644 Dis = 3.654 Dskidwire = 3.804 Dearth = 10.89 Clearance = 1.992

3-60



Metric Conversion of Variables A Area conductor := 1.9735

3

2

Areaconductor = 1.267 × 10

mm

Dconductor := Dc25.4

Dconductor = 46.33

mm

Dcond_shield := Dcs 25.4

Dcond_shield = 46.584

mm

Dinsulation := Din sulation25.4

Dinsulation = 92.558

mm

Dinsl_shield := Dis25.4

Dinsl_ shield = 92.812

mm

Dskidwire := Dskidwire25.4

Dskidwire = 96.622

mm

ODpipe := ODpipe 25.4

ODpipe = 273.05

mm

IDpipe := IDpipe 25.4

IDpipe = 260.35

mm

Dearth := Dearth25.4

Dearth = 276.606

mm 3

burial1 := burial125.4


burial1 = 1.067 × 10

x1:= x125.4

x2:= x225.4

x1 = −381

mm

3

Width cb f := Width cbf25.4

Width cbf = 1.346 × 10

mm

Height cbf := Heightcbf25.4

Heightcbf = 736.6

mm

Center_Depthcbf := Center_Depthcb f25.4

Center_Depthcbf = 990.6

mm

W d = 10.741

W /m/phase

Calculate the dielectric losses: 2

E⎞ −9 ⎟ tanδ10 3 ⎝ ⎠ ⎛ Dinsulatio n ⎞

2πf SIC⎛⎜ Wd :=

18 ln ⎜

⎟ ⎝ Dcond_shield ⎠

Calculate Conductor Resistance: Rdc20 :=

ρ conductor Areaconductor

RdcT := RdcT1.025

RdcT := Rdc20⎡⎢

−5

Rdc20 = 1.361 × 10

⎥ ⎣ 20 − ( −234.5) ⎦

Assume 2.5% Stranding of Conductor

−7

Xs :=

Tc − ( −234.5) ⎤

8πf( ks ) 10

−7

Xp :=

RdcT

Ohms/meter

8πf(kp ) 10 RdcT

2

Ycs :=

Xs

192 + 0.8Xs

2

S := Dskidwire

2 2 ⎞ ⎛ Dco ndu ctor ⎞ 2⎡⎢ ⎛ Xp ⎛ Dconductor ⎞ ⎜ ⎟ Ycp := ⎜ ⎟ 0.312⎜ ⎟ ... ⎜ 192 + 0.8Xp2 ⎟ ⎝ S S ⎠ ⎢ ⎝ ⎠ ⎝ ⎠ ⎢ 1.18 + ⎢ 2 ⎞ ⎛ Xp ⎢ ⎜ ⎟ + 0.27 Racc := RdcT⎡⎣ 1 + 1.5(Ycs + Ycp )⎤⎦ ⎢ ⎜ 2⎟ ⎣ ⎝ 192 + 0.8Xp ⎠

Ycs = 0.056

⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦

Ycp = 0.061

3-61



Calculate the shield and skidwire loss increments: Area of shield tape is width of tape times thickness. Resistance of shield tape is the area times the helical length times the resistivity divided by the area. Shield tape thickness is 0.005in stainless steel, with 1/8" lapped, with typical tape width of 7/8". Assume there are 2 tapes. 7 widthshield _tape := 25.4 8

area shield _tape := thickness shield _tape width shield _tape Rshield :=

⎛ πDinsl_shield ⎞ 1+ ⎜ ⎟ ⎝ lay shield ⎠

ρ shield area shield _tape

1 lapshield := 25.4 8

thickness shield _tape := 0.005 × 25.4

layshield := width shield _tape − lapshield

2

Rshield = 3.804

Ohms/meter

Skid wire resistance Area of elipse is pi * major_radius * minor_radius. Area of skid wire is half this. Skid wire is 0.1 x 0.2, 3-inch lay, 2 wires. Material is stainless steel. minor_radius := 0.1 × 25.4

major_radius := 0.2

25.4

area skidwire :=

2

π 2

minor_radius major_radius

layskidwire := 3 × 25.4 Length of a helix is (1 + (pi*D/Lay)^2)^.5 Rskidwire :=

ρ skidwire

1+

area skidwire

⎛ πDskidwire ⎞ ⎜ ⎟ ⎝ lay skidwire ⎠

2

1

Rs :=

1

1

+

Rskidwire

Rskidwire

+

1 Rshield

+

1

Rskidwire = 0.284

Ohms/meter

Rs = 0.132

Ohms/meter

Rshield

Calculate Mutual Reactance (assume cradled configuration) −7

Xm := 2( 2πf) 10 Ysc :=

Rs

⎛ 2.3Dinsl_shield ⎞ ⎟ ⎝ Dskidwire ⎠

ln⎜

−5

Xm = 5.977 × 10

Ohms

1

Racc

−3

2

Ysc = 1.314 × 10

⎛ Rs ⎞ 1+ ⎜ ⎟ ⎝ Xm ⎠ Racs := RdcT ⎡⎣ 1 + 1.5( Ycs + Ycp + Ysc) ⎦⎤

Calculate the pipe loss increments to AC resistance: Yp :=

0.0438Dskidwire + 0.0226IDpipe

Yp = 0.578

6

RdcT 10

Racp := RdcT ⎡⎣1 + 1.5( Ycs + Ycp + Ysc) + Yp⎤⎦ −5

Racc = 2.06 × 10 Qs :=

3-62

Racs Racc

Qp :=

−5

Racs = 2.063 × 10 Racp Racc

Qs = 1.002

−5

Racp = 3.075 × 10 Qp = 1.493

Ohms/meter AD/DC resistance ratios



Calculate Cable Thermal Resistances Ri :=

ρ insulatio n 2π

⎛ Dinsl_shield ⎞ ⎟ ⎝ Dcond uctor ⎠

ln ⎜

U := 0.26

V := 0

Ri = 0.663 Y := 0.0026

Tmoil = 66.827 Roil :=

Constants for HPGF Estimate of m ean temperature in duct

nU

Roil = 0.175

1 + 0.1( V + YTmoil) Dinsl_shield2.15

Rpipe_coating :=

ρ coating 2π

⎛ Dearth ⎞ ⎟ ⎝ ODpipe ⎠

n ln⎜

Rpipe_coating = 0.022

Calculate External Thermal Resistances Calculate geometric correction factor for backfill envelope: x := Height cbf

x=short dimension of backfill

y := Width cbf

y=long dim ension of backfill

⎤ ⎡⎢⎛ 1 ⎞ ⎛ x ⎞ ⎛ 4 x ⎞ ⎛⎜ y 2 ⎟⎞ ⎜ ⎟ ⎜ ⎟ ⎜ − ⎟ ln 1+ 2 + ln( x)⎥ ⎢⎝ 2 ⎠ ⎝ y ⎠ ⎝ π y ⎠ ⎜ x ⎟ ⎥ ⎝ ⎠ ⎦ Db := e ⎣

Db = 985.973

Lb := Center_Depth cbf

Lb = 990.6

⎛ 2L + 4L 2 − D 2 ⎞ ⎜ b b b ⎟ Gb := ln ⎜ ⎟ Db ⎝ ⎠

Gb = 1.322

Calculate diameter Dx 4

α soil :=

6.71 × 10

(ρ nativ e100)

Dx := 1.02 α soil24 Rearth :=

ρ back fill 2π

2

Thermal diffusivity of native soil 0.8

mm

hour Diam eter beyond which 24 hour average losses apply, mm

⎛ ⎛ 2burial1 + 4burial1 2 − D 2 ⎞ ⎞ ⎜ ⎛ Dx ⎞ ⎜ earth ⎟ ⎟ n ⎜ ln ⎜ + LFln ⎟ ⎜ ⎟⎟ D D x ⎝ ⎝ earth ⎠ ⎝ ⎠⎠

3

α soil = 1.834 × 10

Dx = 213.978 Earth thermal resistance for AC losses at loss factor Rearth = 0.381

Rearth' :=

ρ back fill 2π

⎛ ⎛ 2burial1 + 4burial1 2 − D 2 ⎞ ⎞ ⎜ ⎛ Dx ⎞ ⎜ earth ⎟ ⎟ n ⎜ ln ⎜ + ln ⎟ ⎜ ⎟⎟ D D x ⎝ ⎝ earth ⎠ ⎝ ⎠⎠

Earth thermal resistance for dielectric losses at 100% loss factor Rearth ' = 0.652

3-63



Mutual thermal resistance between two pipes (just for normal ampacities) d'12 := ⎡⎣ ( x1 − x2) + (burial1 + burial2)

2⎤

d 12 := ⎡⎣ ( x1 − x2) + (burial1 − burial2)

⎦

2

2

F12 :=

d'12

Rmutual :=

d12

Rmutual' :=

Rcor rection := LF

Rcor rection ' :=

⎦

2⎤

ρ backfill 2π

(ρ native − ρ backfill) 2π

(ρ native − ρ backfill)

Distance between one cable pipe and image of other cable pipe

.5

Distance between one cable and the other

n LFln( F12)

ρ backfill 2π

.5

Rmu tual = 0.161

n ln ( F12)

Rmu tual' = 0.26 Thermal resistance correction for native soil for AC losses Rcor rection = 0.313

n N Gb

Thermal resistance correction for native soil for dielectric losses

n N Gb

2π

Rcor rection' = 0.505 Calculate Normal Ampacity on primary cable ∑RacRth := Racc Ri + Racs Roil + Racp ( Rpipe_coating + Rearth + Rmutual + Rcorrection)

LF ≡ 0.62

⎞ ⎛ Ri + Roil + Rpip e_coating + Rearth' + Rmutual' + Rcorrection '⎟ ⎝2 ⎠

ΔTd := W d⎜

ΔT := Tc − ΔTd − Ta Irated :=

ΔT = 39.104

ΔT

Adjust "iterated" values below until they equal "calculated".

Irated = 940.2

∑RacRth

Itotal := 2Irated

ΔT d = 20.896

Itotal = 1880.4

Tc calc := Irated ⎡⎣ Racc Ri + Racs Roil + Racp (Rpip e_coating + Rearth + Rmu tual + Rcor rection) ⎤⎦ ... + ΔTd + Ta 2

Tc calc = 85 2

Tshield calc := Tc calc − Irated Racc Ri − W d

Ri 2

Toil calc := Tshield calc − ⎛⎝ Irated Racs + W d ⎞⎠ 2

Roil 2

T earth_interface := Toilcalc − ⎛⎝ Irated Racs + W d ⎞⎠ 2

Roil 2

Tshield calc = 69.357

Tshield ≡ 69.357

Toil calc = 66.827

Tmoil ≡ 66.827

− ⎛⎝ Irated Racp + W d ⎞⎠ Rpip e_coating 2

T earth_interface = 63.477

3-64


APPENDIX 3.2

EXTRUDED AMPACITY EXAMPLE

This appendix contains a sample calculation for a crosslinked polyethylene (extruded) cable ampacity using the


procedures outlined in this chapter and detailed in the references. The cable configuration is as shown in Figure A3.2-1.

Figure A3.2-1 Cable configuration for extruded ampacity example

3-65



Extruded Dielectric Cable (XLPE) Ampacity Worked Example The ampacity calculation is for a 230kV 1750 kcmil segmented copper conductor circuit, with 866mils XLPE insulation, and lead metallic sheath, 2 circuits installed in a vertical duct bank and 0.60 loss factor. The sheath is cross bonded to minize circulating current. Cable Data: A := 1750

Conductor area, CI

ρ conductor := 0.017241

ks := 0.435

Conductor skin effect factor, dry segmental

kp := 0.6

Conductor proximitty effect factor, dry segm ental

Dc := 1.416

Diam eter of the segmental conductor, inches

Tc := 90

Maximum allowable norm al conductor operating temperature, C

tcs := 0.0787


ti := 0.866


tis := 0.0984

Thickness of insulation semiconducting shield, inches

tms := 0.125

Thickness of lead moisture barrier / metallic sheath

tj := 0.125

Jacket thickness, inches

SIC := 2.3

Dielectric constant of the insulation

tan δ := 0.001

Dissipation factor of the insulation, num eric

Duct Data: ODduct := 6.625

PVC Duct outside diameter, inches

IDduct := ODduct − 2⋅ 0.28

IDduct = 6.065

Duct inside diameter, inches

Installation Data: Burial := 42

Depth to center of top conduit, inches

d phases := 10

Distance between adjacent phases, inches

d circuits := 20

Distance between adjacent circuits, inches

Ta := 20

Earth am bient temperature summer, °C

f := 60

Power frequency, Hz

LF := 0.60

24 hour loss factor

E := 230000

System line to line voltage, volts

n := 1

Num ber of conductors per duct

N := 6

Num ber of occupied ducts

Thermal Resistivities: ρ insulation := 3.50 ρ jacket := 3.50

Thermal resistivity of the jacket, C°-m/w

ρ duct := 6.00

Thermal resistivity of the duct, C°-m/w

ρ native := 1.00

Thermal resistivity of the native earth, C°-m /w

ρ backfill := 0.50


Width cbf := 33

3-66

Thermal resistivity of the insulation, C°-m/w

Height cbf := 33


ohm -meters



Calculate Cabl e Geometry: Dcs := Dc + 2⋅ tcs


Dcs = 1.573

Dinsulation := Dcs + 2⋅ ti


Dinsulation = 3.305

Dis := Dinsulation + 2⋅tis


Dis = 3.502

Dms := Dis + 2⋅tms

Diameter over the metallic shield/moisture barrier, inches

Dms = 3.752

Mean metallic shield diameter, inches

Dmms = 3.627

Djacket := Dms + 2⋅ tj

Diameter over jacket, inches

Djacket = 4.002

Clearance := IDduct − Djacket

Clearance in conduit, inches

Clearance = 2.063

Dmms :=

Dis + Dms 2

Metri c Conversion of Variabl es A Areaconductor := 1.9735

2

Areaconductor = 886.749

mm

Dconductor := Dc⋅25.4

Dconductor = 35.966

mm

Dcond_shield := Dcs⋅ 25.4


mm

Dinsulation := Dinsulation⋅ 25.4


mm

Dinsl_shield := Dis⋅ 25.4

Dinsl_shield = 88.956

mm

Dmean_shield := Dmms⋅25.4

Dmean_shield = 92.131

mm

Dmet_shield := Dms⋅ 25.4

Dmet_shield = 95.306

mm

tms = 3.175

mm

tms := tms⋅ 25.4 Djacket := Djacket⋅ 25.4

Djacket = 101.656

ODduct := ODduct⋅ 25.4

ODduct = 168.275

mm mm

IDduct := IDduct⋅ 25.4

IDduct = 154.051

mm

Burial := Burial⋅ 25.4

Burial = 1.067× 10

mm

dphases := dphases⋅ 25.4

d phases = 254.000

mm

dcircuits := dcircuits⋅ 25.4

d circuits = 508.000

mm

3

Calculate the dielectric losses: 2⋅ π⋅f⋅ SIC⋅⎛⎜ W d :=

2

E ⎞ −9 ⎟ ⋅ tanδ⋅ 10 ⎝ 3⎠ ⎛ Dinsulation ⎞

Wd = 1.144

W/m

18⋅ ln ⎜


3-67




ρ conductor

−5

Rdc20 = 1.944 × 10

Areaconductor

Rdc90 := Rdc20⋅⎛⎜

234.5 + Tc ⎞

ohms/meter

−5

⎟ ⎝ 234.5 + 20 ⎠

Rdc90 = 2.479 × 10

ohms/meter

Assume 2.5% Stranding of Conductor −5

Rdc90 := Rdc90⋅1.025

Rdc90 = 2.541 × 10

ohms/meter

−7

Xs :=

8⋅ π⋅ f⋅ ( ks) ⋅ 10

Xs = 2.581

Rdc90 2

Ycs :=

Xs

Ycs = 0.034

2

192 + 0.8⋅ Xs

−7

Xp :=

8⋅ π⋅ f⋅ ( kp) ⋅ 10

Xp = 3.561

Rdc90

2 2 ⎛ ⎞ ⎛ Dconductor ⎞ 2 ⎡⎢ Xp ⎛ Dconductor ⎞ ⎜ ⎟ Ycp := ⋅⎜ ⎟ ⋅ 0.312⋅ ⎜ d ⎟ ... ⎜ 2 ⎟ ⎝ d phases ⎠ ⎢ phases ⎠ ⎝ 192 + 0.8 ⋅ Xp ⎝ ⎠ ⎢ 1.18 ⎢+ 2 ⎞ Xp ⎢ ⎛⎜ ⎟ + 0.27 ⎢ ⎜ 2⎟ ⎣ ⎝ 192 + 0.8⋅ Xp ⎠

Racc := Rdc90⋅ (1 + Ycs + Ycp)

−5

Racc = 2.638 × 10

⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦

−3

Ycp = 4.468× 10

ohms/meter

Calculate the shield losses: Assume that the conductors will lie in a flat (vertical) configuration for purposes of calculating shield losses. The metallic sheath consists of lead, and the bonding scheme is cross-bonded, so there will be no circulating current and only eddy current losses. −8

ρ lead := 21.4⋅ 10

Sheath material is lead Areasheath := π⋅

2 2⎞ ⎛D ⎝ met_shield − Dinsl_shield ⎠

4

2

Areasheath = 918.965

mm −6

Areasheath := Areasheath⋅10 Rsheath :=

ρ lead

−4

Rsheath = 2.329 × 10

Areasheath

Estimated sheath temperature: Rsheath := Rsheath⋅

3-68

Tmshield − (−236.0) 20 − ( −236.0)

Tmshield = 73.856 −4

Rsheath = 2.819 × 10

2

m



Eddy current loss increm ent −7

m :=

2⋅ π⋅ f⋅ 10

m = 0.134

Rsheath

⎛ m2 ⎞ ⎡⎢⎡ ( Dmean_shield)⎤ 2⎤⎥ ⎟⋅ YSe0 := 6⋅ ⎜ ⎢ 2⋅ d ⎥⎥ ⎜ 2⎟ ⎢ phases ⎦ ⎦ ⎝ 1 + m ⎠ ⎣⎣ YSe1 := 0.86⋅ ( m)

3.08

⎛ Dmean_ sh ield ⎞ ⋅⎜ ⎟ ⎝ 2⋅ dphases ⎠

−3

YSe0 = 3.468× 10

1.4⋅ m+ 0.7

−4

YSe1 = 3.852× 10

2

8⋅ π ⋅ f

β 1 :=

β 1 = 47.050

7

ρ lead⋅ 10

1.74

tms −3 ⎛ ⎞ ⎛ ⎞ ⎜D ⎟ ⋅ ⎝ β 1⋅ Dmean_shield⋅ 10 − 1.6⎠ ⎝ mean_ shield ⎠ ⎡ (β 1⋅ tms ) 4 ⎥⎤ ⎛ Rsheath ⎞ ⎢ Yse := ⎜ ⎟ ⋅ gs ⋅ YSe0⋅ (1 + YSe1) + 12 ⎥ ⎝ Racc ⎠ ⎢⎣ 12⋅ 10 ⎦ g s := 1 +

Ysc := 0

g s = 1.008

Yse = 0.038

Single point bonded so no circulating currents

Racs := Rdc90⋅ ( 1 + Ycs + Ycp + Ysc + Yse)

−5

Racs = 2.734× 10

Calculate Cable Therm al Resistances Ri :=

Rj :=

ρ insulation 2⋅ π ρ jacket 2⋅ π

⎛ Dinsl_shield ⎞ ⎟ ⎝ Dconductor ⎠

⋅ ln⎜

⎞ ⎟ ⎝ Dmet_sh ield ⎠ ⎛

Djacket

⋅ ln⎜

Tmduct = 67.629 Rcable_to_du ct :=

Rduct :=

ρ duct 2⋅ π

Ri = 0.504

Rj = 0.036

Estimate of mean temperature in duct 5.2

1 + 0.1⋅ ( 0.91 + 0.01⋅ Tmduct)⋅ (Djacket)

⎛ ODduct ⎞ ⎟ ⎝ IDduct ⎠

⋅ ln⎜

Rcable_to_du ct = 0.304

Rduct = 0.084

3-69



Calculate External Thermal Resistances Calculate geometric correction factor for backfill envelope: x := Width cbf

x := x⋅ 25.4 x = 838.200

y := Height cb f

y := y⋅ 25.4

y = 838.200

⎡⎢⎛ 1 ⎞ ⎛ x ⎞ ⎛ 4 x ⎞ ⎛⎜ y 2 ⎟⎞ ⎤ + ln( x)⎥ ⎜ ⎟ ⋅ ⎜ ⎟ ⋅ ⎜ − ⎟ ⋅ ln 1+ ⎢⎝ 2 ⎠ ⎝ y ⎠ ⎝ π y ⎠ ⎜ x2 ⎟ ⎥ ⎝ ⎠ ⎦ Db := e ⎣

Db = 921.455

Lb := Burial + dphases

Lb = 1.321 × 10

3

⎛ 2⋅L + 4⋅ L 2 − D 2 ⎞ ⎜ b b b ⎟ ⎟ Db ⎝ ⎠

Gb := ln⎜

Gb = 1.714


α n :=

2

6.71⋅ 10

( ρ native⋅100)

Thermal diffusivity of native soil

3

α n = 1.685 × 10

hour

0.8

Dx := 1.02⋅ α n⋅ 24

mm

Diameter beyond which 24 hour average losses apply, mm

Dx = 205.148

The self and mutual earth thermal resistances each consist of two terms. The first term assumes that the concrete resistivity applies everywhere, the second term corrects for the excess of the native earth resistivity over the concrete resistivity. 3

L := Burial + dphases

L = 1.321 × 10

⎛

⎛

ρ backfill ⎜ ⎛ Dx ⎞ ⎜ 2⋅ L + ⋅ ⎜ ln⎜ + LF⋅ ln⎜ Rearth := ⎟ 2⋅ π ⎝ ⎝ ODdu ct ⎠ ⎝

Middle phase has highest total thermal resistance

mm 2

2⎞⎞

4⋅ L − ODduct ⎟ ⎟

⎟⎟ ⎠⎠

Dx

Rearth = 0.171 Earth thermal resistance for AC losses

⎛

Rearth' :=

⎛

ρ backfill ⎜ ⎛ Dx ⎞ ⎜ 2⋅L + ⋅ ⎜ ln⎜ + ln ⎜ ⎟ 2⋅ π ⎝ ⎝ ODduct ⎠ ⎝

Rco rrection := LF⋅

Rco rrection ' :=

(ρ native − ρ backfill) 2⋅ π


⋅ n⋅ Gb

2

2 ⎞⎞

4⋅ L − ODdu ct ⎟ ⎟ Dx

⎟⎟ ⎠⎠

Rearth' = 0.274 Earth thermal resistance for dielectric losses

Rco rrection = 0.082 Correction for native backfill thermal resistance for AC losses

⋅ n ⋅ Gb

Rco rrection ' = 0.136 Correction for native backfill thermal resistance for dielectric losses

3-70



Mutual Heating

⎛ 2⋅ Burial + d phases ⎞ ⎛ 2⋅ Burial + 3⋅ d phases ⎞ F1 := ⎜ ⎟ ⋅⎜ ⎟ d phases d phases ⎝ ⎠⎝ ⎠

⎡ ⎢ ⎡⎣⎡⎣2⋅ (Burial + F21 := ⎢ ⎣

2 2 d phases )⎤⎦ + d circuits ⎤⎦

d circuits

.5⎤

⎥ ⎥ ⎦

.5 ⎤ ⎡ .5 ⎤ ⎡ ⎢ ⎡⎣( 2⋅ Burial + d ph ases) 2 + d circuits2⎤⎦ ⎥ ⎢ ⎡⎣(2⋅ Burial + 3⋅ d ph ases) 2 + d circuits2⎤⎦ ⎥ F22 := ⎢ ⎥ ⋅⎢ ⎥ .5 .5 2 2⎞ 2 2⎞ ⎢ ⎥⎢ ⎥ ⎛d ⎛ ⎣ ⎝ circuits + d ph ases ⎠ ⎦⎣ ⎝ d circuits + d phases ⎠ ⎦ 4 F = 1.262 × 10

F := F1⋅ F21⋅ F22 Mutual thermal resistance for AC losses:

(

)

ρ native − ρ backf ill ρ backf ill ⋅ LF⋅ ln ( F) + ( N − 1) ⋅ n ⋅ LF⋅ ⋅ Gb 2⋅ π 2⋅ π

Rmutual :=

Mutual thermal resistance for dielectric losses: Rmutual' :=

(

)

ρ native − ρ backf ill ρ backf ill ⋅ ln ( F) + ( N − 1) ⋅ n ⋅ ⋅ Gb 2⋅ π 2⋅ π

Rmutual = 0.860

Rmutual' = 1.434

Calculate temperature ris e from dielectric heating 1 ΔTd := W d⋅ ⎛⎜ ⋅ Ri + Rj + Rcable_to_duct + Rdu ct + Rearth' + Rmutual' + Rcorrection'⎟⎞ ⎝2 ⎠

ΔTd = 2.884

Calculate the Ampacity −5 ΣRacRthermal= 5.533 × 10

ΣRacRthermal:= Racc⋅ Ri ... + Racs⋅ Rj ... + Racs⋅ Rcable_to_duct ... + Racs⋅ Rdu ct ... + Racs⋅ Rearth ... + Racs⋅ Rco rrection ... + Racs⋅ Rmutual

C° / A^2

ΔTcond := Tc − ΔTd − Ta Irated :=

ΔTcond = 67.116

ΔTcond ΣRacRthermal

Ito tal := 2⋅ Irated

Am pacity per phase group, amperes:

Irated = 1101.4

Total am pacity, amperes

Itotal = 2202.8

Check and adjust the estimated shield and duc t air temperatures: 2 Loss at the conductor, w/m Wc := Irated ⋅ Racc T's := Tc − Wc ⋅ Ri

Wc = 32.003

Check tempe rature of shield which was estim ated at T's = 73.856 Tmshield ≡ 73.856

2 Ws := Irated ⋅ Racs

⎛ ⎝

T'm := T's − Ws ⋅ ⎜ Rj +

Ws = 33.169 Rcable_to_ duct⎞ 2

⎟ ⎠

Check m ean tem perature between cable surface and T'm = 67.629 inside of duct w hich was esti mated at: Tmduct ≡ 67.629

3-71


CHAPTER 4

Power Transformers

4.1

INTRODUCTION

Power transformers are a crucial link in the electric power system. Power transformer failures can result in extremely high financial losses, both in lost revenue and the capital expenditure of unit itself. Therefore, it is essential that power transformers be operated in a safe and prudent manner. In addition, given the high equipment cost, power transformers must be operated in a manner to give a reasonable service life in order to realize a positive return on investment. Power transformers represent a significant portion of capital investment costs. Under existing conditions in the industry, utility budgets are reduced and networks are being forced to support greater power transfer over existing transmission circuits than ever before. As such, there is increased interest in safely utilizing all available capacity of power transformers. The thermal design of power transformers is based on an assumed daily average ambient temperature of 30°C, with a maximum of 40°C. It is also based on continuous loading at the rated maximum current. These assumptions are essential to the specification and design of power transformers; however, they are probably never realized in service. In most cases, these assumptions result in very conservative thermal ratings for liquid-filled power transformers. Safe utilization of this “latent capacity” is the subject of this chapter. In general, transformer load capacity is limited by equipment (winding and oil) temperatures. Industry standards (IEEE C57.12.00 in the U.S.) specify a maximum average winding rise that defines the rated load. In other words, when operating at rated nameplate current, the average winding rise shall not exceed the given value. For newer transformers with thermally upgraded insulation, manufactured starting in the late 1960s, this maximum average winding rise is 65°C. Combined with the 30°C ambient and a 15°C gradient between the winding hottest spot temperature and the average winding temperature, the peak temperature in the winding is 110°C. This temperature represents a somewhat arbitrary benchmark temperature that gives a reasonable life expectancy based upon the collective experience of the industry. Earlier transformers built before the introduction of thermally upgraded insulation were based upon a rated average winding rise of 55°C, or a hot spot of 95°C.

4-1

Chapter 4: Power Transformers

Chapter 4 includes seven sections:

• Section 4.2, Transformer Design, describes the general construction of power transformers, types of cooling, losses generated by transformers, and factory testing.

• Section 4.3. Risks of Increased Loading, outlines short- and long-term risks related to the loading of transformers.

• Section 4.4, Thermal Modeling, provides an overview of heat transfer mechanisms and describes the four most prevalent thermal models.

• Section 4.5, Thermal Ratings, discusses factors behind thermal ratings, including ambient air temperature, load, and maintenance considerations.

• Section 4.6, Winding Temperature Measurement, describes methods of measuring and monitoring winding temperature.

• Section 4.7, Modest Increases in Capacity from Existing Transformers, outlines methods of increasing cooling.

• Section 4.8, Examples, provides two examples of increasing capacity. 4.2

TRANSFORMER DESIGN

4.2.1

General Construction

Power transformers are commonly categorized into two main construction configurations: core form and shell form. These two categories are clearly defined in the case of three-phase power transformers. The definition becomes less distinct in the case of single-phase transformers, especially in the smaller sizes. In this range, the distinction is of minor importance, however. Core-Form Construction A core-form power transformer is constructed with windings that are in the general form of concentric cylinders (Figures 4.2-1 and 4.2-2). The magnetic core consists of stacks of laminated grain-oriented silicone steel sheets. The width of these sheets is varied so that, as stacked, the cross section of each leg conforms as nearly as practical to the circular form of the innermost wind-

Figure 4.2-1 Typical core-form construction (front view).

4-2


ing. With very few exceptions, the winding assemblies and core legs are assembled with their axis in a vertical or upright plane. The magnetic circuit is completed with yoke assemblies that bridge the three legs at the top and bottom. On some of the larger transformers, part of the required cross section of the yokes might be provided by outer legs at each end. These are referred to as “fifth legs” and allow a reduction in the vertical dimensions of both the top and bottom yokes. This reduction is often an important factor in meeting shipping clearances since core form power transformers are shipped with the coils and core legs in an upright or vertical position. The legs and yoke assemblies are joined with mitered interfaces that have alternating steps that overlap to provide good magnetic coupling. Modern practices are to use laminations of 0.009-in. thickness with at least five overlapping steps. This pattern is repeated across the entire build of the core assembly. The legs and yokes are maintained as an independent assembly by banding the legs with a nonconducting material such as fiberglass and in some cases, metallic bands that must be provided with an insulating gap to prevent circulating currents to flow around the band. Ducts for the flow of cooling oil are provided between concentric winding sections and sometimes within winding sections if required by the thermal characteristics of the design (Figures 4.2-3 and 4.2-4). Cooling ducts may also be required in the core legs and/or yokes (Figures 4.2-5 and 4.2-6). These ducts are formed by providing spacers between laminations at discrete intervals determined by the dimensions of the core. These ducts between laminations are usually mirrored in the top and bottom yokes.

Figure 4.2-2 Typical core-type internal assembly.



In a core-form transformer, the winding design permits cooling oil to flow vertically through the concentric windings and the core leg ducts (Figure 4.2-7).

Figure 4.2-3 Core-type winding assembly with concentric cooling ducts.

Figure 4.2-6 Cross section of core form construction.

Figure 4.2-4 Cooling duct being assembled on winding.

Figure 4.2-7 Oil flow in core-type winding.

Figure 4.2-5 Inner winding assembled on core (note oil ducts in core and below windings).

Shell-Form Construction In shell-form power transformers, the windings consist of phase assemblies produced by winding individual sections in a flat plane on a winding machine (Figures 4.2-8 and 4.2-9). These windings are initially assembled flat with insulation and cooling ducts between sections. Complete phase assemblies are then clamped and oriented in a vertical direction so that the plane of the individual sections are upright. The core laminations are inserted through and around the windings in the final 4-3


assembly process. The core and coil assembly is not designed to be lifted as a unit in most cases. In shell-form construction, the oil flows vertically through the ducts between individual winding sections (Figure 4.2-10). The spacers in these ducts are positioned to direct the oil across the width of each winding section.


Directed Flow Designs When forced oil cooling is employed, the transformer internal assembly may be designed with oil manifolds that direct the incoming cool oil to the lower part of the core and windings. In a nondirected flow transformer, the incoming cool oil is pumped into the bulk oil of the lower tank and moves through the core and windings in much the same manner as normal convection currents but with greater velocity (Figures 4.2-11 and 4.2-12). A directed flow design is normally used with larger sizes of transformers equipped with heat exchangers rather than radiators (Figures 4.2-13 and 4.2-14).

Figure 4.2-8 Typical shell-form construction (plan view).

Figure 4.2-10 Shell-form phase assembly under construction (cooling ducts are assembled between sections).

Figure 4.2-9 Shell-form transformer.

4-4

Figure 4.2-11 Core-form transformer designed for directed flow.



4.2.2

Types of Cooling

Oil-immersed power transformers are cooled by four different cooling configurations, each with unique heat transfer. They are as follows:

• ONAN (OA) – Also referred to as self-cooled, no pumps are used to circulate oil, and no fans are used to increase airflow over the radiators. Oil circulates upward through the windings and down through the radiators by natural thermosiphon flow.

• ONAF (FA) – No pumps are used to circulate the oil. Fans are used to force air over the radiators to increase heat transfer from the bulk oil to the surrounding air. As with ONAN, oil circulates upward through the windings and down through the radiators by natural thermosiphon flow.

• OFAF (Non-directed FOA) – Pumps are used to cirFigure 4.2-12 Directed oil flow in core-form construction.

culate the oil. Fans are used to force air over the radiators. The forced circulation of the oil increases the convective heat transfer from the windings to the oil. The forced air increases the convective heat transfer from the oil to the air. With OFAF, there are no ducts to direct the oil over the winding. In general, the bulk of the forced oil flow passes upward between the winding and the tank, bypassing the windings. Natural convection is still the predominant mode of heat transfer from the windings to the adjacent oil.

• ODAF (Directed FOA) – Pumps are used to circulate

Figure 4.2-13 Heat exchangers assembled on transformer.

the oil. Fans are used to force air over the radiators or heat exchangers. The forced circulation of the oil increases the convective heat transfer from the windings to the oil. The forced air increases the convective heat transfer from the oil to the air. With ODAF, ducts are added to direct the oil over the winding. This forces a significant portion of the forced oil to flow upward through the vertical winding ducts. Washers may also be employed in a zig-zag fashion to force the oil to flow back and forth between disk sections of a disk winding, further increasing the convective heat transfer from the winding to the oil. 4.2.3

Figure 4.2-14 Radiators assembled on transformer.

Losses

As with all electrical apparatus, transformers generate losses. These losses are manifested in the form of heat. This heat increases the temperature of the transformer components, and therefore limits the load capacity. Therefore, it is essential to discuss losses when discussing loading. The losses in a transformer are due to several different mechanisms, but are generally lumped into two categories: load losses and no-load losses (Figure 4.2-15). Load losses are losses that vary with load current, but not with excitation. No-load losses are losses that do not vary with load current, but rather vary with excitation or voltage.

4-5



ment of the magnetic domains produces losses. These losses are termed hysteresis losses.

Figure 4.2-15 Transformer equivalent circuit.

Load losses and no-load losses may be further broken down. Load losses consist of three components: winding I2R losses, winding eddy losses, and stray losses. Winding I2R losses are the Ohmic losses due to the load current flowing in the windings. Skin effect is generally ignored, but would be included in the I 2 R losses. Depending upon the conductor dimensions, the increase in winding I2R losses may or may not be negligible. In addition to the intended load current, unintended eddy currents flow within the winding conductor due to the presence of leakage flux, or flux that does not flow within the core. These eddy currents result in additional Ohmic losses in the winding conductors. The eddy losses can be reduced by using a stranded conductor, breaking the path for eddy current flow into smaller regions. If parallel strands or conductors are used, circulating currents between parallel sections can flow due to differing amounts of flux linkage. These losses can be reduced by transposing the cable, as in the cases of CTC (continuously transposed cable) or transposing the winding conductors at various points along the winding. Stray losses comprise the remainder of the load losses. Stray losses are losses due to currents induced in various metallic structures of the transformer, including the winding clamping structure, tie plates, core bolts, etc. Stray losses are parasitic in nature, and difficult to calculate. In some cases, the losses can result in high localized temperatures of various metal components. Often, in larger power transformers and GSUs (generation step ups), this is a serious concern and must be carefully examined during design and construction. No-load losses are composed mainly of losses in the steel core. The steel that comprises the core contains many microscopic regions of like magnetic polarity, called magnetic domains. When magnetic flux passes through the core, these domains shift to orient their magnetic poles in the direction of the flux. Since the flux varies sinusoidally, the domains must change direction as the flux changes direction. This continuous move-

4-6

Like the winding conductors, the flux passing through the steel core, which is electrically conductive, induces a current flow around the core. The magnitude of these induced currents is reduced by dividing the core cross section into thin sheets or laminations. Each sheet is coated with an insulating film. This reduces the total eddy current, and therefore the eddy loss, in the steel core. The core losses in any transformer are dependent on the core flux density. The core flux density is determined by the magnitude and frequency of the primary voltage and the cross-sectional area of the core leg according to Equation 4.2-1.

BM =

225 V × × 10 − 3 fA T

4.2-1

Where: Bm = maximum flux density in Tesla. f = operating frequency. A = cross-sectional area of core in mm2. V = primary voltage (RMS) per phase. T = number of primary winding turns per phase. The flux density, and therefore the principal core losses, are thus independent of load. There may be some localized heating of the outer core laminations or the core support structure by stray flux due to winding current that will be exacerbated by overloads. These losses are usually of little consequence to either short-term or long-term reliability of the transformer because they are removed from the winding insulation and affect the oil only in the local area involved. If a transformer has displayed a tendency, in normal service, to produce methane or ethane close to or in excess of condition #1 as described in ANSI C57.104, dissolved gas analyses should be performed at daily intervals when overloading to a level that has not been previously experienced. Continued operation at that level may normally be considered safe from this point of view if gas accumulation rates do not exceed condition #2 as detailed in ANSI C57.104. 4.2.4

Factory Testing

Little information on a particular power transformer is available to the user. Generally, the only information a user has on a unit is the information given on the factory test report and on the nameplate. Combined, these reports give the user key performance characteristics needed to operate the transformer. Included in this information is the heat run data, giving the temperature rises of the windings and the oil at the benchmark loading of the nameplate rating, and the loss data. In order



to interpret the data given on a factory test report properly, at least a passing understanding of the underlying test is necessary. This understanding will assist the reader in interpreting the numbers and any remarks that may be associated with the test values.

20°C plus the rated average winding rise. For 55°C or 55/65°C transformers, the reference temperature is generally 75°C. For 65°C rise transformers, the reference temperature is generally 85°C. This should be explicitly specified on the test report.

Factory Loss Tests

The I2R losses vary with temperature in a predictable fashion. The difficulty is in determining the appropriate temperature for an operating condition since the temperature variation between parts of a winding can be considerable.

No-Load Loss Testing No-load loss testing is performed with one winding open-circuited and rated voltage applied to the other winding. For practical reasons, voltage is usually applied to the low-voltage winding. This results in full excitation on the transformer, with only the exciting current flowing through the excited winding (Figure 4.2-16). Load Loss Testing The load losses in an operating transformer consist of:

•

I2R

losses in the current carrying components due to load current in all active windings.

• Joule losses caused by circulating currents in winding conductors due to impedance inequalities in parallel conductors.

• Eddy currents in winding conductors due to radial gradients in the induced voltages.

• Stray losses due to induced currents in the tank walls

ANSI standards require reporting of transformer losses at a reference temperature of 85°C for 65°C transformer ratings and 75°C for 55°C transformer ratings. For copper, these I2R losses are corrected to an operating temperature (T) as shown in Equation 4.2-2. PR(T) = PR(Tm ) (234.5 + T)/(234.5 + Tm )

4.2-2

Where: Pr(T) = I2R loss due to load current at operating temperature T (°C). Tm = reference temperature of the test report losses. PR(Tm) = test report I2R losses at Tm.

and internal support structures. Load losses are measured by short-circuiting either the high-voltage or low-voltage winding and then applying a voltage to the other winding that results in rated current flowing through the windings (Figure 4.2-17). The power loss measured, as measured by the wattmeter, is then the load loss at the temperature of the windings during the test. Since losses are dependent upon temperature, the load losses must be corrected to a standard reference temperature.

(The test report will give total load losses at the reference temperature and the measured winding resistances corrected to this temperature. The tested I2R can be calculated using the test report resistance at the reference temperature and rated winding current. Note that the test report resistance values for each winding are equal to the sum of the three phases as required by ANSI standards. Use of rated winding phase current with the test report resistance allows calculation of the threephase I2R loss for each winding.)

Prior to the test, the transformer is allowed to sit deenergized long enough for the oil temperature to stabilize. The temperature of the windings is then assumed to be equal to the average oil temperature. The load losses are corrected to a standard reference temperature of

The stray and eddy losses vary inversely with temperature. For copper, these losses are corrected as shown in Equation 4.2-3.

Figure 4.2-16 Basic circuit for no-load loss testing.

Figure 4.2-17 Basic circuit for load loss testing.

Ps(T) = Ps(Tm) (234.5 + Tm)/(234.5 + T)

4.2-3

4-7


Where: Ps(T) = stray losses at operating temperature T (°C) Tm = reference temperature of the test report losses Ps(Tm) = test report load losses at Tm minus PR(Tm) calculated above. The load losses at operating temperature T are the sum of PR(T) and Ps(T). Factory Temperature Rise Tests The basis for all practical transformer thermal models used in the evaluation of transformer loading is the factory heat run. The factory heat run provides a direct measurement of the thermal performance of a transformer at a particular benchmark, the nameplate rating. Given the temperature rises at this benchmark loading, it is possible to estimate the temperature rises under other loading conditions. Therefore, to understand the thermal models and their application to transformer loading and rating calculations, one must know the basic principles behind the factory heat run. This knowledge will prove invaluable when interpreting the data presented on the certified test report.

This test must be performed on the tap position and winding connection that gives the highest winding temperature as required by ANSI standards. The temperature rises over ambient should be given in the certified test report for each winding—along with the tap position, total losses, and line currents. The calculated winding hot spot temperature rise over ambient should given for the maximum transformer rating. Two methods are used to perform factory heat runs: the “short-circuit” method and the “loading-back” method. Of these two methods, the short-circuit method is by far the most common and will be covered in the greatest depth here. In addition to these two methods, it is also possible that a heat run may be performed by connecting the transformer to a load and loading the transformer at rated voltage and current simultaneously. This method is generally only practical for small power transformers and is not often used. Short-Circuit Method The short-circuit method, also sometimes referred to as loss injection, consists of two segments. In both segments of the test, one winding is short-circuited and a voltage is applied to the other winding. In this manner, each winding temperature can be checked. For transformers with multiple windings, the test load levels are usually agreed upon before hand, and each winding is tested with the other windings short-circuited.

4-8


For the initial segment of the test, one winding is shortcircuited and a voltage is applied to the other winding such that the active power supplied equals the total losses (load losses plus no-load losses) previously measured by other means (refer to IEEE C57.12.90 or IEC 76-1). Note that temperature rise tests are usually performed at the combination of taps that gives the highest losses. The power is applied continuously to bring the oil temperatures up to their steady-state values. Steadystate is defined in the respective test standards, but usually is such that the average oil temperature has not increased more than 1°C (or 2.5%, whichever is greater) for three consecutive hours. The purpose of this segment of the test is to establish the oil temperature rise over ambient. The second segment of the test is to measure the winding temperature rises. Once a steady-state average oil temperature has been reached, the applied voltage is reduced such that rated current flows in the windings under test. This load is held continuously for one hour. At the conclusion of one hour, the winding resistance is measured shortly after the windings have been disconnected, allowing just enough time for the inductance effects to dissipate. The winding resistance is measured several different times after shutdown, recording the resistance and time after shutdown each time (Figure 4.2-18). These points are then used to extrapolate the winding resistance back to the instant of shutdown. With this winding resistance and the cold winding resistance (measured prior to the heat run with the windings at a known ambient temperature), the average winding rise at the instant of shutdown can then be determined. This procedure may have to be repeated for each winding unless the available test equipment and transformer design allow simultaneous resistance readings on all windings. After completion of the above procedures, the oil temperature rises and average winding rises for each winding are known, given the test conditions. Since it is not

Figure 4.2-18 Example winding cooldown curve illustrating extrapolation of resistance measurements to shutdown.



always possible to maintain the exact loadings required to give the total loss or rated current, the raw results obtained above must be corrected to the rated losses and loads. This is done using simple empirical equations as shown in Equations 4.2-4 and 4.2-5. For oil temperatures:

θ o,corr

⎛P = θ o, meas ⎜ t, rated ⎜P ⎝ t, meas

⎞ ⎟ ⎟ ⎠

m

4.3.1 4.2-4

For winding temperatures:

⎛ I w , rated ⎜I ⎝ w , meas

θ w, corr = θ w , meas ⎜

⎞ ⎟ ⎟ ⎠

term degradation of the insulation paper and short-term reduction in dielectric strength due to bubble formation. Understanding these risks and their mechanisms is essential to any discussion on transformer loading. Users must be aware of the risks, take steps to assess these risks, and develop a methodology for maintaining risks at acceptable levels.

2n

4.2-5

Where: θo,corr = oil temperature corrected to rated losses. θo,meas = oil temperature measured during the heat run. Pt,rated = total losses at rated load. Pt,meas = total losses applied during oil rise portion of the heat run. m = oil rise exponent (0.8 for ONAN, ONAF, OFAF; 1.0 for ODAF). θw,corr = average winding rise corrected to rated load. θw,meas = average winding rise measured during test. Iw,rated = rated winding current. Iw,meas = winding current measured during the winding rise portion of the test. n = winding rise exponent (0.8 or ONAN; 0.9 for ONAF; 1.0 for OFAF, ODAF). Loading-Back Method This method is rarely used, and as such will not be described in any great detail here. For more information, consult the relevant test standards, IEEE C57.12.90 and IEC 76-2.

Short-Term Risks

Risks classified as “short-term” are those that would result in the immediate failure of the transformer. Reduction in dielectric strength due to gas evolution from the winding conductor insulation is the principal short-term risk. Additional short-term risks include gas evolution from lead conductors, gas evolution from wood and cellulose materials adjacent to metallic hot spots from stray flux heating, delamination of phenolic resin tap boards, and reduction of short-circuit withstand capability in epoxy-bonded CTC. Some of these risks will not result in failure in and of themselves, but when combined with an abnormal transient voltage or throughfault, may result in failure. Bubble Evolution Through destructive testing of model coils, researchers have discovered that under certain loading conditions, a significant decrease in dielectric strength of the winding assembly occurs. In the transformers considered here, specially refined petroleum oil is used as an electrical insulation material and, concurrently, as a heat transfer fluid. Gas-filled bubbles can be formed in the transformer oil in units in service. The electrical breakdown strengths of these gases are significantly lower than that of the transformer oil surrounding these bubbles. Bubbles that find their way into an electrically stressed oil gap can significantly reduce the breakdown voltage of the gap and interfere with the functioning of a transformer (Figure 4.3-1). Sixty-Hertz Breakdown Voltage in Percent of 25C Strength 100

90

80


Any energized transformer has a finite risk of failure. This risk of failure is generally very low. Loading transformers above the nameplate rating results in higher risks, eventually reaching the extreme where failure would be certain. The challenge is to determine loading levels that represent an acceptable level of risk, given the circumstances.

70 Breakdown Voltage, %

4.3

Paper Insulated Cable - Dry (<0.5%)

Paper Insulated Winding Conductor Dry (<0.5%)

60

50

40 Paper Insulated Winding Conductor Wet (3%)

30

20

10

0 0

50

100

150

200

250

300

Hot Spot Temperature, C

There are several risks related to the loading of transformers. The most significant of these risks are long-

Figure 4.3-1 Example of 60-Hz breakdown vs. temperature illustrating bubble formation.

4-9



Henry’s Law states that the concentration, Ci, of a single ideal gas, i, dissolved in a liquid is proportional to the partial pressure of that gas, Pi, over the liquid:

Ci = Ki * P i

4.3-1

At equilibrium, the drive of the dissolved gas to escape is balanced by the drive of the gas over the liquid to enter the liquid. Ki is a constant dependent on temperature, T, in a typical exponential manner:

Ki ~ exp (Bi /T)

4.3-2

The magnitude of Ki and its dependence on temperature reflect the particular intermolecular interactions of a given gas – liquid combination and are unique to that combination. Bi can be either positive or negative algebraically; it is negative for gases whose solubility increases as the temperature decreases. If, at constant temperature, the partial pressure of the gas over a liquid is decreased, the liquid will be supersaturated and gas will vaporize in order to reach a new equilibrium concentration as defined by Henry’s Law. Likewise, if the temperature changes so that Ki becomes smaller while the pressure of the gas over the liquid is held constant, additional gas will make its escape. In the reverse of these happenings, gas will dissolve. When the reduction in pressure of the gas over the liquid is slow or the local mass transport processes are relatively fast, the dissolved gas will diffuse through the liquid to and across the gas-liquid interface. The gas will “steam” away. The escape of the gas tracks the slow decrease in the external partial pressure. If, however, the pressure of the gas over the liquid drops so rapidly that dissolved gas does not have time to move to the surface, local supersaturation can occur and bubbles can nucleate. The bubble presses aside the surrounding liquid, and continues to grow as it absorbs supersaturating gas from the liquid. A bubble will grow so long as the pressure within the bubble exceeds the external pressure. The primary constraint to bubble growth is the pressure of the atmosphere over liquid. The effect of surface tension of the liquid at the bubble surface and the hydrostatic pressure of the liquid over the site of bubble growth are minor. An example – warm beer bubbles and foams when the bottle cap is removed and the pressure of carbon dioxide (CO 2 ) in the neck of the bottle is suddenly released. Colder beer bubbles and foams less, in part because the pressure to be released in the neck of the bottle is less, but also because CO 2 is more soluble in cold water (BCO2 is algebraically negative).

4-10

Oil in transformers normally contains more than one gas. Some transformers are designed to allow access of air to the interior. The gases dissolved in the oil are those present in air: nitrogen, oxygen, carbon dioxide, and traces of other gases. Other transformers are sealed and evacuated and then filled with nitrogen. The primary gas dissolved in the oil is nitrogen. Only small amounts of oxygen and traces of carbon dioxide remain. In general, gases dissolved in transformer oil behave as ideal dilute solutions in that the solubility of one gas is independent of the presence of any other gas; e.g., KN2 is the same whether CO2 is present or not, and CN2 is not affected by P CO2 . However, in forming bubbles, gases behave collectively. Each gas dissolved in the oil contributes to the internal pressure of the bubble according to Henry’s Law, shown in Equation 4.3-3. Pbubble = ∑ Pi = ∑ (C i / K i ) > Patm

4.3-3

A bubble forms when the sum of the partial pressures resulting from local concentrations of gases in the liquid exceeds the pressure over the surface of the liquid phase – Patm. The major solid electrical insulation in typical transformers is cellulose in the form of paper and press board impregnated with transformer oil. Water is absorbed by the cellulose. It distributes itself between the bulk oil and paper so that the concentrations of water in the solid and liquid media are in equilibrium with the water vapor pressure over the insulation system. Unlike nitrogen and oxygen, water vapor is a condensable gas. A very high percentage of the total mass of water in the system is contained in the paper. In most transformers the amounts of free oil and impregnated cellulose are comparable. In a subsystem containing equal volumes of paper (with 0.5% moisture content by weight) and transformer oil and equilibrated at 80°C, the paper will contain approximately 99.9% of the total weight of water. In effect, the paper in a transformer acts as an almost infinite reservoir supplying additional water to the oil at the higher internal temperatures occurring during operation. Water will re-absorbed on the paper when the electrical load on the transformer is reduced and will again be available for desorption when the transformer is next loaded. Desorption of water from the cellulose in the oil/paper insulations system is an example of a physical reaction that can increase the local concentration of gases in the oil to produce bubbling. Local concentrations can also change as a result of chemical reactions within the system.



Thermal decomposition of cellulosic insulation can occur in an operating transformer. The decomposition reaction can increase the local concentration of gases in the oil. The primary products of thermal decomposition of cellulose are water vapor, CO2, and CO. Decomposition of the oil/paper insulation at a sufficiently high temperature generates gases more rapidly than they can diffuse away into the surrounding oil. Again, the local concentration of gases builds to the point where the summation of partial pressures exceeds the pressure in the transformer and a bubble forms. To summarize, formation of bubbles in transformer oil reflects a complex interplay of variables in an operating transformer. Bubbles result from an abrupt departure from equilibrium between dissolved gas and oil – resulting from some change in pressure and/or local temperature in a transformer. Bubbles form when a local increase in gas concentration results in a local pressure that exceeds the pressure over the oil. Evaluation of bubble formation is difficult. The mechanisms are complex and dependent upon local conditions. The most influential factor is the moisture content of the paper. The temperature at which bubbles form is highly dependent upon moisture content, as illustrated in Figure 4.3-2. Note that this plot is for an example loading condition, and therefore, the values depicted are not to be taken as absolute truths. Given the importance of moisture in the determination of bubble evolution risk, accurate determination of moisture content would be necessary to use any sort of analytical model. Currently, there are no means of determining the moisture content distribution throughout an operating transformer with the required precision. Moisture content in oil is often related to moisture content in the paper using equilibrium curves. This,

however, has two problems. First, the moisture distributes throughout the winding inversely proportional to temperature. The moisture in oil could only give an average content of the entire bulk insulation. Second, the paper-oil system is rarely at equilibrium. The time constant of moisture diffusion is on the order of several days or weeks. Without any practical means to precisely assess the risk of bubble evolution, we must fall back on general guidelines that have been proven by experience. The general consensus in the industry is that bubble evolution does not occur at hot spot temperatures up to 140°C. This is probably valid for moisture contents up to 1.5–2%. Newer, dryer transformers could probably be safely loaded to temperatures approaching 160°C. Transformers in service for less than 6 months should be limited to temperatures of 120°C. Oil Expansion As with any fluid, oil expands as temperature increases. Specifically, the coefficient of expansion for oil is 0.000756, or the oil expands 0.08% for every degree C rise in temperature. This expansion is anticipated, and transformers are equipped with devices to handle oil expansion to some degree. IEEE C57.12.10, the IEEE standard for power transformers below 230 kV, requires that a transformer be capable of operating with temperature to 105°C. If the oil temperature exceeds 105°C, the oil may expand beyond the capacity of the gas space or conservator tank, resulting in operation of the mechanical pressure relief device and the expelling of oil. Not only does this present a maintenance and environmental headache, this can cause problems if enough oil is expelled such that upon cooling the oil level drops to a level exposing the active parts. This could result in a dielectric failure. 4.3.2

Long-Term Risks

200

Aging of Cellulose and Oil in Transformers For liquid-immersed transformers, the insulation system consists of the paper and pressboard solid insulation (cellulose) and the oil liquid insulation. Both the cellulose and liquid insulation are adversely affected by heat. However, while the liquid insulation can be replaced or reprocessed relatively easily, the properties of the solid insulation cannot be easily or effectively restored, nor can the insulation be economically replaced. Therefore, the loss of the paper insulation life is of utmost importance when considering transformer load capability.

190

Gas Evolution Temperature (deg C)

180

170

160

150

140

130

120

110

100 0

0.5

1

1.5

2

2.5

3

Moisture Content (% dry weight)

Figure 4.3-2 Gas evolution temperature vs. moisture content for example conditions.

3.5

Oil Aging Oils in transformers are mainly mineral oils. The oils can be grouped in two types: inhibited oils, which are heavily refined, reducing the amounts of aromatics and

4-11


polyaromatics, and then inhibited with an antioxidant to reduce oxidation, and the uninhibited oils, where natural aromatics and polyaromatics are natural inhibitors. When oils are subjected to oxygen and heat, they start to oxidize: the aldehydes, ketones, and finally carboxylic acids, presumably with a high molecular weight, are formed. The neutralization value and loss factor of the oil gradually increase, and the interfacial tension is reduced. At an even later stage, sludge may form. The oxidation rate increases with increasing temperature. For an inhibited oil, first the inhibitor is consumed (the period this takes is called the induction period). When it is fully consumed, the oils quickly start to oxidize. Before the inhibitor is gone, one may re-inhibit the oil, but the induction period is now be shorter, unless the oil is reclaimed. The main risk from the oil aging is sludge formation and clogging of cooling channels. The oil aging is not governed by the oxygen concentration but by catalytic processes, where hydroxyl radicals are formed via interaction with active metals like copper and iron. The oil condition may be followed by several diagnostic markers: Neutralization value, interfacial tension, loss angle, inhibitor content, and sludge measurement. It is important to take maintenance precautions before the condition becomes too severe.

Cellulose Aging Paper and pressboard are made from cellulose fibers (Figure 4.3-3). They contain 93% cellulose, with molecules that are long, straight polysaccharide chains, which may form crystalline regions. The average number


of cellulose molecules, called the degree of polymerization (DP), describes the length of the cellulose molecule. The cellulose also contains 5-6% hemicelluloses, which are polysaccharide chains with branches that do not easily crystallize, and lignin, which is a large branched molecule. The last two act as a thermoplastic. When cellulose ages, the cellulose chains are cut in a process called chain scission, reducing the average length of the cellulose chains and resulting in shorter fibers. The number of chain scissions (η) is defined as η= DPnew/DPold –1, where the DP value is taken before and after the aging period. Paper may be chemically modified to allow for operation at higher temperatures (thermally-upgraded paper). Upgraded paper is paper that is chemically changed by different chemical additives that reduces the aging rate compared to untreated kraft paper. A paper is considered “thermally upgraded” if it meets the life criteria as defined in ANSI/IEEE C57.100—50% retention in tensile strength after 65,000 h in a sealed tube at 110°C. However, upgrading can be done in various ways, so it is not a uniform group and may react differently to chemical aging accelerators. To retard aging, one can thermally upgrade the paper by linking bulky substituents such as cyanoethyl ether groups to the HO-groups in the cellulose and hemicellulose; or add weak, organic bases such as dicyandiamide, urea, or melamine (a cyclic trimer of urea) so as to neutralize acids produced by oxidation of the oil and paper. Beginning in the late 1960s, transformers in the U.S. were manufactured using thermally-upgraded paper, whether specified or not. Cellulose degrades at any temperature. The rate of degradation is very slow at room temperature. At elevated temperatures, however, the rate of degradation increases exponentially, effectively doubling for approximately every 8°C increase in temperature. Management of insulation degradation is necessary to maintain a reasonable life expectancy for the transformer. The shortening of the cellulose chains results in a reduction of the mechanical properties of paper and board, such as tensile, bursting, and folding strength. It is well known that the aging rate increases with increasing temperature; Montsinger states that the aging rate doubles (or life is halved) by every 6-8 oC temperature increase (Montsinger 1930).

Figure 4.3-3 Graphic depiction of cellulose chain (light gray is carbon, dark gray is oxygen, white is hydrogen).

4-12

The insulation aging rate has been studied extensively, and several mathematical models have been proposed. The most accepted of these models for insulation aging is that given in IEEE C57.91-1995 (IEEE 1995b), which



expresses insulation aging as an Arrhenius reaction rate equation. The equation is as shown in Equation 4.3-4. FAA = e

⎛ ⎞ A A ⎜ ⎟ − ⎜θ ⎟ ⎝ HS , R + 273 θ HS + 273 ⎠

(IEEE 1995b, Section 5.2, Equation 2) 4.3-4 Where: FAA is the insulation aging rate. A is a constant equal to 15,000 for most insulation types. θHS,R is the reference hot spot temperature for the insulation. θHS is the hot spot temperature at which aging is evaluated. The IEEE insulation model requires two parameters, the constant A and the reference hot spot temperature. For all cases, it is safe to assume that A is 15,000. The reference hot spot temperature varies depending upon whether the insulation is thermally upgraded and what standard is applied. For 55°C insulation, the reference hot spot temperature is 95°C. For 65°C insulation, the reference hot spot temperature is 110°C. Equation 4.3-4 can also be expressed in a form for per unit life: B

PerUnit Life = At e T

Hot

− 273

transformer condition on aging is hard to find. It is all about getting information about the At factor.

Chemical Description of Aging For the purposes of insight, aging considerations can be based not on changes of a functional property like tensile strength, but on changes of the chemical properties of the paper—the degree of polymerization. A disadvantage of doing this is that the link is lost to the directly relevant mechanical properties, though only applicable on laboratory aged samples. The main advantages are that the approach uses a property that can be measured from samples from service-aged transformers and that it is closer to considerations on the chemical kinetic processes taking place. If the aging analyses are based on DP changes, a correlation between the functional critical tensile strength and the DP, as shown in Figure 4.3-4, is needed. One usually considers aging under normal conditions (nameplate conditions and specified overload) to be due either to hydrolysis or to oxidation, and that a third process (pyrolysis) may take place under failure conditions (thermal defects). The aging due to one kinetic mechanism follows Equation 4.3-6 −E

1 1 − = Ae R⋅(T + 273) ⋅ t DPold DPnew

4.3-6

4.3-5

Where: B describes how sensitive the ageing is to temperature (15,000 in C57.91). THot is the hotspot temperature of the transformer. At is a factor describing the influence of the environment on the change in tensile strength (9.8 x 10-18 in C57.91).

where the DP is given before and after an aging period ( t ) at a temperature T. E is the so-called activation energy, which describes the sensitivity to the temperature, A depends on the chemical environment, and R is the molar gas constant. Note that this is of the same form as the Arrhenius reaction rate equation first proposed by Dakin in 1948 (Dakin 1948). Usually the paper has a DP around 1000 in a transformer after

The base of all this is a definition of a material test where the criterion is that paper aged under a certain condition (e.g., T Hot = 110 o C) should not lose more than a certain percentage of its functional property (tensile strength) within the period. This is referred to as the expected life of a transformer (e.g., 30 years) at nominal load under specified ambient conditions where the hotspot condition has to be mastered. The dependence of aging on temperature is fairly well known; However, the big problem for a utility when managing an aging transformer population is that Equations 4.3-4 and 4.3-5 are based on experiments under optimum clean conditions for the paper, and that quantitative information on the importance of the

Figure 4.3-4 Correlation between tensile index and DP value for nonthermally upgraded kraft paper.

4-13



vapor phase drying, and often a DP of 200 is used as an end-of-life criterion. We can rearrange and change the equation to: −E

⎤ 1 ⎡ DPnew − 1⎥ = Ae R ⋅(T + 273) ⋅ t ⎢ DPnew ⎣ DPOld ⎦

4.3-7

and further to

1 ⋅η = k ⋅ t DPnew

4.3-8

where η is the chain scissions and k the aging rate. We can see that the aging rate depends on temperature (T), the activation energy (E), and the environment (A). For a first-order single process, this dependence can be described by an Arrhenius plot, plotting the natural logarithm of the rate versus the inverse absolute temperature (T + 273) as shown in Figure 4.3-5. The principle here is that, if the points end along a straight line, this aging can be described by one single aging process. Thus far, focus has been on the temperature dependence. Recent investigations indicate that the environment may be of even greater importance. Let us first consider non-upgraded kraft paper.

The other major mechanism of paper aging is hydrolysis. The significance of water content is paramount: a humidity of 3-4% may increase the degradation rate of paper by a factor of 10 or more, compared to dry paper. In addition, it is commonly acknowledged that a high acidity in the oil accelerates aging but in a nonspecific way. Lately, models have been developed outside the power engineering community (Lundgaard et al. 2004). It is now understood that the hydrolysis is specific-acid catalyzed and unimolecular. This means that it is catalyzed exclusively by hydrogen ions from dissociated acids; undissociated carboxylic acids do not depolymerize cellulose. It is the hydrogen ion activity (or “pH”) that matters, not the total (undissociated) acid concentration. It also means that water does not participate in the rate-controlling step. Water does, however, affect the acidity by causing carboxylic acids to dissociate, and in this way it exerts a profound influence upon the aging process. During this process, carboxylic acids (like formic, acetic, and laevulinic acids) are produced, which makes the process auto-acceleratory. These acids mainly reside in the cellulose and may to a large degree be extracted from oil and paper using water extraction. This applies to kraft paper. The processes for thermallyupgraded papers are more complicated. It is likely that the activation energy of oxidation is different and lower than for hydrolysis, and that for pyrolysis, it is even higher than for hydrolysis. This can be illustrated by the plot in Figure 4.3-6, where lines with different slopes are plotted for the different mechanisms.

ln (reaction rate)

Kraft Paper One major mechanism of paper aging is oxidation. The oxidizing agent in this environment is oxygen from air ingress. The ultimate end products of oxidation are the same as for combustion—i.e., water and carbon dioxide. The mechanism of low-temperature oxidation is quite different from that of combustion, though. The oxygen

concentration is, of course, an important parameter to determine the rate of oxidation. However, most experimental studies show that the aging rate is not so strongly influenced by oxygen content. Typically, the overall degradation rate no more than doubles in experiments with oxygen present, compared to when oxygen is totally excluded. We can, therefore, say that the importance of oxygen is limited.

H2O

Figure 4.3-5 Arrhenius plot and significance of parameters for kraft paper at 0.5% (dry) and 3% (wet) moisture.

4-14

O2

1/T

Figure 4.3-6 Total aging as a sum of several mechanisms.


Thermally Upgraded Paper Upgraded paper is paper that is chemically changed by different chemical additives that reduce the aging rate compared to untreated kraft paper. A paper is considered “thermally upgraded” if it meets the life criteria as defined in ANSI/IEEE C57.100—50% retention in tensile strength after 65,000 h in a sealed tube at 110°C. However, upgrading can be done in various ways, so it is not a uniform group and may react differently to chemical aging accelerators. To retard aging, the paper can be thermally upgraded by linking bulky substituents such as cyanoethyl ether groups to the HO-groups in the cellulose and hemicellulose, or weak, organic bases such as dicyandiamide, urea or melamine (a cyclic trimer of urea) can be added so as to neutralize acids produced by oxidation of the oil and paper. In one study it was found that the aging rate for one upgraded paper type (Insuldur from Avery Dennison) showed both lower reaction rates at a specific temperature, and that the acceleration due to presence of water was lower, as shown in Figure 4.3-7 (IEEE 1995c). In another study on an upgraded paper (Rotherm) from Tullis Russel, a similarly reduced sensitivity to water was observed (Schroff 1985). The different sensitivity to water indicates that the acid catalyzed hydrolysis is suppressed. In (Lundgaard et al. 2004), the experimental results indicated that aging for oxygen-rich oil could increase by a factor of about seven in the temperature range below 90oC, while water (3%) increased it around 3 times as shown in Figure 4.3-7. Plastic Deformation and Winding Slackness The transformer winding is clamped with a pressure strong enough to give friction forces between windings that may withstand the forces from a short-circuit current. The cellulose can undergo plastic deformation;

Figure 4.3-7 Arrhenius plots of aging rate for standard Kraft paper and thermally-upgraded insuldur paper (IEEE 1995c).


water will in this context act as a plasticizer. Changes in pressure may result from the following reactions:

• Increased moisture will cause swelling and increase the pressure.

• Drying may cause shrinking of the insulation and reduced pressure.

• Thermal cycling will cause expansion and retraction of the materials, cyclic pressure variation, and loss of pressure. Diagnostics of the Cellulose Accurately diagnosing the condition of the cellulose, and therefore the remaining useful life of the transformer, is a most difficult, if not impossible, task. The only way of accurately determining the condition of the cellulose insulation system is to take samples from various places throughout the transformer and measure the DP. This is impractical for several reasons. First and foremost, this involves disturbing the solid insulation in areas of high electrical stress. Additionally, many areas are simply inaccessible. A limited sampling can be done by taking paper from relatively accessible areas. This, however, involves draining all of the oil, physically breaching and entering the tank, collecting the sample while avoiding contamination, and refilling the unit under vacuum. Breaching the tank introduces the possibility of contamination by particulates or moisture and carries a finite risk. Without entering the tank, the only remaining alternative for measurement is to draw an oil sample and measure the level of a chemical marker indicative of cellulose aging. Fortunately, several furanic compounds, measurable by High-Performance Liquid Chromatography, are produced during the aging process. By measuring the levels of these compounds in the oil, the average condition of the entire insulation system can be estimated. This method, however, carries with it several drawbacks. First, the measurement represents only the average of all of the cellulose in the unit. In reality, only a small percentage of the cellulose is subject to high temperatures during overload. It is this cellulose, and in particular the cellulose that is exposed to high temperatures and high electrical stress, that is important. In addition, furan analysis is incapable of discerning localized defects that result in high heating in a small area. Furan production is also a function of the paper-to-oil ratio of a transformer, which varies widely depending upon winding construction, BIL, and rating. Finally, if the oil is replaced or reclaimed, the aging information derived from furan analysis up to that point is lost. A final method of estimating the condition of the cellulose is to simply examine the typical loading and ambient

4-15



air temperatures over the transformer’s service life and approximate the cumulative insulation aging by the standard thermal models and insulation aging models. While not precise, this method is remarkably simple and gives a general feel for the serviceability of a particular unit. Concluding Remarks on Thermal Aging of the Insulation Historically, too little attention has been given to the changes in thermal performance of a transformer due to changes in the condition of the insulation system. Depending on the materials used, the acceleration of aging due to chemical contamination may exceed that from increased temperature. Together with a poor condition of the transformer, a long-term temperature increase may result in a very short life. The life may be estimated using the formulae below. The life expectancy of the solid insulation is difficult to define precisely. The “end-of-life” of any device or system is when the system can no longer perform its intended function. In the case of electrical insulation, this is when the insulation no longer provides sufficient dielectric strength to prevent dielectric breakdown. In the case of cellulose insulation, such as that used in power transformer, the electrical properties of the paper do not significantly degrade until well after the mechanical properties become unworkable. The paper will became extremely brittle and crack or tear at the slightest mechanical disturbance. If this were to occur in an operating transformer, the loss of solid insulation by displacement could detrimentally weaken the insulation structure. Therefore, the mechanical strength of the paper is the defining evaluation criterion with respect to aging.

Several different mechanical strength properties have been used by various investigators to quantity the degradation of cellulose. The burst strength, fold strength, elongation to break, abrasion resistance, and tensile strength have all been used as indicators of mechanical strength. In addition, degree of polymerization (a measure of average polymer chain length of the cellulose molecule) has been used. Degree of polymerization, DP, varies nearly proportionally to reduction and mechanical strength. Of these measures, tensile strength and DP are used most commonly to define end-of-life criteria. Table 4.3-1 lists several different end points for insulation thermal life based upon 50% tensile strength retention, 20% tensile strength retention, and a degree of polymerization value of 200 (McNutt 1992). Also illustrated in this table are the detrimental effects of moisture and oxygen. Since there are many different valid end-of-life criteria, it is ultimately up to the user to select a criterion. The recommendation of this guide is that the DP of 200 end point be used when evaluating life consumption. As an alternative, the user could forgo the definition of an insulation life end point and instead consider aging in relative terms—i.e. per unit aging rate (FAA) or equivalent aging hours. However, the question still remains of when to remove a unit from service. The failure risk of transformers has often been represented by the “bathtub” curve, so named for its shape (Figure 4.3-8). This curve represents the failure risk over time for a particular transformer, with all else constant. External factors, such as loading, throughfault fre-

Table 4.3-1 Insulation Thermal Life Expectancies for Various Endpoint Criteria, Moisture Contents, and Oxygen Levels (McNutt 1992) Basis

50% Tensile

20% Tensile

200 D.P.

4-16

Moisture in Paper (%)

Oxygen Level

Life (hrs)

0.5%

Low

65,020

1.0%

Low

32,510

2.0%

Low

16,255

0.5%

High

26,000

1.0%

High

13,000

2.0%

High

6,500

0.5%

Low

152,000

1.0%

Low

76,000

2.0%

Low

38,000

0.5%

High

60,800

1.0%

High

30,400

2.0%

High

15,200

0.5%

Low

158,000

1.0%

Low

79,000

2.0%

Low

39,500

0.5%

High

63,200

1.0%

High

31,600

2.0%

High

15,800


quency, and maintenance (or lack thereof) all shift portions of the curve in some fashion. If the failure rate with time is represented by a bathtub curve, the time axis can be viewed as a “cumulative thermal aging” rather than actual age of the unit. As the insulation system ages thermally, the system approaches the “wear out” portion of the curve, where failure risk increases, although failure is not necessarily imminent. The transition point from a relatively flat failure risk to an increasing failure risk is the thermal end-of-life, in rough terms. Of course, this is only approximate and varies with several factors, including condition, design, vintage, etc. One major point of confusion and misunderstanding when performing loading calculations and making loading decisions is the discussion of percent loss-of-life (in percent total life expectancy) and of the end-of-life or life remaining. In rough terms, the “end of life” for an insulation system is the point at which the insulation no longer performs reasonably. For electrical insulation, this means the point at which the insulation system no longer maintains a majority of its original dielectric strength. As insulation ages, the dielectric strength of the paper does not decrease significantly until well after the paper has become brittle. Given the need for transformer insulation to withstand mechanical forces, especially during throughfault, the point at which the paper loses enough strength to withstand the mechanical forces is the practical end of life for the insulation system. Given this, a precise definition becomes difficult because this is dependent upon the application of the material, both electrically and mechanically. Therefore, general measures of mechanical strength have been historically


used. Some criteria include 50% tensile strength retention, 20% tensile strength retention, and more recently, a degree of polymerization of 200. In addition, functional life testing has been performed on distribution transformers subjected to impulse voltages and shortcircuits. Each of these criteria gives a different life end point, ranging from 65,000 hrs to 180,000 hrs. These values are largely artificial. A transformer that is not subject to high throughfault duty may operate reliably well after the 180,000-hr end point. Therefore, if %loss of life (LOL) is discussed, the value for a given temperature can vary by a factor of three. It is well known that insulation aging rates increase with the presence of increased moisture and oxygen. The original equations in the IEEE Loading Guide (IEEE 1995b) are based mostly upon sealed tube aging tests with moisture contents less than 0.5% and presumably lower oxygen contents. This does not reflect the reality of operating transformers and misleads the user on the actual aging rate. The importance of keeping transformers dry and oxygen free are not reflected in the guide, and are best addressed by including quantitative estimates of the effects of moisture and oxygen in the aging equation. It is proposed that this be done by applying multiplying factors to the “Age Acceleration Factor” calculated as shown in Equation 4.3-9. F AA = kH O kO e Θ 2

2

B o+

B 273 Θ HS + 273

4.3-9

Where: FAA is the insulation aging rate. A is a constant equal to 15,000 for most insulation types. θHS,R is the reference hot spot temperature for the insulation. θHS is the hot spot temperature at which aging is evaluated. kH2O and kO2 are determined from Tables 4.3-2 and 4.3-3, respectively Table 4.3-2 Aging Rate Correction Factor for Moisture in Paper Moisture Content in Paper (roughly)

kH2O

Dry (< 0.5%)

1

Moist (0.5-2.5%)

2

Wet (> 2.5%)

4+

Table 4.3-3 Aging Rate Correction Factor for Oxygen Content of Oil Oxygen Content

Figure 4.3-8 Example bathtub curve demonstrating thermal end-of-life.

kO2

Low

1

High

3-5

4-17



The factors developed in the tables were derived from data published by Emsley, Lundgaard and McNutt (Emsley and Stevens 1994; Lundgaard et al. 2004; and McNutt 1992). They are approximations. However, insulation aging calculations, as a whole, are gross approximations. By applying these factors directly in the equation, users are well aware of the importance of moisture and oxygen, and are given a method for evaluating the impact of moisture and oxygen, as well as estimated life consumption for transformers with moisture contents in paper greater than 0.5% and with increased oxygen levels. % LOL =

FAA ⋅ t Expected Life

4.3-10

Where: t is the number of hours at the hot spot temperature. Expected life is a value selected from Table 4.3-1. 4.3.3

Additional Risks

Ancillary Components Following insulation loss of life and bubble formation, the most significant risk associated with transformer overload is damage to the ancillary components, such as bushings, on-load tap changers (LTCs), off-load tap changers (DETCs), and current transformers (CTs). This risk is often overlooked as a rating consideration. Generally, these components are oversized due to their relative cost when compared to the transformer itself. However, it is possible that some limitation on the overload capability of a particular transformer may be due to an ancillary component.

Bushings Oil-impregnated, paper-insulated, capacitance-graded bushings are designed with 105°C bushing hot spot limit at rated load and 95°C top oil temperature average over 24 hrs. Overload, based upon the rated bushing current, is possible. Overload risks of bushings include:

• • • •

Pressure build-up due to oil expansion. Deterioration of gaskets and seals. Thermal deterioration of paper insulation. Increase in dielectric loss, possibly resulting in thermal runaway.

• Gas evolution at extreme hot spots. Overload limits, as specified in C57.19.100-1995:

4-18

• • • •

40°C ambient temperature 110°C transformer top oil temperature 2x rated bushing current 150°C bushing hot spot temperature

The bushing hot spot is usually located adjacent to the central conductor in the area of the mounting flange. It is here that the insulation is the thickest and the external heating, via the bulk oil, is highest. The hot spot temperature of the bushing conductor may be calculated as shown in Equation 4.3-11 (IEEE 1995c). Δθ HS = K1I n + K 2 ΔθO

4.3-11

Where: ΔθHS is the bushing hot spot temperature. K1 is a bushing-specific constant, typically ranging from 15 to 32. K2 is a bushing-specific constant, typically ranging from 0.6 to 0.8. n is a bushing-specific constants, typically ranging from 1.6 to 2.0 with 1.8 typical. I is the bushing current in per unit of the rated bushing current. Δθ O is the bushing immersion oil temperature (transformer top oil). The transient temperature rise may then be calculated as shown in Equation 4.3-12. Δθ HS ,2 = Δθ HS ,1 + ( Δθ HS ,U

Δt ⎛ − τB ⎜ − Δθ HS ,1 ) 1 − e ⎜ ⎝

⎞ ⎟ ⎟ ⎠

4.3-12

Where: ΔθHS,2 is the bushing hot spot rise at time t1 + Δt. ΔθHS,1 is the bushing hot spot rise at time t1. ΔθHS,U is the steady-state temperature given in the previous equation. τB is the bushing time constant. The determination of the constants is the greatest obstacle to the use of these equations. Accurate determination can only be made through tests on duplicate bushings. These tests are not performed routinely by the bushing manufacturer. This infor mation may be requested from the manufacturer. If the data is not available, however, typical default values can be used without a significant sacrifice in accuracy. The paper used in paper-insulated bushings is not thermally-upgraded, unless otherwise specified. As such, the standard loss-of-life model given in C57.91-1995 for 65°C rise insulation systems should not be used to cal-



culate the loss-of-life for bushing insulation. Instead, Equation 4.3-13 should be used: 15,000

FAA = e

368

−

Δθ C = Δθ C , R I n

15,000

θ HS + 273

4.3-13

Where: FAA is the aging acceleration factor. Percent loss-of-life and cumulative aging can be calculated as outlined in C57.91-1995. The above method may be applied to resin-bonded or resin-impregnated bushings. The above method does not apply to draw-lead connected bushings. Draw-lead connected bushings are limited by the temperature rise of the draw-lead. Therefore, the bushing temperature is determined by the size and construction of the drawlead. Accurate determination of draw-lead current carrying capability would require detailed information on the lead and its application. However, in a properly designed application, the draw-lead does not limit the thermal rating of the transformer. On-Load Tap Changers (LTCs) The critical component of an on-load tap changer, from a thermal standpoint, is the contacts. LTCs are properly designed with a contact rise over oil of less than 20°C at 1.2 times rated load (rated load here is the rated load of the LTC, not the transformer itself). In addition, LTCs are designed to break twice rated current at least 40 times without detrimental degradation of the contacts. In some instances of high overloads, it may also be advisable to switch an LTC to manual control and minimize or eliminate operation. Overload risks of LTCs include:

• Increased contact wear and ablation with increased load during break operations

• Increased contact temperature increases probability and rate of coking of contacts (>120°C)

• Higher overloads result in prolonged arcing during break operation. Dragging the arc across the contacts could result in short-circuiting the regulating winding. Overload limits, as specified in C57.131-1995 (IEEE 1995a):

• 120°C contact temperature (higher is OK, but may result in greater maintenance).

• 2x LTC rated load current (limit breaking operations at high load level to few times/year).

The temperature rise of the contacts is calculated as shown in Equation 4.3-14 (IEEE 1995c) 4.3-14

Where: ΔθC is the LTC contact temperature rise over oil. ΔθC,R is the LTC contact temperature rise over oil at rated load. I is the LTC current in per unit of the rated LTC current. n is an exponent that varies from 1.6 to 1.85, with 1.8 as the default.

θ C = θ A + Kθ TO + Δθ C

4.3-15

Where: θC is the total contact temperature. θA is the ambient air temperature. θTO is the transformer top oil temperature. K is a constant to account for the difference between transformer top oil temperature and LTC compartment oil temperature. This is typically around 0.8. It is important to note that the main difficulty associated with elevated temperatures in LTCs is the increased tendency toward contact coking. Since coking increases the electrical resistance across the contact assembly, coking can result in even higher temperatures and possible thermal runaway. If frequent high loading periods are expected, the temperature differential between the main tank oil and the LTC compartment oil should be checked, if possible. In addition, the LTC oil should be clean oil with high interfacial tension (IFT) and low acidity. Reduced Capacity Taps The load dependent losses, and therefore the heating of the transformer windings, is a function of the winding current. Often the transformer load is expressed in terms of apparent power, or MVA, since this number is essentially the same for all windings (neglecting losses). However, in the case of rated MVA when taps are present, the rated current varies inversely proportional to the voltage. The consequence for loading is that, for lower voltage taps, the rating in MVA for a given size conductor decreases.

Often, to maintain the same MVA load capability for all taps, the conductors are sized according to the current at the lowest voltage time. However, occasionally, to reduce cost, the transformer may be specified with reduced capacity taps. In this case, the conductors are sized for the rated current at the neutral position. For higher-voltage taps, the transformer is capable of carrying full rated MVA. However, for lower voltage taps, the

4-19



transformer is capable of carrying only a reduced MVA, corresponding to the rated current at the neutral tap. Transformers with reduced capacity taps can easily be identified by referring to the table of tap positions, voltages, and rated currents on the nameplate. Transformers with reduced capacity taps have the same rated current for all taps at voltages below neutral. An example of this is shown in Table 4.3-4.

It is important to examine the nameplate when determining the load capability of a particular transformer to determine if the unit was designed with reduced capacity taps. If it was designed with reduced capacity taps, and the unit is operated at taps below neutral, the load capability in MVA will be lower than the nameplate MVA.

Table 4.3-4 Nameplate Showing Tap Positions, Voltages, and Currents CONNECTIONS CRT LOAD TAP CHANGER WINDING

“H” VOLTAGE WYE

CONNECTS IN EACH PHASE

VOLTAGE

MAXIMUM FOA AMPERES

PCS

P1 TO

P3 TO

R TO

120175

432

16L

11

11

3

119495

435

15L

11

10

3

118610

437

14L

10

10

3

118130

440

13L

10

9

3

117445

442

12L

9

9

3

116765

445

11L

9

8

3

116080

448

10L

8

8

3

115395

450

9L

8

7

3

114715

453

8L

7

7

3

114030

456

7L

7

6

3

113350

458

6L

6

6

3

112665

461

5L

6

5

3

111980

464

4L

5

5

3

111300

467

3L

5

4

3

110615

470

2L

4

4

3

109935

473

1L

4

3

3

109250

476

NEUT

11

11

11

108565

476

1R

11

10

11

107885

476

2R

10

10

11

107200

476

3R

10

9

11

106520

476

4R

9

9

11

105835

476

5R

9

8

11

105150

476

6R

8

8

11

104470

476

7R

8

7

11

103785

476

8R

7

7

11

103105

476

9R

7

6

11

102420

476

10R

6

6

11

101735

476

11R

6

5

11

101055

476

12R

5

5

11

100370

476

13R

5

4

11

99690

476

14R

4

4

11

99005

476

15R

4

3

11

98325

476

16R

3

3

11

NO LOAD TAP CHANGER

4-20


WINDING

VOLTAGE

AMPERES

A

B

“X” VOLTAGE WYE

59000

753

2

1 TO 19

13 TO 15

06000

787

1

1 TO 18

13 TO 14

POS


Bushing or Internal CTs Detailed evaluation of bushing CTs is difficult, if not impossible. The location of the CT can be in the bushing adapter or “turret,” or mounted on the active assembly in the tank. Bushing CTs are usually limited by transformer top oil temperature. Maintaining a top oil temperature of less than 110°C should avoid excessive temperatures. Aging rates should be lower than that of the winding insulation over the average of the loading conditions. De-Energized Tap Changers (DETCs) De-energized tap changers are similar, in a thermal sense, to on-load tap changers, albeit much simpler. The same general considerations and risks apply to DETCs as to LTCs. Coking may become a greater problem for DETCs, as they are seldom operated. It may be advisable to periodically operate the DETC over the range of taps to “wipe” the contacts clean of any deposits. Lead Heating Internal connecting leads may be a concern. The same hot spot limits, and associated risks, apply for leads as for windings. In general, it is impossible to evaluate lead heating without detailed design data. In a properly designed transformer, the connecting leads should not limit the overload capability. However, lead hot spots have been a limitation in the load carrying capability of many transformers because of lack of attention in the design stage or manufacturing practices that permitted or even encouraged liberal application of insulating tape at lead connection points.

Evaluation of lead heating problems outside of the factory is rather difficult. Even with dimensions of the leads and construction details, it is difficult to assess the oil flow conditions in the vicinity of the lead. The best method for assessing lead heating problems is by examining the DGA records for the unit for any hint of heating gases involving cellulose decomposition, particularly CO and CO2 , and eventually CH4 and C 2 H6 . If these gases are present in significant quantity or have a generation rate that increases sharply with load, load should be reduced immediately. At the earliest convenience, an internal inspection should be performed to locate the source of the gassing. In addition to DGA, partial discharge detection and perhaps Furan analysis may also yield useful information. Stray Flux Heating Heating of non-current carrying metal components by the leakage flux of the windings and leads is termed “stray flux heating.” The leakage flux induces eddy current in any conducting material that it passes through. This includes the steel clamping structure, tie rods or tie plates, metal core bands, and the tank wall itself. Since


leakage flux varies proportionally with load current, the stray flux heating increases roughly with the square of winding current. For larger power transformers and GSUs in particular, the problem of stray flux heating can be substantial. Special design measures must be taken to reduce the induced currents. The most common areas of stray flux heating problems are tie plates, used to connect the upper and lower core yoke clamping structure, and bushing penetrations. As with lead heating, evaluation of stray flux heating potential is difficult. The best method for assessing stray flux heating problems is by examining the DGA records for the unit for any hint of hot metal gases, specifically methane and ethane. Should either of these gases exceed 120 ppm or 65 ppm, respectively, high loading should be discontinued and the source of the gases investigated. In addition, sudden increases in these gas levels concurrent with increased loading should be considered additional cause for alarm. In addition to DGA, stray flux heating in the tank wall can be evaluated by examining the transformer with an infrared camera. Particular attention should be paid in the area of bushing penetrations and bushing adapters. A visual examination for discolored paint could also reveal stray flux heating. 4.4

THERMAL MODELING

Given the extreme complexities of heat transfer within a transformer, as well as the lack of information typically available, drastic simplifications must be made. It is important to recognize the simplifications and to know the areas in which these simplifying assumptions are not sufficiently accurate. Therefore, this section begins with a brief and somewhat academic overview of the various heat transfer mechanisms involved. Following this, the section describes available thermal models. 4.4.1

Mechanisms of Heat Transfer

In a power transformer, two heat transfer mechanisms are predominant: radiation and convection. Conduction plays a smaller role and will not be described at length here. It should also be noted that even the most modern treatments of the subject are largely empirical. This initial discussion parallels that of Montsinger in (Montsinger 1951), with additional emphasis on variables that may not be constant. Radiation All bodies at a temperature above their surroundings radiate heat energy to the surroundings. The mathematical relationship between heat lost due to radiation and

4-21



the temperature rise are fairly well known, as shown in Equation 4.4-1 (Cengel 1997)

Qrad = εσA(Tb − Ta ) 4

4

4.4-1

This relationship can be simplified to a simple power relationship of the form shown in Equation 4.4-2.

Qrad = KΔθ x

4.4-2

This relationship, for a given exponent x, is generally valid over a limited temperature range (Figure 4.4-1). The curve fits in Figure 4.4-1 are generally valid from a 0°C rise to about a 70°C rise. The exponents vary from 1.133 for a 0°C ambient to 1.117 for a 40° C ambient. Note that the emissivity will change the multiplicative constant but not the exponent. This relationship could also be expressed inversely as: m Δθ = CQrad

4.4-3

where m = 1/x. For the ranges of x derived above, m varies from 0.883 for a 0 ° C ambient to 0.895 for a 40 ° C ambient. The absorption rate in the infrared region for transparent liquids such as transformer oils is relatively high. Therefore, the radiant energy from transformers windings is absorbed by even a thin layer of oil, and is therefore negligible. Air, on the other hand, has a negligible absorption rate, and radiant energy loss must be considered when determining the heat loss from the tank, and therefore the oil.

Forced Convection When heat is transferred from a solid to a moving fluid medium, the adjacent fluid is heated by conduction. Since the fluid medium is moving, the heated fluid is quickly replaced by cooler fluid. This results in an increased rate of heat transfer than would occur by conduction alone. The heat loss due to convection can be expressed by Newton’s Law of Cooling, as shown in Equation 4.4-4 (Cengel 1997).

Q = hA(Tc − Ta ) 4.4-4 Where: Q is the rate of heat loss. h is the heat transfer coefficient. Tc is the temperature at the surface of the object (solid). Ta is the temperature of the surrounding fluid.

For cross-flow over a cylinder or similar-shaped object (Cengel 1997): ⎛ ρVD ⎞ k ⎟⎟ h = C ⋅ Re Pr ⋅ = C ⋅ ⎜⎜ D ⎝ μ ⎠ m

n

m

⎛ μC p ⎜ ⎜ k ⎝

⎞ ⎟ ⎟ ⎠

n

4.4-5

Where: C is a constant. Re is the Reynold’s Number. Pr is the Prandtl Number. k is the thermal conductivity of the fluid. D is the characteristic length of the immersed object (diameter of cylinder). ρ is the density of the fluid. V is the velocity of the fluid. μ is the viscosity of the fluid (varies with temperature). Cp is the specific heat of the fluid. m, n are constants. From this, it can be seen that h is a function of several parameters, including geometry, fluid velocity, and fluid viscosity. The exponent n is typically 1/3. The exponent m, determined empirically, ranges from about 0.3 to 0.8, depending upon the geometry. Note that if the exponents are equal, the viscosity cancels out and is no longer a factor. Summarizing, the heat loss can be expressed by: Q = KΔθ

4.4-6

or, solving for the temperature rise: Δθ = KQ Figure 4.4-1 Radiative heat transfer at various ambient temperatures.

4-22

4.4-7

Natural Convection Natural convection is slightly more complex than forced convection. The heat transfer is still a function of the



velocity of the fluid, as described above. However, now the velocity of the fluid is the result a varying fluid density with temperature. This is known as thermosiphon flow. The basic relationship is the same as for forced convection. Q = hA(Tc − Ta )

4.4-8

However, h is now a function of the temperature rise as well. For natural convection along a vertical plate (also applicable to a vertical cylinder), h is given by: h =C ⋅

k k m ⋅ (Gr ⋅ Pr ) = C ⋅ L L

⎛ gρ β (Tc − Ta )L μC p ⎞ ⎟ ⋅⎜ ⋅ ⎜ k ⎟⎠ μ2 ⎝ 2

3

forced convection, the viscosity is generally not a factor. For natural convection, the temperature rise is a function of viscosity as follows: 1 ( m + 1) Δθ = KQ nat ⋅ μ −m

4.4-14

Transient Formulation For any temperature rise, the temperature at any time, t, can be determined by equating the heat input to the sum of the change in heat storage and the heat loss:

Heat generated = Change in heat storage + Heat loss.

m

Q gen = mC p

dθ + KΔθ x dt

4.4-15

4.4-9

m varies from 1/3 to 1/4. Note that h is also a function of viscosity, μ, to the -m power.

Combining the temperature component of h with the equation for convection heat transfer: Q = KΔθ m + 1

4.4-10

Taking the inverse to solve for the temperature rise: 1 ( m + 1) Δθ = KQ nat

4.4-11

Since m varies from 1/3 to 1/4, the exponent in Equation 4.4-11 varies from 0.75 to 0.80. Combined Heat Transfer Summarizing the above discussion, the temperature rise (or, conversely, the heat loss) for a particular mechanism of heat transfer can be expressed in the following form:

Δθ = KQ x

4.4-12

or Q = K Δθ

1

x

4.4-13

Where: Δθ is the temperature rise above the surrounding medium. K is a constant. Q is the heat loss (or gain). x is an exponent that varies with mechanism as shown in Table 4.4-1. The constant K is generally constant over the range of temperatures and materials considered in transformer thermal modeling. The only variable that changes appreciably with temperature is the viscosity of oil. For

Traditionally, transient temperatures have been calculated by approximating an instant of time as a stepchange in load and calculating the temperature at the end of the time step as follows: − Δt ⎛ ⎞ Δθ = Δθ i + (Δθ u − Δθ i )⎜1 − e τ ⎟ ⎜ ⎟ ⎝ ⎠ 4.4-16 Where: Δθ is the calculated temperature at time t + Δt. Δθi is the initial temperature at time t. Δθu is the ultimate steady-state temperature. Δt is the time step. e is the time constant.

This closed form solution to the transient differential equation has several drawbacks. First, it is difficult to correct for the change in losses with temperature. The losses at the ultimate temperature rise are a function of the ultimate temperature. The ultimate temperature is, of course, a function of these losses, requiring an iterative calculation at each time step to find the ultimate temperature rise. In addition, the closed form solution above is only truly correct for heat transfer function with an exponent of 1.0 (i.e., forced convection). A more robust approach is to solve the differential equation using a finite difference approach, as taken by Pierce (Pierce 1994) and Lesieutre (Lesieutre et al. 1997) Table 4.4-1 Exponents for Radiation, and Forced and Natural Convection Mechanism

Exponent

Radiation

0.883-0.895

Forced Convection

1.0

Natural Convection

0.75-0.8

4-23



Referring to the differential equation above, the difference equation would take the form:

Q gen,2 = mC p 4.4.2

θ 2 − θ1 Δt

+ KΔθ x

temperature, the hot spot temperature, is located at the top of the winding. This hot spot temperature represents the hottest temperature endured by the insulation and therefore the highest aging rate (1995b).

4.4-17

Top Oil Model (IEEE C57.91-1995, Clause 7)

The following is an outline of the temperature calculation methods presented in Clause 7 of IEEE C57.911995 (IEEE 1995b) (Figure 4.4-2). The thermal mechanisms of a transformer are extremely complex and difficult to model. To reduce complexity, the transformer is analyzed as a lumped system, and several assumptions are made. The transformer is essentially reduced to two systems, the bulk oil and the winding, with an additional “hot spot” temperature located at the top of the winding.

The IEEE top oil method relates the steady-state oil temperature rises to the total losses by a power function. The steady-state winding rises are also related to the winding current by a power function. In addition, certain corrections are made to account for additional considerations such as increased mixing due to forced-oil cooling systems and change in winding resistance with temperature. The following is an outline of the temperature calculation method presented in IEEE C57.91-1995, Clause 7. Symbols:

C

The oil temperature is presumed to be lowest at the bottom of the winding. As the oil rises upward along the winding, the oil adjacent to the winding is heated at a constant rate. Therefore, the oil temperature is assumed to increase linearly from the bottom of the winding to the top of the winding, with the highest oil temperature located at the top of the winding. At rated load, the winding temperature distribution is assumed to be higher than the oil temperature distribution by a constant value, Δw, and thus parallel to the oil temperature distribution. Due to stray flux concentration near the top of the winding, a further increase in

is the thermal capacity (Watt-hours/deg C).

WCC is the weight of the core and coils (kg). WTank is the weight of the tank and fittings in contact with the oil (kg). VFluid is the volume of oil (L). τO

is the oil thermal time constant (min).

τw

is the winding time constant (min).

t

is the time (min.).

Δt

is the calculation time step (min).

ΔθTO is the top oil rise over ambient temperature (deg C).

Figure 4.4-2 Graph of temperature rises vs. height for IEEE Clause 7 Model. 4-24



ΔθHS is the hot spot rise over the top oil temperature (deg C). PT

is the total loss (W).

K

is the load (per unit of the nameplate rating).

R

is the ratio of load loss to no-load loss at the nameplate rating.

m

is the winding temperature rise exponent.

n

is the oil temperature rise exponent.

θHS

is the hot spot temperature (deg C).

θA

is the ambient temperature (deg C).

A combined thermal capacity can be calculated by combining the specific heats of the various component materials with the component weights. However, the components are not at a uniform temperature. The oil temperature varies from the bottom of the tank to the top. For OA (ONAN) and FA (ONAF), the assumption has been made that the mean oil temperature is 76% of the maximum top oil temperature. In addition, 2/3 of the tank weight is used. For OA and FA (ONAN and OFAF), the thermal capacity, C, equals:

C = 0.06 * WCC + 0.04 * WTank + 1.33 * VFluid

4.4-19

Subscripts:

For DFOA and NDFOA (ODAF and OFAF), the thermal capacity, C, equals:

R

indicates a rated quantity.

i

indicates an initial quantity.

U

indicates an ultimate or steady-state quantity.


At top oil temperatures other than rated, the time constant must be corrected as follows:

Oil Thermal Time Constant:

In order to calculate the transient response of the bulk oil, it is necessary to calculate an oil thermal time constant. The thermal time constant of the bulk oil at rated temperature equals:

τO,R = C * ΔθTO,R / PT,R 4.4-18 Where: τO,R is the oil thermal time constant at rated load (min). C is the combined thermal capacity of the transformer (W-min/lbs-C). Δθ TO,R is the measured oil temperature rise over ambient at rated load (C). PT,R is the total loss at rated load (W). The thermal capacity, C , is the combined thermal capacity of all transformer components in contact with the bulk oil. This includes the core, windings, tank and fittings, and the oil itself. The specific heat for each component material is shown in Table 4.4-2.

τ O = τ O, R

⎛ Δθ TO ,U ⎜ ⎜ Δθ ⎝ TO , R ⎛ Δθ TO ,U ⎜ ⎜ Δθ ⎝ TO , R

⎞ ⎛ Δθ TO , i ⎟−⎜ ⎟ ⎜ Δθ ⎠ ⎝ TO , R 1

⎞ n ⎛ Δθ TO , i ⎟ −⎜ ⎜ Δθ ⎟ ⎝ TO , R ⎠

Table 4.4-2 Specific Heat for Copper, Steel, and Oil Specific Heat (W-min/lbs-C)

Copper

0.05

Steel

0.06

Oil

14.6

⎞ ⎟ ⎟ ⎠ 1

⎞n ⎟ ⎟ ⎠

4.4-21

Initial Temperatures:

The following equations are used to calculate the initial temperatures based upon the assumption that the load prior to the calculation period was constant long enough for the temperatures to reach their steady-state limits. This assumption is reasonable if the load is fairly constant for a period of time prior to the overload equal to two to three times the oil thermal time constant.

(

)

⎡ K 2R + 1 ⎤ Δθ TO , i = Δθ TO , R ⎢ i ⎥ ⎣⎢ (R + 1) ⎦⎥ Δθ HS , i = Δθ HS , R ⋅ K i2 m

Material

4.4-20

n

4.4-22

Transient Temperatures:

The following equations are used to calculate the transient temperature rises based upon the oil time constant calculated above, the user-determined winding time constant, load, losses, and initial and ultimate temperature rises. For a graphical representation of the various temperature rises, see Figure 4.4-2.

4-25



For all cooling modes: The top oil rise at time t2 = t1 + Δt is given by the following: Δθ TO ,U

(

)

⎡ K 2R +1 ⎤ = Δθ TO , R ⎢ U ⎥ ⎢⎣ (R + 1) ⎥⎦

Δθ TO ,2 = (Δθ TO ,U

n

4.4-23

Δt ⎛ − − Δθ TO ,1 )⎜1 − e τ ⎜ ⎝ O

⎞ ⎟ + Δθ TO ,1 ⎟ ⎠

4.4-24

The hot-spot rise over top oil at time t2 = t1 + Δt is given by the following: Δθ HS ,U = Δθ HS , R ⋅ K U2 m Δθ HS ,2 = (Δθ HS ,U

4.4-25

Δt ⎛ − τ ⎜ − Δθ HS ,1 ) 1 − e ⎜ ⎝ W

⎞ ⎟ + Δθ HS ,1 ⎟ ⎠

4.4-26

The hot-spot temperature at time t2 = t1 + Δt is given by:

θ HS ,2 = θ A,2 + Δθ TO ,2 + Δθ HS ,2

4.4-27

The above calculation is repeated for each time step of the overload period, with the initial temperatures rises equal to the temperature rises from the previous time step. In addition, loss-of-life calculations are performed at each time step (IEEE 1995b). 4.4.3

Bottom Oil Model (IEEE C57.91-1995, Annex G)

This model was originally developed by Linden Pierce with GE in the early 1990s based upon detailed temperature measurements on a model coil (Pierce 1992, 1994). The model was included in the 1995 revision of IEEE C57.91 as Annex G (IEEE 1995b). In the top oil model, the hot spot temperature consisted of three components: ambient temperature, top oil rise over ambient, and hot spot rise over top oil (Figure 4.4-3). In the bottom oil model, which is the approach that will be developed here, the hot spot temperature consists of four components: ambient temperature, bottom oil rise over ambient, top-of-duct oil to bottom oil gradient, and hot spot rise over top of duct oil. These components are shown schematically below. In addition to these components, the average winding rise over average duct oil needs to be developed, as the winding losses are a function of this temperature and not the hot spot temperature.

θ HS = θ A + Δθ BO + Δθ DO / BO + Δθ HS / DO

4-26

Average Winding Rise over Average Duct Oil It will be assumed that the temperatures of the winding and the duct oil vary linearly from bottom to top, and both are parallel. This results in a winding temperature rise over adjacent duct oil that does not vary over the height of the winding, and a constant heat flux from the winding to the duct oil. In line with the finite difference transient formulation described above, a heat balance will be developed for the winding-duct oil system.

The heat generated by the winding at time t2 = t1 + Δt is given by: Q gen,W = L2 (PI 2 R ⋅ K W + PE K W )

4.4-29

Where: Qgen,W is the average heat generated by the windings. L is the winding current, in per unit rated. PI2R is the Ohmic losses in the windings due to the winding current at rated current. is the eddy losses in the windings at rated PE current.

⎛ θW ,1 + θ K ⎞ ⎟ KW = ⎜ ⎜θ ⎟ + θ K ⎠ ⎝ W,R 4.4-30 Where: θW,1 is the average winding temperature calculated at the previous time step, t1. θW,R is the average winding temperature at rated load. θK is 234.5°C for copper windings and 225°C for aluminum windings. The heat lost by the windings to the duct oil is dependent upon the mechanism of heat transfer. For ONAN, ONAF, and OFAF, the predominant mode of heat

θDO θHS

θBO

θA

Figure 4.4-3 Components of bottom oil model. 4.4-28



transfer is natural convection. As outlined above, the heat loss for natural convection can be expressed by: m +1

m

⎛ θW ,1 − θ DO,1 ⎞ ⎛ μW , R ⎞ ⎟ (PI 2 R + PE ) ⎟ ⎜ Qloss ,W = ⎜ ⎟ ⎟ ⎜μ ⎜θ θ − DO , R ⎠ ⎝ W ,1 ⎠ ⎝ W ,R 4.4-31 Where: Qloss,Wis the average heat lost by the windings to the average duct oil. θW,1 is the average winding temperature at the previous time step. θDO,1 is the average duct oil temperature at the previous time step. θW,R is the average winding temperature at rated current. θDO,R is the average duct oil temperature at rated current. μW,R is the oil viscosity at a temperature equal to the average of the average winding temperature and average duct oil temperature at rated load. μW,1 is the oil viscosity at a temperature equal to the average of the average winding temperature and average duct oil temperature at the previous time step. m is a constant, usually between 1/3 and 1/4. For ODAF transformers (directed forced oil), the predominant mode of heat transfer is forced convection. The heat loss for OFAF can then be expressed by:

⎛ θW ,1 − θ DO,1 Qloss,W = ⎜ ⎜θ ⎝ W , R − θ DO, R

⎞ ⎟(PI 2 R + PE ) ⎟ ⎠

4.4-32

Note that it is assumed that the effect of the change in oil viscosity with temperature is negligible for this case. Completing the heat balance, the heat absorbed by the windings is given by:

Qabs ,W = mW C P ,W

(θ

W ,2

− θW ,1 )

Δt 4.4-33 Where: Qabs,W is the heat absorbed by the winding during incremental time step, Δt. mW is the mass of the windings. CP,W is the effective specific heat of the windings. θW,1 is the average winding temperature at time t1. θW,2 is the average winding temperature at time t2 = t1 + Δt. Δt is the incremental time step.

constant calculated from the winding cooldown curves taken during the factory heat run. From the definition of a thermal time constant:

mW C P ,W =

τ W (PI 2 R + PE ) (θW , R − θ DO, R )

4.4-34

Summing the three terms of the heat balance and solving for θW,2:

θW , 2 =

(Q

gen,W

− Qloss ,W )Δt

mW C P ,W

+ θW ,1 4.4-35

Duct Oil Gradient over Bottom Oil The oil entering the winding ducts is at a temperature equal to the bottom oil temperature. The oil is then heated as it rises up the winding duct, either by forced oil flow or natural thermosiphon flow. The temperature at the duct exit, for a constant heat flux along the duct, is dependent upon the mass flow rate, as follows:

Te = Ti +

q s As

ρVAcC P

4.4-36

Where: Te is the temperature of the fluid exiting the duct. Ti is the temperature of the fluid entering the duct. qs is the constant heat flux along the duct. As is the surface area of the duct. ρ is the density of the fluid. V is the fluid velocity (average). Ac is the cross-sectional area of the duct. Cp is the specific heat of the fluid. For ODAF, the mass flow rate through the duct remains essentially constant for varying load levels. For ONAN, ONAF, and OFAF, the oil flow through the duct is by natural thermosiphon flow. The flow rate through the duct in these cases is a complex function of the temperature rise in the duct, the temperature drop through the radiators, and the relative height of the windings and the radiators. The temperature rise in the duct, in turn, is a function of the mass flow rate through the duct (Figure 4.4-4). Lacking sufficient data, the following simple approach will be taken, relating the temperature rise through the vertical ducts (top-of-duct oil – bottom oil) to the loss by an exponent, y, as follows:

Δθ DO / BO,2 = H HS ⋅ Δθ TDO / BO, R * L2 y

4.4-37

Where: ΔθDO/BO is the duct oil rise over bottom oil.

The term mWCP,W is usually not known directly. Instead, this term can be calculated from a winding thermal time 4-27



that, for ONAN, ONAF, and ODAF, this value is equal to the rated top oil rise. For OFAF, Pierce suggests using the average winding rise. These recommendations appear to be based upon the tests of the model coil in (Pierce 1992). Hot Spot Rise over Top Duct Oil By following a development similar to the average winding rise over average duct oil, only considering an incremental portion of the winding at the hot spot (top of winding), the hot spot temperature rise over top duct oil can be calculated.

The heat generated by the winding at the hot spot at time t2 = t1 + Δt is given by: Figure 4.4-4 Oil flow throughout the duct.

Q gen, HS = L2 (PI 2 R ⋅ K HS + PE K HS )

4.4-38

is the height of the winding hot spot in per unit of the winding height (1.0 = top). ΔθTDO/BO,R is the top-of-duct oil rise over bottom oil at rated load (see discussion below). L is the per unit load. y is an exponent.

Where: Qgen,HS is the heat generated by the windings at the hot spot. L is the winding current, in per unit rated. PI2R is the Ohmic losses in the windings due to the winding current at rated current. PE is the eddy losses in the windings at rated current.

In almost all cases, it can be assumed that the hot spot is at the top of the winding, and hence adjacent to the top duct oil temperature, making HHS equal to 1.0. The data from tests done on model coils in Pierce (1994) suggests that, for most cases, the hot spot is within the top 10% of the winding. When the increased eddy loss at the top of the winding is factored in, the hot spot should be even closer to the top, most often within a few turns or disc sections. However, HHS has been included to allow the engineer to assume a hot spot position below the top of the winding.

⎛ θ HS ,1 + θ K ⎞ ⎟ K HS = ⎜ ⎟ ⎜θ + θ HS , R K ⎠ ⎝ 4.4-39 Where: θHS,1 is the winding hot spot temperature calculated at the previous time step, t1. θHS,R is the winding hot spot temperature at rated load. θK is 234.5°C for copper windings and 225°C for aluminum windings.

HHS

The exponent, y, is as yet undetermined. Lacking measured data, the values given by Pierce (1994) can be used. For ONAN, ONAF, and OFAF, y is given as 0.5. For ODAF, y is given as 1.0. Since the mass flow rate does not change for ODAF over varying loads and the heat flux is proportional to the losses, the exponent of 1.0 for ODAF should be correct. For the other cooling modes, however, the mass flow rate is a function of both the oil temperatures within the duct and the oil temperatures in the bulk oil and radiators. Therefore, a more complex relationship is needed. The temperature of the oil exiting the ducts, expressed as the rise over bottom oil ΔθDO/BO, at rated load is difficult to determine. It cannot be measured easily. Even when measurements are made, the values vary considerably for the various vertical ducts around the circumference of the winding (Pierce 1992). Pierce (1994) suggests

4-28

The heat lost by the windings to the duct oil is dependent upon the mechanism of heat transfer. For ONAN, ONAF, and OFAF, the predominant mode of heat transfer is natural convection. As outlined above, the heat loss for natural convection can be expressed by: Qloss , HS

⎛ θ HS ,1 − θ DO,1 =⎜ ⎜θ ⎝ HS , R − θ DO, R

⎞ ⎟ ⎟ ⎠

m +1

⎛ μ HS , R ⎜ ⎜μ ⎝ HS ,1

⎞ ⎟ ⎟ ⎠

m

(PI 2R

+ PE ) 4.4-40

Where: Qloss,HS is the heat lost by the winding hot spot to the top duct oil. θHS,1 is the winding hot spot temperature at the previous time step. θDO,1 is the duct oil temperature at the previous time step. θHS,R is the winding hot spot temperature at rated current.



θDO,R is the duct oil temperature at rated current. μHS,R is the oil viscosity at a temperature equal to the average of the winding hot spot temperature and top. μHS,1 is the oil viscosity at a temperature equal to the average of the winding hot spot temperature and top duct oil temperature at the previous time step. m is a constant, usually between 1/3 and 1/4.

For ODAF transformers (directed forced oil), the predominant mode of heat transfer is forced convection. The heat loss for OFAF can then be expressed by: ⎛ θ HS ,1 − θ DO,1 Qloss, HS = ⎜ ⎜θ ⎝ HS , R − θ DO, R

⎞ ⎟(PI 2 R + PE ) ⎟ ⎠

4.4-41

Note that it is assumed that the effect of the change in oil viscosity with temperature is negligible for this case. Completing the heat balance, the heat absorbed by the windings is given by: Q abs, HS = mW C P ,W

(θ

HS ,2

− θ HS ,1 ) Δt

4.4-42

Where, Qabs,HS is the heat absorbed by the winding during incremental time step, Δt. mW is the mass of the windings. CP,W is the effective specific heat of the windings. θHS,1 is the average winding temperature at time t1. θHS,2 is the average winding temperature at time t2 = t1 + Δt. θt is the incremental time step. Summing the three terms of the heat balance and solving for θHS,2:

θ HS ,2 =

(Q

gen , HS

)

− Qloss, HS Δt

mW C P ,W

+ θ HS ,1

The heat generated by the active assembly (core and coils) at the hot spot at time t2 = t1+ Δt is given by: Q gen, O = L2 (PI 2 R ⋅ K W + (PE + PS ) K W ) + PC

4.4-44

Where: Qgen,O is the heat generated within the transformer. L is the winding current, in per unit rated. PI2R is the Ohmic losses in the windings due to the winding current at rated current. PE is the eddy losses in the windings at rated current. PS is the stray loss. PC is the core (no-load) loss. ⎛ θW ,1 + θ K ⎞ ⎟ KW = ⎜ ⎜θ ⎟ + θ W , R K ⎝ ⎠ 4.4-45 Where: θW,1 is the average winding temperature calculated at the previous time step, t1. θW,R is the average winding temperature at rated load. θK is 234.5°C for copper windings and 225°C for aluminum windings.

The heat loss is given by: Qloss , AO

⎛ θ AO ,1 − θ A,1 =⎜ ⎜θ ⎝ AO, R − θ A, R

⎞ ⎟ ⎟ ⎠

1

y

PT 4.4-46

Where: Qloss,AO is the heat lost by the bottom oil to the surrounding air. θA,1 is the ambient temperature at the previous time step. θA,R is the ambient temperature during the heat run. θAO,1 is the average oil temperature at the previous time step. θAO,R is the average oil rise at rated load. y is an exponent equal to 0.8 for ONAN, 0.9 for ONAF and OFAF, 1.0 for ODAF.

4.4-43

Bottom and Top Bulk Oil Rise Pierce (1994) calculates the average oil rise and then applies a top-to-bottom oil gradient to that average oil rise. This gradient is calculated as a function of the losses raised to an exponent. This exponent is given by Pierce (1994) as 0.5 for ONAN and ONAF, and 1.0 for OFAF and ODAF.

Completing the heat balance, the heat absorbed by the bulk oil is given by: Qabs , AO = ∑ mC P

(θ

AO ,2

− θ AO ,1 )

Δt 4.4-47 Where: Qabs,AO is the heat absorbed by the average bulk oil during incremental time step, Δt. θAO,1 is the average bulk oil temperature at time t1. θAO,2 is the average bulk oil temperature at time t2 = t1 + Δt. Δt is the incremental time step.

4-29



The value ΣmCP is a sum of product of the masses of the transformer in contact with the oil, as well as the oil itself, and the specific heat of those components:

∑ mC

P

4.4.4

The IEC 354-1991 (McNutt 1992) model is similar to the IEEE Clause 7 model (Figure 4.4-5). The two models differ in a few important respects. First, the calculation of the rated hot spot rise is done by applying a “hot spot factor” to the average winding rise over average oil temperature gradient. This “hot spot factor” is a design specific constant that generally varies between 1.0 and 1.4, with 1.2 being typical for power transformers.

= C P , steel (WC & C + WTank ) + C P , fluidW fluid 4.4-48

Summing the three terms of the heat balance and solving for θAO,2:

θ AO ,2 =

(Q

gen , O

− Qloss, AO )Δt

∑ mC P

+ θ AO ,1

Note: The winding temperature rise exponent in this document differs slightly from that described in IEC 354. The equations listed below apply a multiple of 2 to this exponent, whereas in IEC 354, this multiple is included in the exponent definition. Therefore, the winding temperature rise exponent listed here is equal to half of the winding temperature rise exponent in IEC 354.

4.4-49

Once the average bulk oil temperature has been determined, a top-to-bottom bulk oil gradient must be calculated. This is done by the following equation:

θ TO / BO = (θ TO , R

⎛ Qloss , AO ⎞ ⎟ − θ BO , R )⎜ ⎜ Q gen, O Δt ⎟ ⎠ ⎝

z

Oil Thermal Time Constant: 4.4-50

Where, θTO/BO is the top-to-bottom bulk oil gradient, C. θTO,R is the top oil rise at rated load, C. θBO,R is the bottom oil rise at rated load, C. Δt is the incremental time step. z is an exponent (0.5 for ONAN, ONAF; 1.0 for OFAF, ODAF). The top and bottom oil temperatures are then solved for by adding and subtracting, respectively, half of the topto-bottom bulk oil gradient:

θ TO = θ AO +

θ BO = θ AO −

θ TO / BO 2

4.4-51

θ TO / BO 2

IEC Model (IEC 354-1991)

In order to calculate the transient response of the bulk oil, it is necessary to calculate an oil thermal time constant. Since IEC 354 does not include this information, the IEEE C57.91-1995 equations can be offered as an option:

(

0.1 ) 1.108

For OA and FA (ONAN and OFAF), the thermal capacity, C, equals: C = 0.0272 * WCC + 0.01814 * WTank + 5.034 * VFluid (1) (IEEE Clause 7) 4.4-53

For DFOA and NDFOA (ODAF and OFAF), the thermal capacity, C, equals: C = 0.0272 * WCC + 0.0272 * WTank + 7.305 * VFluid (2) (IEEE Clause 7) 4.4-54

4.4-52

Figure 4.4-5 Diagram illustrating assumed temperature profile within transformer for IEC model. 4-30



The thermal time constant of the bulk oil at rated temperature equals: τO,R = C * ΔθTO,R / PT,R (3) (IEEE Clause 7)

4.4-55


τ O = τ O, R

⎛ Δθ TO ,U ⎜ ⎜ Δθ ⎝ TO , R

⎞ ⎛ Δθ TO , i ⎟−⎜ ⎟ ⎜ Δθ ⎠ ⎝ TO , R 1

⎛ Δθ TO ,U ⎞ n ⎛ Δθ TO , i ⎟ −⎜ ⎜ ⎜ Δθ ⎟ ⎜ Δθ ⎝ TO , R ⎝ TO , R ⎠ (4) (IEEE Clause 7)

⎞ ⎟ ⎟ ⎠ 1

⎞n ⎟ ⎟ ⎠

The top oil rise at time t2 = t1 + Δt is given by the following:

(

)

n

⎡ K 2R +1 ⎤ Δθ TO ,U = Δθ TO , R ⎢ U ⎥ ⎢⎣ (R + 1) ⎥⎦ (8) (IEC 2.4.1, Equation 1) Δt ⎛ − τO ⎜ Δθ TO ,2 = (Δθ TO ,U − Δθ TO ,1 ) 1 − e ⎜ ⎝ (9) (IEC 2.5)

4.4-60

⎞ ⎟ + Δθ TO ,1 ⎟ ⎠ 4.4-61

The hot-spot rise over top oil at time t2 = t1 + Δt is given by the following: 4.4-56


Δθ HS ,U = Hg R ⋅ K U2 m

(10) (IEC 2.4, Equation 1+2)

The following equations are used to calculate the initial temperatures based upon the assumption that the load prior to the calculation period was constant long enough for the temperatures to reach their steady-state limits. This assumption is reasonable if the load is fairly constant for a period of time prior to the overload equal to two to three times the oil thermal time constant. ⎡ K 2R + 1 ⎤ Δθ TO , i = Δθ TO , R ⎢ i ⎥ ⎢⎣ (R + 1) ⎥⎦ (5) (IEC 2.4.1, Equation 1)

(

)

n

⎡ K R +1 ⎤ Δθ BO , i = Δθ BO , R ⎢ ⎥ ⎣⎢ (R + 1) ⎦⎥

)

n

(

2 i

4.4-57

(6) (IEC 2.4.2, Equation 2)

In addition, for DFOA (ODAF) cooling modes a correction factor is applied to account for the change in winding Ohmic losses due to temperature as follows:

θ HS ,U ′ = θ HS ,U + 0.15(θ HS ,U − θ HS , R ) (11) (IEC 2.4.3, Equation 3)

4.4-63

For other types of cooling, the change in winding Ohmic losses is negligible. Note that the IEEE method neglects the change in winding resistance with temperature for all cases, assuming that this change is always offset by the change in oil viscosity with temperature. The transient hot spot rise is then:

4.4-58

Δθ HS , i = Hg R ⋅ K i2 m

(7) (IEC 2.4, Equation 1+2)

4.4-62

Δθ HS ,2 = (Δθ HS ,U

4.4-59

g is difference between average winding and average oil temperatures. H is a multiplier that equals 1.3.

Hg is the hot spot rise above top oil. Transient Temperatures:

The following equations are used to calculate the transient temperature rises based upon the oil time constant calculated above, the user-determined winding time constant, load, losses, and initial and ultimate temperature rises. For a graphical representation of the various temperature rises, see Figure 4.4.5. For OA and FA (ONAN and ONAF) cooling modes:

Δt ⎛ − τW ⎜ − Δθ HS ,1 ) 1 − e ⎜ ⎝

(12) (IEC 2.5)

⎞ ⎟ + Δθ HS ,1 ⎟ ⎠ 4.4-64

The equation form is the same as IEEE if the hot spot rise over top oil term is calculated with the IEC method. Note that the IEC method calculates the hot spot rise over top oil temperature at rated load through the use of a multiplier, H, applied to the difference between the average winding temperature from test and the average top oil temperature from test. For power transformers, H is typically approximately 1.3. The hot-spot temperature at time t2 = t1 + Δt is given by:

θ HS ,2 = θ A,2 + Δθ TO ,2 + Δθ HS ,2 (13) (IEC 2.4.1, Equation 1)

4.4-65

4-31



For NDFOA and DFOA (OFAF and ODAF) cooling modes: For forced-oil cooling modes, the increased mixing introduced by the forced circulation of the oil increases the complexity of the model. The top oil temperature leaving the winding is greater than the measured top oil. Therefore, the top oil temperature leaving the winding is calculated using the sum of the ambient temperature, the bottom oil temperature rise, and the difference between the top oil and the bottom oil rises. Note that this differs from the IEEE methodology. The IEEE method assumes that the measured top oil temperature is equal to the temperature of the oil leaving the top of the winding for all cooling modes. The bottom oil rise at time t2 = t1 + Δt is given by:

(

)

Rather than taking an analytical approach to the problem, as had been taken by Pierce with the IEEE Annex G model, the authors of the model took the approach of applying corrective factors and multiple time constants. The constants would be adjusted empirically to fit measured temperature data. Like the IEEE Clause 7 model, the revised IEC model lumps the hot spot temperature into a top oil rise over ambient and a hot spot rise over top oil.

θ HS = θ A + Δθ TO + Δθ HS / TO

4.4-71

n

⎡ K R +1 ⎤ Δθ BO ,U = Δθ BO , R ⎢ ⎥ ⎢⎣ (R + 1) ⎥⎦ (14) (IEC 2.4.2, Equation 2) Δt ⎛ − τO ⎜ Δθ BO ,2 = (Δθ BO ,U − Δθ BO ,1 ) 1 − e ⎜ ⎝ (15) (IEC 2.5) 2 U

this new model recognized that the hot spot temperature increases more rapidly initially than is currently predicted with traditional equations. This is commonly attributed to an increase in the duct oil that occurs more quickly than the increase in bulk oil. This phenomenon they have dubbed the "hot spot bump" (see Figure 4.4-6).

4.4-66

⎞ ⎟ + Δθ BO ,1 ⎟ ⎠ 4.4-67

The top-to-bottom oil rise at time t2 = t1 + Δt is given by the following: Δθ T − BO ,U = Δθ T − BO , R K U2 m

The computation of the constituent rises is a complex arrangement of factors and time constants. The intent of these factors is to simulate the “hot spot bump” by inclusion of an additional exponential term in the calculation of the hot spot rise over top oil. The calculation of the top oil temperatures proceeds in a similar fashion to the IEEE Clause 7 model. First, the ultimate top oil temperature for the given load level is calculated: x

(16) (IEC 2.4.2, Equation 2)

4.4-68

⎛ − Δθ T − BO ,2 = (Δθ T − BO ,U − Δθ T − BO ,1 )⎜1 − e τ W ⎜ ⎝ (17) (IEC 2.5)

Δt

⎞ ⎟ + Δθ T − BO ,1 ⎟ ⎠ 4.4-69

The hot-spot rise above top oil, ΔθHS, is calculated using the same equations as used for OA and FA cooling modes described above.

⎡ K 2 R + 1⎤ Δθ TO ,U = Δθ TO , R ⎢ ⎥ ⎣ R +1 ⎦ 4.4-72 Where: ΔθTO,U is the ultimate top oil temperature rise, C. ΔθTO,R is the rated top oil temperature rise, C. K is the per unit load. R is the ratio of load losses to no-load losses. x is a constant exponent.


θ HS ,2 = θ A,2 + Δθ BO ,2 + Δθ T − BO ,2 + Δθ HS ,2 (18) (IEC 2.4.2, Equation 2)

4.4-70


Proposed IEC Model

The proposed IEC model (IEC 1991) takes a bit of a radical departure from the earlier models. The authors of 4-32

Figure 4.4-6 Example of “hot spot bump.”



dewatering, backfilling, and other activities. The ambient temperature recorded at the start of an in situ thermal resistivity test is an important value to record for the cable designer. In the laboratory, a soil sample is prepared to evaluate thermal dry-out characteristic– the variation in thermal resistivity of the material as a function of moisture content. The results of these tests (dry-out curves) are presented on charts that show thermal resistivities at the in situ moisture content (if known), at “critical moisture content,” and in totally dry condition (worst case). Some degree of drying beyond the native moisture levels should be expected in the presence of energized power cables, so an adjusted soil thermal resistivity that factors in the drying should be incorporated into ampacity calculations. Once the soil thermal resistivity results are known, they can be used in ampacity calculations. For the case of installed cable systems, it may be necessary to do testing outside the cable trench to get native conditions, and within the cable backfill to characterize the special thermal backfill that may have been used around the cables. If the trench is known to have a common material throughout, testing of the backfill material may only be needed at a few selected locations. Thermal Diffusivity Although thermal diffusivity is not commonly recorded (typical transient needle TPA equipment can measure this parameter) for most applications, its application is in “transient” calculations. In simple terms it can be treated as the “inertia” in the heat and mass transfer equation. The three terms—resistivity (ρ), diffusivity (α) and heat capacity (C)—are related by Equation 3.6-1.

ρ ⋅ α ⋅C = 1

3.6-1

Thermal Stability Thermal stability is a system-driven parameter and is a soil characteristic that describes how well a soil maintains a constant thermal resistivity when exposed to cable heating. The main issue is to consider if the heat leaving a cable would result in the soil being below its critical moisture content, in which case the soil would experience net drying and an increase in thermal resistivity. Smaller diameter cables with direct contact to the soil are more likely to result in thermal instability because of a larger heat flux (temperature gradient) at the cable-soil interface.

A classic example of a thermally instable material is modeling clay. The clay can be dried at room temperature over time. If the dried sample is then placed in water, it does not readily reabsorb water to return to a

3-32

malleable substance. Some soils—including soils with high clay and silt contents—have these characteristics. A common situation where this may be an issue for power cables is the use of bentonite as a grout material either in trenchless casing installations or for cable conduits; pure bentonite has high thermal resistance and is prone to drying. Bentonite is prone to shrinkage and cracking (leaving voids) if drying does occur. A better solution is to use as much sand as possible while minimizing the bentonite content, and to seal the ends of the casing or ducts so that the grout cannot dry. Moisture Migration in the Soil For any given soil or backfill, the major influence on the thermal resistivity is the moisture content. In a dry state, the pore spaces between soil particles are filled with air (thermal resistivity of about 45°C-m/W). As water (thermal resistivity of about 1.65°C-m/W) replaces air, the soil resistivity decreases substantially by as much as 3 to 7 times, as the good heat conduction paths are expanded (additional thermal “thermal bridges”). This is illustrated by the “thermal dry-out curve” (thermal resistivity vs. soil moisture content) shown in Figure 3.6-3. A soil that is better able to retain its moisture, as well as being able to efficiently re-wet when dried, will have better thermal performance characteristics. The soil water content is expressed as a percentage of the weight of water to the dry weight of soil solids, as determined by oven drying at 105°C.

The heat generated by energized cable tends to cause soil moisture to migrate away from the cable/backfill interface. In unstable backfills or soils, this drying increases the resistivity substantially, inducing further heating of the cable and thus more drying of the soil. Eventually this cycle may create a totally dry zone of the backfill around the cable, resulting in excessive heating and potential thermal runaway. In a stable backfill, the heatinduced drying raises the resistivity marginally, thus minimizing the potential for thermal runaway. Thermal stability is best illustrated by means of thermal dry-out curves (Figure 3.6-3). The “critical moisture” is defined as the moisture content below which the relatively flat nature of the thermal dry-out curve gives way to a disproportionate increase in the thermal resistivity. Above the critical moisture a soil will resist thermal drying (by means of capillary suction), whereas below this value, thermal runaway is inevitable (unless soil moisture is externally replenished, (i.e., rain). Although some native soils at high moisture content (10–25%) may exhibit fairly low thermal resistivity (0.4 to 0.6 °C-m/W), this value may increase a few fold when dry. Well-graded sands and stone-dust containing 10–



15% fines (-200 Sieve size material) make good corrective thermal backfills.

thermal resistivity, heat transfer takes place by radiation instead of conduction that is much less efficient.

Cable Route Soil Test Spacing The soil testing and sampling frequency for thermal resistivity testing along the cable route can vary depending on the area and the length of the route. In rural areas, where the use of fills is minimal and historical construction has not been significant, sampling and insitu testing every 500 m might be done. In urban areas or locations where fill materials have been used, sampling might be done every 200–500 m. Known variations in geology or other conditions might affect how often along the route testing and sampling are done. The goal of testing is to capture test results for any unique soils and potential hot spots along the cable route while categorizing where each soil type is found.

Soil Texture and Dry Density The soil texture is also critically important to thermal resistivity. The grain size distribution and grain shape are evaluated by a sieve analysis (e.g., ASTM D422, etc.) to determine the variation in particles both in backfill materials and native soils. Figure 3.6-5 shows a sieve analysis for four materials and a band of “good” granular thermal backfill.

Factors Affecting Soil Thermal Resistivity

Soil Composition The soil composition is an important characteristic affecting soil thermal resistivity. Soils are typically a conglomerate of various materials, and the ratio of these materials within a soil affects the thermal resistivity. Table 3.6-1 summarizes the dry thermal resistivity values of various components.

Because the soil components are so important in affecting the thermal resistivity, a good understanding of the geology along a cable circuit is valuable to assessing where soil testing should be performed and how much variation might be expected along a given cable route. It is important to note from Table 3.6-1 and Figure 3.6-3 that dry soils have a much higher thermal resistance than moist soils because the thermal resistivity of water (1.65 C°-m/Watt) is much lower than that of air (~45 C°-m/Watt). In addition to the air having higher

Table 3.6-1 Thermal Resistivities of Soil Components Component

Dry Thermal Resistivity C°-m/Watt

Quartz

0.12

Granite

0.30

Limestone

0.40

Sandstone

0.50

Shale (sound)

0.60

Shale (highly friable)

2.00

Mica

1.70

Ice

0.45

Water

1.65

Organics (peat, etc.)

~5.00

Petroleum Oil

~8.00

Air

~45.00

Water Content and Ground Water Level As is seen in Figure 3.6-3, soils with higher moisture content generally speaking have better thermal resistivity. Some soils naturally retain water better than others. Certain soils may not retain water well—e.g., they have a high hydraulic porosity—but are below the water table so they remain saturated even though the dry density is low and dry thermal resistivity would otherwise be high. Dry Density The dry density of a soil determines its ideal ability to conduct heat away from the cables. Factors that influence the dry density are porosity, solids content, interparticle contacts and pore size distribution. Having a well-graded material with a range of particle sizes improves the dry density and minimizes pores and voids in the material. Other Subsurface Characteristics Concerns for solutes and hysterisis apply only in areas where significant fluctuation in the water table may “wash out” fines from the backfill, making it thermally poor. For most applications, this is not a concern for cable system uprating and, in any case, would be found during soil thermal resistivity testing. Surface Characteristics and Vegetation Surface conditions have an impact on soil thermal resistivity. For example, soils below asphalt roadways generally will not gain or loose moisture readily under normal conditions. However, in the presence of cables, the drying that does occur may not be mitigated by heavy rains since the water will not be easily reabsorbed.

Surface vegetation can be significant factor affecting soil thermal resistivity. The root systems on large trees and plants will draw moisture out of the soil, drying it. Also, the decaying components of plants and their root systems will tend to increase the organic component of soils, which tends to increase the soil thermal resistivity (see Table 3.6-1). Surface cover has strong influence over earth ambient temperatures, especially at shallower depths. A difference of 4–5°C has been measured between grasses versus asphalt cover over cables. 3-33



Engineered Thermal Backfills The general goal of engineered thermal backfills (ETB) is to enhance the removal of heat away from buried cables. In most cases, the native soil materials have a higher thermal resistivity than good quality backfills and, in any case, are difficult to reconstitute in the trench with the same density as the native soil. For this reason, special backfill materials are often designed for use in a cable trench. These include well-graded sands, stone screenings, and concrete or Fluidized Thermal Backfill. In addition to having excellent thermal properties, they are engineered to meet civil requirements (strength and ease of voids-free installation) that are associated with the particular application. The criteria considered for these ETB are:

• Low thermal resistivity over the expected range of operating conditions

• Low critical moisture content and high thermal stability limits

• No adverse affects on materials used for cable conduits, cable jackets, or pipe coatings

• Easy to install • Inexpensive and locally available to the location where the materials will be used Types of engineered thermal backfills are discussed in the following sections. Granular Backfill Materials These materials should be composed of hard, wellgraded, natural or crushed mineral aggregate (limestone, granite, quartz or other similar rock). The material should be sound (porosity less than 2%) and be free of any organic material (peat, root matter, topsoil, vegetation) and foreign matter (wood, rubble, cinders). The sieve analysis should match closely to that given in 3.6-5. The maximum particle size should be no larger than 1/4in. sieve size with a fines content (material finer than #200 sieve size) of 12% to 18%.

During supply and installation of this material, quality assurance is very important. Sieve analysis on the delivered materials should be performed periodically to check and verify its compliance with the above characteristics.

Figure 3.6-5 Grain size distribution for soil samples.

3-34


Fluidized Thermal Backfill (FTB) One of the difficulties with any granular backfill is that it must be installed properly, regardless of its ideal thermal properties. Granular backfills should be installed in shallow lifts 15 cm (6 in.) at a time and well compacted to give good density. This is labor intensive, and great care must be used when working close to directly-buried cables or conduits so as not to damage either.

Leading up to and during installation, FTB delivered to the project site should conform to the respective mix design and performance specifications of low-strength and/or high-strength FTB. This should be checked with samples collected during the project. When installed by pouring into the cable trench, the material should be free flowing and without any segregation. This will help ensure that the material completely surrounds the cables, conduits, or pipes. The amount of water in the FTB mix may be adjusted to increase or decrease the flow (slump) as directed by the field engineer. If lower slump FTB is required for a particular area, it is generally better to adjust the water content at the batch plant rather than as the material goes into the trench. Air content (natural trapped) should not be higher than 2%. Mixing at the batch plant and transportation to the project site should be done in accordance with ASTM or American Concrete Institute (ACI) specifications.


If trench shoring and sheathing is being used, these should be removed immediately after the installation of FTB, unless otherwise required by the field engineer. If FTB is installed in cold conditions, care should be taken to protect the installed FTB from freezing. This applies to both low-strength and especially high-strength FTB. ASTM or ACI specifications should be followed for such installations. Sampling and testing for quality control/assurance should be performed on FTB samples taken every 250 ft along the cable trench, or every 100 cubic yards of material installed, or as directed by the field engineer. Component materials from an FTB mix design are shown in Figure 3.6-6. Grouts for Cable Conduits and Trenchless Casings For extruded or self-contained cables in ducts or the space between inner-ducts and trenchless (directional drilling, pipe jacking, etc.) casings, the air space between the cable and conduit or conduit and casing is often filled with air, which is a poor thermal conductor. Filling the duct with a thermally conductive material improves the cable ampacity by 5–10%, depending on the configuration and the type of filler. The annular space is generally small, and utilities usually want to retain the ability to remove the cables from the conduits later in the event of a failure or for upgrading. Therefore, it is not practical to fill the annular space with a solid filler material (or one

Figure 3.6-6 Component materials used in a typical Fluidized Thermal Backfill.

3-35



that becomes solid over time), so a pumpable material that will not hard set is ideal.

locations of other underground utilities that may impact cable ratings.

IEC-60287 allows that cables with grouted conduits may be treated as direct-buried cables for the purposes of ampacity. Various materials that have been considered for conduit grouts are:

The plan drawings will show a variety of factors that may be relevant to determining the cable ampacity and possible locations where uprating could be considered:

• • • • •

Bentonite and sand/bentonite slurry Sand-cement grout Flyash-cement grout Grease and viscous oil, along with other compounds Water

Factors that must be considered when selecting a grout are the total length that must be filled and the amount of annular space. For trenchless installations, the potential softening of a plastic duct at elevated temperatures— including potentially the heat generated as cement-based grouts cure—could soften ducts and cause partial collapse. The safe pumping pressure for the grout material must therefore be considered when a grout is pumped on the outside of air-filled cable conduits. The grout material typically will have a thermal resistivity of 0.4 to 1.4 C°-m/Watt, which is much lower than air (45 C°-m/Watt) at the set moisture content. A sandbentonite slurry backfill with a thermal resistivity of approximately 0.7 C°-m/Watt is easy to formulate and generally easy to install. Varying the amount of sand, bentonite and water affects the pumpability of the grout. Bentonite tends to absorb a lot of water, so this must be factored into the mix. Mixing the sand/bentonite slurry also requires special equipment (i.e., colloidal mixer). The thermal resistivities of these components are as follows:

• Sand: 0.12-0.20 C°-m/Watt—optimizes the thermal resistivity but negatively affects pumpability.

• Phase and circuit or pipe spacing among the cables being studied, which would impact mutual heating effects.

• The locations of other utilities that cross the cables, especially other transmission or distribution cable circuits that could produce mutual heating effects. Also, steam lines may be present.

• Sections of the route that parallel other utilities, including power cables. Parallel cables within a certain range may produce sufficient mutual heating to cause derating. A general guideline is, if the horizontal spacing is within 25% of the depth, mutual heating may be a factor (e.g., if the cables being studied are at 4 m depth, parallel cables or other heat sources within 1 m horizontal spacing should be examined for mutual heating effects).

• Topographical profiles may show areas where overburden has accumulated above the cable route. Profile drawings mainly indicate the cable circuit’s depth of cover below grade and usually the locations of other utilities that cross the cable circuit. Areas that are important to note on the profile drawing are:

• Entry/exit to manholes since cables frequently dip to enter a manhole

• Road crossings where the cable burial depth may be increased to accommodate the required road bedding materials

• Directional drilling locations where the burial depth is significantly greater than conventionally-trenched sections

• Water: 1.65 C°-m/Watt—optimizes the flowability but negatively affects shrinkage.

• Bentonite: 3.50 C°-m/Watt—optimizes the pumpability but negatively affects thermal resistivity. These materials are combined by a soil specialist for use by the contractor or utility during installation. 3.6.2

Review Circuit Plan and Profile

A classical approach to performing uprating on underground cable circuits is to review the circuit plan and profile drawings, preferably the “as-built” versions, which may show additional details about the locations of the buried power cables, as well as better illustrate the

3-36

3.6.3

Evaluate Daily, Seasonal, or Other Periodic Load Patterns

Load shape is generally not that important for most transmission equipment, particularly overhead lines where the thermal time constant is relatively short. With underground transmission cables, the long thermal time constant—35–150 hours—can significantly impact loading patterns for both normal and emergency ratings, particularly for short-duration emergencies. In typical normal ampacity ratings on cables, daily load cycles are modeled by rating techniques through the application of a load factor or loss factor. The load fac-


tor relates the average daily load to the peak load, usually following a relationship similar to the following: Loss Factor, p.u. = 0.3 (Loss Factor, p.u.) + 0.7 (Loss Factor, p.u.)2 This relationship is graphed in Figure 3.6-7. As mentioned earlier, the loss factor (or load factor of the losses) considers the average daily heat output relative to the peak heat output. Consider Figure 3.6-8, which shows several load shapes that all have the same peak current but substantially different load and loss factors. All of the curves in Figure 3.6-8 have the same peak current (1000 A), but substantially different loss factors. On a daily basis, the different loads shown will release different amounts of energy into the surrounding soil. This has a significant impact on conductor sizing for a desired rating or on the available current for a given conductor size. Note that the loss factor is also the perunit power delivered on a daily basis.


If the cable construction and installation conditions are held constant and the loss factor is varied, the cable ratings will vary substantially. From the standpoint of uprating, increases in loss factor over time mean that the ampacity will tend to decrease. For example, on a recent uprating study for a New England utility, the loss factor in 1959 when the circuit was built was 57% but had grown to 83% in 2001. While the utility was able to increase capacity on the circuit with some extraordinary methods, the normal book rating actually decreased with respect to time because of the increasing loss factor. Load shape may also play an important role from the standpoint of emergency ratings. If the daily load cycle is such that the load during portions of the day (typically at night) is lower than at other times of the day (typically mid-afternoon), short duration emergencies can vary greatly. This is illustrated in Figure 3.6-9, where the normal ampacity (1.0 per unit), A, is determined for a peak temperature of 90°C, and two 4-hour emergency ratings are determined:

• Emergency Rating B: The peak temperature is 105°C with a rating of 2.6 per-unit (as compared to the normal rating). This emergency starts going into a lowload period, so the pre-emergency load temperature is about 73°C.

• Emergency Rating C: The peak temperature is also 105°C with a rating of only 1.3 per-unit (as compared to the normal rating). This emergency starts going into a peak load period, so the pre-emergency temperature is about 85°C. Figure 3.6-7 Ampacity as a function of loss factor.

Figure 3.6-8 Graph of load profiles showing the same peak current with different load and loss factors.

The above example illustrates that considering the load shape for emergency ratings is important. Dynamic ratings (see Section 3.8) is a main benefit for this type of analysis in optimizing—and generally increasing—the current carrying capacity of an underground cable circuit.

Figure 3.6-9 Temperature plots and ratings as a function of rating starting time.

3-37


3.6.4

Temperature Monitoring

Using Thermocouples Temperature measurements are an important part of verifying assumptions when calculating ampacity and studying ways to improve ratings. Ideally, one would want to measure the cable conductor temperature—the hottest location in the cable system—to be sure that insulation temperature limits are not exceeded. However, because the conductor is energized, this is typically difficult to do. Instead, it is common to measure the temperature on the outer surface of the cable either on the pipe coating of a pipe-type cable or the jacket of the other cable types. For conduit installations, temperatures might be measured in the conduits.

To perform these measurements, thermocouples are often used. Thermocouples are temperature sensors based on the principle that when two dissimilar metals are joined, a predictable voltage will be generated that relates to the difference in temperature between the measuring junction and the reference junction (connection to the measuring device). The types of metals that are used depend on the application (temperature range, location, cost, etc.). There are varieties of thermocouple types (T, F, N, J, etc.). For cable-related measurements, “Type-T” thermocouples are most often used because they have a temperature range most closely matched to typical cable operating temperatures. The Type-T thermocouple has a blue outer jacket in the United States, France and the United Kingdom (up until 1993) or dark brown outer jacket in the United Kingdom (since 1993) and Germany. Inside, the thermocouple wire consists of a copper electrode (positive, +) and a constantan electrode (negative, -). Each electrode has an insulating coating that varies in color depending on the country of origin (United States is blue on the positive and red on the negative; the United Kingdom is white on the positive and blue on the negative (pre-1993) or brown on the positive and white on the negative; France is yellow on the positive and blue on the negative; and Germany is red on the positive and brown on the negative). When connecting thermocouple wire to a meter, data logger, or other measuring device, it is important to verify that the polarity is correct. Otherwise, the schematic will essentially create three thermocouple junctions in series (rather than one), which could provide misleading results. Also, the thermocouple wire or extension grade thermocouple wire must also be run from the measurement location all the way to the test instrument. A thermocouple junction is created by joining the copper and constantan wires together as shown in Figure 3.6-10. The junction can be left bare, which minimizes thermal capacitance and increases temperature mea-

3-38


surement response. However, depending on the environment, the junction may need to be coated or soldered to protect the thermocouple junction from corrosion, etc. Laboratory-grade thermocouples are typically welded together. A thermocouple has an accuracy of typically less than 1 C°. A key advantage to thermocouple temperature measurement is that the wire itself and the equipment to measure thermocouple temperatures are both relatively inexpensive and minimal training is required to use the technology. Several companies including Telog Instruments, Omega, and Fluke make data loggers that cost less than US $1000 to read and possibly record thermocouple temperatures. Battery-powered recorders can log data for 6–18 months, recording temperatures every 15 minutes for an extended period. Once suspected or known cable circuit hot spots are identified, low-cost thermocouples and data loggers may be placed at these locations and checked periodically, particularly during periods of high load. By comparing measured temperatures with those predicted using load history and the equivalent thermal circuit from ampacity calculations, it is possible to evaluate the assumptions used in ampacity calculations. From an operations standpoint, monitoring the cable temperatures gives some assurance that the cables are not exceeding their allowable temperature during typical load cycles. The main disadvantage to thermocouple measurements is that they only take a temperature measurement at one location. It is, therefore, possible to miss hot spots if they are not already identified. Also, the practical lead length limit of thermocouples is about 300 m (1000 ft), and each thermocouple requires its own pair of wires to

Figure 3.6-10 Thermocouple wires (copper and constantan with U.S. color scheme – left) and completed junction (right).


make a measurement. Therefore, it is difficult to instrument more than a few tens of locations. Distributed Fiber Optic Temperature Sensing (DFOTS) Distributed fiber optic temperature sensing (DFOTS) uses a specialized optical time-domain reflectometer (OTDR) to measure the temperature along a multimode optical fiber. The process works by taking advantage of temperature-dependent reflections (called “backscatter” based on the Raman Effect) in the fiber. The special OTDR instrument, such as York Sensors (Sensa) DTS80 or SensorTran’s Model 5000 (see Figure 3.6-11), records the magnitude of the reflection (proportional to temperature) and the time for reflections to return after sending an incident 1080 nm laser pulse into the fiber, which, when combined with the fiber’s propagation velocity, gives the distance to the measurement location. By successively sending light pulses into the fiber, the special OTDR can scan the entire fiber and obtain a temperature trace along the fiber with a spatial resolution of approximately 1 m and a temperature accuracy of 1°C. The obvious advantage of DFOTS is that a continuous end-to-end temperature measurement is possible, allowing the ampacity study to reveal all of the hot spots along the cable route. Later, these hot spots could be instrumented with thermocouples for extended temperature measurements at key locations.


buried system is impractical unless there is a conduit (communications or power) within a meter or so of the energized cables in which the fiber may be installed. An example of fiber that might be installed directly buried or in a conduit is shown in Figure 3.6-12. The fiber optic cable typically consists of four to six 50 x 125 μm fibers, each with a 900 μm tight buffer (only 1 or 2 fibers are needed, but some may be damaged during installation so spares are desirable), Kevlar strength members to improve pulling strength (usually only 3000N, 675 lb), and a fire-retardant PVC jacket. Some XLPE cable manufacturers are embedding optical fibers under the jacket of the cable to facilitate temperature measurements (Figure 3.6-13). Since this is physically closer to the conductor—ultimately where we would like to know the temperature—this has some advantages. A disadvantage of DTS equipment is the cost of the electronics to measurement the fiber temperature, which may be upwards of US $60,000. Also, the equipment is

Depending on the configuration of the fiber (number of splices, etc.) and the temperature measurement mode (single or double ended), a fiber length of 5–10 km may be scanned. Equipment is also available that works with single-mode fiber and can measure up to 30 km. However, this equipment suffers from both lower spatial resolution (4–10 m) and lower accuracy (2–3°C). All fiber test loops are limited by the losses in the system, so fusion splicing is the preferred method for joining fibers. Fiber used for DTS measurements is typically installed in a parallel conduit or directly buried alongside an existing cable or pipe. Retrofitting a fiber on a direct-

Figure 3.6-11 Distributed temperature sensing equipment.

Figure 3.6-12 Optical fiber cable used for DTS measurements.

Figure 3.6-13 XLPE cable with integrated optical fiber under the jacket. 3-39


not well suited for operation in the field on an extended period of time, which makes “spot” measurements or extended measurements in manholes or stations difficult. Most of the equipment has an operating range of 10–35°C, which is fairly limited in particularly warm or cool climates. 3.6.5

Ampacity Audit

An “ampacity audit” involves investigating ampacity for a cable circuit by applying the various techniques described in this chapter. The basic concepts include performing a soil thermal survey to determine soil characteristics and ambient temperatures, evaluating load history, and then calculating ampacity. If AEIC guidelines are being followed on a circuit that previously had used assumed soil parameters, the 10°C increase in conductor temperature by itself generally allows a 20% increase in ampacity.


constructed using an alcohol-water or ammonia-water mixture in a partially filled copper tube. A partial vacuum is drawn on the tube to adjust the vapor pressure to the operating temperature range for the particular application. The heat pipe is then installed at an angle with the low point installed near the heat source (cable, steam main, etc.). Heat from the source is absorbed by the liquid alcohol-water or ammonia-water solution, causing a phase change to vapor, which rises, carrying the heat away. The gaseous vapor then condenses back to a liquid away from the hot spot and then drains back to the hot spot location. This continuous process removes heat from the location. The number and installation geometry of the heat pipes are typically designed by a specialist. An example of a heat pipe installation to mitigate the effects of crossing cable circuits is shown in Figure 3.6-14.

The ampacity audit is geared towards verifying the ampacity by whatever means are available and assessing which locations along the route limit the overall circuit ampacity. This might possibly include obtaining a DFOTS temperature trace for the route to find hot spots, or looking at route plan and profiles to find limiting installation conditions. These “hot spots” would then be investigated further to see how they might be mitigated. 3.6.6

Remediation of “Hot Spots”

Remediation of hot spots is sometimes possible if the scope of the hot spot is limited. If the hot spot is the result of overburden, or increased burial depth, it might be possible to remove some of the overburden above the cables. This reduces the thermal resistance to heat leaving the cable and may improve ampacity. Poor soil thermal resistivity can often lead to hot spots, particularly if a low quality thermal backfill was used – or not backfill at all. A hot spot may be eliminated or partially mitigated by excavating around the cables and installing a good quality thermal backfill. This will improve the heat transfer characteristics away from the cable, lowering the operating temperature for a given load condition. Heat Pipes In extreme cases, usually where one circuit experiences a hot spot from mutual heating of another circuit, the installation of heat pipes can help. The heat pipe is a passive device that takes advantage of the heat of vaporization to remove heat from a location. A heat pipe is

3-40

Figure 3.6-14 Heat pipes being installed to mitigate a hot spot where a steam main crosses a pipe-type cable.

3.6.7

Active Uprating

The following methods are mostly applicable to pipetype cables, although there are applications that could extend to extruded or self-contained cables.


Fluid Filling Gas-filled pipe-type cables may be uprated slightly by replacing the dry nitrogen gas with a dielectric liquid such as polybutene or alkylbenzene. Since a liquid is a more efficient heat transfer media than a gas, fluid-filling alone provides a small ampacity improvement (~23%). However, this allows for additional uprating methods to be applied. Fluid Circulation Fluid circulation is a relevant uprating technique when a short section, relative to the overall circuit length, is limiting the pipe-cable rating. By circulating the dielectric liquid within the cable pipe, the heat generated in the hot section will be transferred to other portions of the route, mitigating the hot temperatures at that location. One requirement for this to be implemented is to have a fluid return pipe or a parallel cable pipe that will permit a continuous circulation path as shown in Figure 3.6-15. Flow rates may be up to 800 liter/min (200 gpm), but slow circulation with only 20 liter/min (5 gpm) may be used for small hot spots or where the fluid viscosity limits the flow rate.

If no fluid return pipe or parallel cable pipe is present, fluid oscillation may be used. In this configuration, fluid is moved through the pipe at 4–40 liter/min (1–10 gpm) and cycled between the 4,000–11,000 liter (1000–3000 gallon) fluid reservoirs at either end of the pipe circuit. Major considerations for fluid circulation are the free area in the pipe and the viscosity of the dielectric liquid used in the pipe. As a result, the pressure rise when pumping dielectric fluid through a pipe could be too excessive for practical uses. If the flow rate is limited to a value below what is necessary to mitigate a hot spot, circulation may not be possible to mitigate a hot spot; the utility might consider changing to a lower viscosity dielectric liquid or re-examining pressure rise limitations.


The basic principle of fluid circulation is based on work done by CIGRÉ and discussed in Electra (CIGRÉ 1979). The approach is to evaluate sections of the fluid circulation route that have basically the same characteristics and then use boundary conditions to match the flow rate from one section to the next. Dielectric liquid (or water in parallel circulation/cooling tubes) is relatively noncompressible, although the density varies with temperature around the circulation loops. To consider this, the dielectric fluid characteristics—density and specific heat—are adjusted for each section that is being modeled. As fluid circulates through the pipes, the temperature of the fluid leaving one section is assumed to be the temperature entering the next section, satisfying the boundary conditions. To model each section, the “un-cooled” (temperature that would result absent of any cooling or circulation movement in the pipes) temperature is calculated based on circuit loading, the cable construction, and installation conditions at each section. Then, heat absorbed or removed would cause increases or decreases in the dielectric fluid temperature as it moves through the pipes. The temperature change with respect to distance is of the form shown in Equation 3.6-2. T ( x ) = TUN −COOLED − K ⋅ A ⋅ exp( P ⋅ x )

3.6-2

In the equation, x is the distance, K is a value proportional to the maximum change in temperature possible for a section of infinitively long length, A is a value relating the mutual heating affects among the pipes (either cabled or fluid return), and P is a value characterizing the rate of temperature change as air moves along the pipe section. There is one exponential term for each pipe in which fluid is circulating.

Figure 3.6-15 Example pipe cable dielectric fluid circulation loop with heat exchangers.

3-41



The “un-cooled” temperature is the steady-state temperature of the dielectric liquid inside the cable pipe that would result if the loading remained fixed on the energized cables and no fluid circulation was in place. As the flow rate is reduced, the value of K approaches zero. As the flow rate increases, the value of K approaches the difference between the inlet temperature of the dielectric liquid and the uncooled temperature for a given section. Changes in dielectric liquid temperature as it passes through the cable pipes provide an indication of the heat being removed in each section based on the mass flow through the section as defined by Equation 3.6-3. •

m = ρ ⋅ A ⋅υ

3.6-3

from the cable pipe, passed through a heat exchanger to remove heat, and then reintroduced to the cable pipe. This has the potential of increasing the ampacity by 50– 70%, although the cost and maintenance of these active systems can be high. Considerations for Active Uprating With fluid circulation or forced cooling in pipe-type cables, there are some cautions associated with using these uprating methods. Pressures along the hydraulic loop may become excessive as a result of hydrostatic head pressure, fluid flow restrictions near joints, and cross-over plumbing between feeders and fluid return pipes. The high pressures could cause the termination housing to fracture, potentially resulting in a cable failure, dielectric fluid leak, and fire.

Where: •

m is the mass flow rate in kg/sec. ρ is the density in kg/m3. A is the free area within the pipe in m2. υ is the velocity in m/sec. The heat removed, Watts, in a given section can then be found from Equation 3.6-4. •

q = m⋅ CP ⋅ (TOUT − TIN )

3.6-4

Where: CP is the specific heat in kJ/kg-°C. TOUT and TIN represent the outlet and inlet temperatures, respectively, of the dielectric liquid in a given section. By knowing the net heat absorbed or lost in a given section and the length of that section, it is possible to evaluate the net heat removed (or gained) in a given section. For a forced-cooled system (described next), the net heat gained by the system will assist with sizing the forced-cooling plant and heat exchangers. Fluid circulation could be applied to extruded dielectric or self-contained liquid-filled cables by installing parallel water cooling pipes next to the cables and then circulating water through those pipes. Although technically feasible, this is not often done. In addition, some utilities such as National Grid in the United Kingdom circulate the dielectric liquid in the fluid channel of self-contained liquid-filled cables. Again, this is relatively rare. Forced Cooling (Water or Oil) Forced cooling is an extension of fluid circulation. The main difference is that, rather than just moving heat around from “hot spots” to “cold spots” in the cable route, the dielectric liquid (or water in the case of water cooling of extruded or self-contained cables) is diverted

3-42

Pressure drop along long circulation loops must be considered. The degree of snaking of the cable phases within the pipe can affect the fluid flow and pressure drop, potentially limiting the flow rate. The pressure drop as a function of length can found by evaluating the Darcy-Weisbach equation, as shown in Equation 3.6-5. dP ν ⋅V 2 = f 2 ⋅ Dh dL

3.6-5

Where: f is the friction factor, empirically determined based upon the Reynolds Number cable-topipe inner diameter ratio. γ is the density, kg/m3. V is the flow velocity, m/sec. Dh is the hydrostatic diameter, m. The pumping plant, in particular the fluid circulation pump, must be able to accommodate the circulation pressure. The density and viscosity of the dielectric liquid will impact the allowable pressure drop, in addition to the free area within the pipe and the degree of cable snaking. On long circulation loops, multiple loops may be needed with intermediate fluid circulation stations to limit the pressure drop. Complex control systems, particularly in the event of a cable failure, must also be developed to manage the various cooling loops and to stop fluid circulation in the event of a fault. Fluid circulation is often considered for the buried pipe sections. However, when forced cooling is used, the riser sections—lengths of pipe between the trifurcator and termination—may become limiting and could require specialized plumbing to allow circulation in these areas. Diffusion chambers may also be necessary to avoid damaging the outer layers of insulation. A factor to consider for uprating older pipe circuits, where the riser


section may be limiting, is that installation of a diffusion chamber on a riser that is not so equipped can be difficult. This is because working “close in” on the riser pipe would be difficult with the cable already in place, and removing and installing a new termination to put in the diffusion chamber may be impractical. 3.6.8

Shield/Sheath Bonding Scheme

As discussed to some extent in Section 3.4, there are three methods for grounding the shield/sheath on singleconductor (extruded dielectric, self-contained fluidfilled) cable systems: multipoint bonding, single-point bonding and cross-bonding. Multipoint bonding involves tying the shield/sheath connections together and to local ground at both terminals and usually at intermediate manholes, resulting in a path for induced circulating currents but with minimal induced voltages. Single-point bonding involves grounding the shield/sheaths at only one location along a given section, preventing circulating currents but leaving the other end un-grounded where a standing voltage will appear. Cross-bonding involves dividing the cable sections into groups of three minor sections that are close to the same length and transposing sheath connections at the one-third and two-third locations, thereby eliminating net circulating currents and minimizing induced voltages. Generally, single-conductor transmission cables are designed with cross-bonding or single-point bonding to minimize shield/sheath circulating currents in the presence of relatively high phase currents. The one exception to this common practice is submarine cable installations, where multipoint bonding of the sheath is almost mandatory because of the long installation lengths and typically wide phase spacing. Contrary to transmission practice, most distribution circuits are multipoint bonded where the utility transformer and customer service panel are both grounded for safety and so the neutral can carry imbalance currents. The circulating currents in multipoint bonded systems generate additional I2R losses (heat) in the shield/sheath that impacts ampacity. Multipoint bonding systems generally have about 2030% lower ampacity than single-point bonded or crossbonded systems constructed with similar cable sizes. If the ampacity audit reveals that a circuit has lower ampacity than desired and happens to be multipoint bonded, the shield/sheath connections might be reconfigured for sectionalized single-point bonding or crossbonding to eliminate the circulating current and gain a significant improvement in ampacity. The reconfiguration may require changing out some or all joints since


the joints must have shield interrupts to provide for single-point bonding or to facilitate transposing the sheath connections for cross-bonding. If a system that was previously multipoint bonded is being reconfigured for single-point bonding, a ground continuity conductor should be installed to provide a low impedance path for fault current; the shield breaks will otherwise block the flow of fault current. Also, single-phase or three-phase link boxes or cross-bonding boxes will be needed. If uprating using a reconfigured sheath bonding scheme is being considered, and utility practice is typically with multipoint bonding systems, care should be used to clearly mark all manholes where standing voltages may appear. A shield that is not grounded locally, but is connected to ground at the adjacent manhole, may experience a significant voltage rise with respect to local ground during nearby system fault conditions from a combination of induced voltages and system potential shifts. This is not a phenomenon peculiar to single-point grounded arrangements, as any shielded cable is susceptible when the shield is connected to a remote ground yet remains ungrounded locally. The remedy for this situation is to provide secure, temporary shield grounding as appropriate. This has always been a recommended practice. This is particularly important when working on a de-energized single-point bonded circuit that parallels an energized circuit, since the parallel circuit can induce a voltage. Also, single-point bonded or cross-bonded cable systems require periodic maintenance to check the jacket integrity and ensure that there are no unexpected current circulation paths. Fault location efforts may also be complicated by single-point bonded or cross-bonded sheaths, possibly requiring that the bonding connections be reconfigured during cable fault location. Jacket fault location in duct bank installations is difficult unless the ducts are under the water table. Although not technically necessary, many cross-bonded cable systems are installed with a parallel ground continuity conductor. Induced currents in this parallel conductor can generate enough I ^ 2 x R losses to produce mutual heating that can affect ampacity of the phase conductors. 3.7


3.7.1

Introduction

In contrast to uprating, which is generally defined as improving the capacity of existing equipment, upgrading considers using available infrastructure to economically put in new cables, replacing existing conductors. This section discusses some of these issues.

3-43



A basic assumption for this section is that the cable system is either pipe-type or a duct installation. Reconductoring a direct buried cable is impractical and really should be considered a new installation, along with the installation of a parallel circuit when there is no existing infrastructure (pipe or conduits). Neither of these cases is covered by this chapter. One possible scenario might be reconductoring one of two parallel cable circuits. The condition of the older circuit should be evaluated to see if loss of life or higher operating temperatures might affect reliable performance. The upgrading topics in this guidebook would apply to the scenario, although the details of evaluating the impact on the older circuit or other connected equipment are beyond the scope of this chapter. 3.7.2

Larger Conductor Sizes

The main issue with considering a larger conductor size is whether the cable will fit within the same conduit or pipe. Paper-insulated insulation thicknesses are fairly standardized based upon voltage class, but the designer might consider using a larger conductor size combined with a switch from conventional Kraft paper insulation to laminated paper polypropylene paper (PPP) insulation, which has a higher dielectric strength and, therefore, a lower insulation wall thickness. With pipe-type cables, the issue is to maintain sufficient clearance in the cable pipe. The traditional guideline for new pipe installations is to have at least 12.5 mm (0.5 in.) of clearance in the pipe, as determined by Equation 3.7-1. However, with older pipes, where upgrading would more often be considered—either pipes that have cables to be replaced or old but unused empty pipes that might have new cables installed—a minimum clearance of 25 mm (1 in.) is often considered prudent to allow for the possibility that overburden or settling may have increased the ovality of the pipe that possibly could affect a successful installation. C=

D 1 ⎛ d ⎞ − 1.366d + ( D − d ) 1 − ⎜ ⎟ 2 2 ⎝ D−d ⎠

diameter of the conduit and the outer diameter of the cable. Again, it is typical to have 12.5–25 mm (0.5– 1.0 in.) of clearance in the conduits. If cables are not already in the conduits, a mandrel through the conduits should be used to check the maximum size cable that can pass through the pipe or conduit. For extruded cables in particular, the construction of the metallic moisture barrier and metallic shield could be adjusted to allow for a larger cable. As an example, Commonwealth Edison (now ComEd, An Exelon Company) removed 138-kV paper-insulated cables from ducts to be replaced by cross-linked polyethylene cables. If the typical 3.2 mm (0.125 in.) lead sheath moisture barrier and full-wall 138-kV insulation 21.6 mm (0.85 in.) were used, it would have meant the standard XLPE cable design could not fit in the existing conduits. Instead, the installation included a reduced insulation wall (16.5 mm, 0.65 in.), a copper laminate tape with copper shield wires, and a reduced jacket wall (as compared to typical industry practice for that size cable), greatly reducing the outer cable diameter and allowing the cable system to fit in the conduits. The relative effect of reconductoring on ampacity is discussed in Section 3.4. 3.7.3

Cupric Oxide Strand Coating

Some cable manufacturers have investigated using cupric oxide coated strands to make conductors. By coating the strands with cupric oxide, each strand has a slightly increased resistance (in the radial direction) to each adjacent strand. This improves the skin and proximity effect factors of the conductor—reportedly down to 0.3 for both values—over conventional copper stranded insulations. This reduction in ac incremental losses significantly improves the ac to dc resistance ratio and ampacity. To illustrate, the pipe-type cable example

2

3.7-1

Where: D is the inner diameter of the cable pipe. d is the diameter of the cable over the insulation, plus 1.5 times the height of a skidwire, all values in inches. Figure 3.7-1 shows the clearance in a pipe-type cable. For extruded or self-contained cables where normally a single phase would be installed in each conduit, the clearance is simply the difference between the inner

3-44

Figure 3.7-1 Clearance in a pipe-type cable.


in Appendix 3.1 would show an increase in ampacity by almost 3% if a cupric oxide strand coated conductor were used. 3.7.4

Voltage Upgrading

Voltage uprating, possibly combined with an increase in conductor size, would significantly improve the power transfer limits. As an example, an 8-in. cable pipe that is typically used for 138-kV cables with 11.2 mm (0.44 in.) of Kraft paper insulation might be reconductored with 11.4 mm (0.45 in.) of PPP insulation, allowing an increase to 230-kV cable with virtually no change in the outer cable diameter and a 67% increase in power transfer. Additional improvements in capacity might be possible if a larger conductor size can also be used. Section 3.2 lists typical insulation thicknesses for the various cable constructions and insulation materials.


• Sumitomo: 100 m of 66-kV cable with 1000 A. • Southwire: 30 m of 12.5-kV cable with 2600 A (operated in parallel to an overhead line on Southwire's property).

• NKT: 30 m of 30-kV cable with 3000 A (utility substation).

• Condumex: 5 m of 2000 A (Condumex test facility). • Nexans / American Superconductor / LIPA: 610 m circuit 138-kV cable with 2510 A is being developed for a new installation on Long Island.

The main issue with voltage upgrading is that, in addition to possibly significant costs in new cables, several pieces of substation equipment must also be replaced to accommodate the new voltage level. This is sometimes not so significant if the higher voltage level being considered for voltage upgrading already exists within both terminals. Otherwise, the cost and effort generally make voltage upgrading infeasible. 3.7.5

Superconducting Cables

At the time this chapter is being prepared, superconducting cables are largely in the research stage. Limited sections of cable have been installed in controlled settings (e.g., parallel to a 100% redundant overhead line, in a “laboratory” setting, or in a nonessential capacity underground). Several high-temperature superconducting (HTS) cable projects have been demonstrated largely with U.S. Department of Energy funding, using either warm or cold dielectric technology (Figure 3.7-2). As the names imply, the “warm dielectric” cable uses insulation that is at or above room temperature to support the energized line-to-ground voltage, while “cold dielectric” cable utilizes cryogenic (liquid nitrogen ~80°K) insulating medium. Examples of recent research in superconducting cables are summarized below: 1996-1999

• Pirelli/EPRI: 50 m of 115-kV cable with 2000 A. • Sumitomo/TEPCO: 30 m of 66-kV cable with 1000 A. 2000-2002

• Pirelli/Detroit Edison: 130 m of 24-kV with 2500 A (system could not be energized because of a vacuum leak in the cryostat).

Figure 3.7-2 Examples of superconducting cables (courtesy of American Superconductor Inc.).

3-45


While favorable results have been observed, the available technology is not yet practical for typical transmission voltages, and the operating lengths have not been increased sufficiently to allow “transmission” at what have typically been considered medium-voltage levels (e.g., transferring bulk power at high-current/low-voltage). At this point, superconducting cables do not yet offer a commercially viable means for uprating existing transmission circuits, though this is likely to change within the next decade.


tion aging and “acceptable loss of life” has not often been considered for underground cable ampacity. The main benefit to dynamic ratings is the ability to track the cables’ temperatures with time and changing load conditions and then base emergency ratings on the actual, rather than assumed, pre-emergency temperatures. The benefits of this type of evaluation were illustrated in Section 3.6.3 and Figure 3.6-9. 3.8.2

3.8


3.8.1

Background

As discussed in Section 3.3.1, the thermal time constants of underground transmission lines are significantly longer than those of overhead lines and power transformers. This is a result of the thermal inertia (or heat capacitance) of the earth that surrounds the cables. As a result of this thermal inertia, the dynamic rating of underground transmission lines significantly exceeds their steady-state ratings, provided that there are significant variations in the line loading. Conversely, the dynamic rating of underground transmission lines is not much higher than their steady-state ratings if the lines are consistently loaded near their steady-state ratings. The term “dynamic rating” means the present rating of a line, taking into account its load history and real-time measurement of parameters (mainly ambient earth temperature). In actuality, the “normal” ampacity of a circuit does not change, except for changing ambient temperature, since it is generally based on an assumed daily loss factor and installation conditions. Therefore, a “dynamic” normal rating remains relatively constant unless some decision about future loading is evaluated. Predicting future loading patterns is difficult since unplanned system changes may affect loading patterns, but the use of predicted load patterns, usually based on utility SCADA systems, does allow for some future load estimations (usually limited to 24 hours). Tracking the cable conductor temperature is the main goal of dynamic ratings, since this is ultimately what limits the power transfer on the circuit. For paper-insulated cables, tracking the conductor temperature also permits an assessment of insulation aging and ultimately the life of the cable system. EPRI funded a detailed investigation of paper-insulated pipe-type cables in the 1990s. Transformer ratings have been based on a variety of factors including the insulation aging and loss-of-life criteria. However, application of insula-

3-46

EPRI Dynamic Ratings on Cables

Development of the EPRI Dynamic Thermal Circuit Rating (DTCR) system was started in 1991 with advanced models for overhead transmission lines, power transformers, and underground cables. The cable model used in DTCR was initially based largely on the underground cable ampacity program “Alternative Cable Evaluation (ACE)” in the EPRI Underground Transmission Workstation (UTW) that was started in 1990. ACE was an off-line ampacity program that would determine normal and emergency ratings based on userspecified input data. The ratings generated by ACE were similar to what many utility engineers refer to as “book ratings” in that they were static ratings based on assumptions (usually worst-case) and then tabulated for reference by engineers and operators. As the utility industry changed dramatically during the 1990s, toward achieving higher profits, there was increased pressure to get more capacity from existing equipment while minimizing new construction whenever possible. To this end, DTCR was developed to take realtime data from “off the shelf ” monitoring hardware, and determine optimal ratings (not worst-case) for the conditions at the time the ratings were performed. Although this required some philosophical changes at utilities to consider circuit ratings as moving, changing entities rather than fixed parameters, the overall benefit was to demonstrate a greater capacity in transmission assets, including underground transmission cables. The general theory behind DTCR is that, probabilistically, there are relatively rare circumstances where the worst-case rating conditions occur at the same time that the greatest possible circuit loading is required or desired. As a result, by evaluating the ratings on a realtime basis using actual, rather than worst-case conditions, the real-time rating is much higher and the allowable power transfer is greater. This is illustrated graphically in Figure 3.8-1. In Figure 3.8-1, there is a relatively small region (rating regime) where the dynamic rating distribution overlaps the loading, indicating that at most times, the dynamic



Figure 3.8-1 Probabilistic view of dynamic ratings and actual circuit loads.

rating is greater than the “book” ampacity. DTCR allows the circuit to operate closer to the limit by performing a real-time rating evaluation using measured (rather than conservative or worst-case estimates) parameters. Cable Models One approach to dynamic ratings on cables—that used in the Underground Cable Module in DTCR—is based on the paper by Neher and McGrath (1957), and on the International Electrotechnical Commission (IEC) Publications 287 and 853 (International Electrotechnical Commission 1982, 1989). These same calculation methods are used in off-line rating tools such as EPRI’s UTWorkstation ACE program.

The numerical technique used in DTCR to track conductor temperatures is an “additive wave method,” whereby the temperature response to a constant heat input is tracked into the future. For cables, DTCR looks at “small” intervals (< 0.5 hours), over which the load can be treated as constant. The temperature response to the load with respect to time is a function of the heat input to the cable (either positive for increasing load or negative for decreasing load). Each time the load changes, a new temperature response “wave” is launched. As the load changes from interval to interval, the total temperature response at a given time is the summation of all the previous temperature response functions from each change in heat from the cable (as a function of load and the change in resistance with temperature). This basic concept is described in a paper by Neher (Neher 1963) and illustrated in Figure 3.8-3 with an arbitrary load. The numerical calculations are based on equations from IEC-287 and IEC-853 and make use of attainment fac-

tors for changes in heat output from the cables. The cable temperature changes with respect to time and changing load based on the thermal response of the cable and environment. The cable or pipe temperature response is defined by Equation 3.8-1.

θCable (t ) = Wi ⎡⎣ RA (1 − exp( −at ) ) + RB (1 − exp( −bt ) ) ⎤⎦ 3.8-1

Where: Wi is the heat output from the cable. RA, RB is the thermal resistance at steady state. a, b are time constants representing how the temperature changes with respect to time for a given heat input. For the temperature response of the environment, there are two models in DTCR: one that assumes all circuits/cables carry identical currents, and a second where two circuits may carry unequal loading. Equal Loading For the case of two three-phase circuits of extruded or self-contained cable, all six (6) cables are assumed to carry the same load even if the circuits are electrically disconnected. The temperature rise above ambient from ac loading is described by Equation 3.8-2, utilizing exponential integrals, for the cable that is identified to be the hottest cable in the trench.

⎡ ⎛ D2 ⎞ ⎛ L2 ⎞ ⎢ −Ei ⎜ − earth ⎟ + Ei ⎜⎜ − ⎟⎟ ⎜ 16δ t ⎟ ⎝ δt ⎠ ⎝ ⎠ ρs ⎢ θ HottestCable (t ) = Wi ⎢ ⎛ rj 2 ⎞ ⎛ r ' j2 4π ⎢ 6 ⎜ ⎟ ⎜− + − − + Ei Ei ⎢ ⎜ 4δ t ⎟ ⎜ 4δ t ⎢⎣ j = 2 ⎝ ⎠ ⎝

∑

⎤ ⎥ ⎥ ⎥ ⎞⎥ ⎟⎥ ⎟⎥ ⎠⎦ 3.8-2

3-47



Where: is the heat generated by each cable. Wi Ei is an exponential integral. Dearth is the earth diameter for the cable or conduit. L is the burial depth for the “hottest” cable among the group. is the actual distance between the hottest rj cable and adjacent cables. is the distance between the hottest cable and r’j the image of adjacent cables. The watts generated by each cable, Wi, are identical for all cables in the group. Unequal Loading For the case of two circuits with unequal loading, the heat output from the second circuit is defined separately from the first circuit. The mutual heating effects with respect to time are then evaluated as shown in Equation 3.8-3.

⎡ ⎛ D2 ⎞ ⎛ L2 ⎞ ⎢ − Ei ⎜ − earth ⎟ + Ei ⎜⎜ − ⎟⎟ ⎜ ⎟ ⎝ δt ⎠ ⎝ 16δ t ⎠ ρs ⎢ θ Pr imaryCable1 (t ) = Wi1 ⎢ ⎛ rj 2 ⎞ ⎛ r' 2 4π ⎢ 3 ⎟ + Ei ⎜ − j ⎢ + − Ei ⎜ − ⎜ 4δ t ⎟ ⎜ 4δ t ⎝ ⎠ ⎝ ⎣⎢ j = 2

∑

+Wi 2

⎤ ⎥ ⎥ ⎥ ⎞⎥ ⎟⎥ ⎟⎥ ⎠⎦

⎛ r2 ⎞ ⎛ r ' 2 ⎞⎤ ρs ⎡ 6 ⎢ − Ei ⎜ − j ⎟ + Ei ⎜ − j ⎟ ⎥ ⎜ 4δ t ⎟ ⎜ 4δ t ⎟ ⎥ 4π ⎢ j = 4 ⎣

∑

⎝

⎠

⎝

⎠⎦

3.8-3

Where: Wi1 , Wi2 are, respectively, the heat generated by each cable in circuit 1 and circuit 2. Cable Dynamic Rating Model The combined effects of the two temperature response functions gives the complete temperature response of the cable conductor to a given cable heat output. When there is changing load, typical of most transmission circuits, the accumulated temperature responses for each change in load will give the conductor temperature with respect to time. The general procedure and flow of the DTCR cable model are illustrated in Figure 3.8-2.

Graphically, the changing load is illustrated in Figure 3.8-3, where the top graph shows an arbitrary load pattern, with loads that are both increasing and decreasing over time. The bottom graph shows the individual temperature response waves to each change in load (fine lines) and the summation of all the temperature response waves (dark line). Also shown in the graph is the addition of the dielectric temperature rise, which remains constant with respect to time as long as the lineto-ground voltage remains constant (this is an assumption). As compared to other modules (overhead lines and power transformers) within DTCR, the cable model requires extensive computations since the long earth thermal time constant requires “looking back” hundreds of hours in the loading history. As a result, ratings are normally not performed more often than once every 15 minutes or so. Fortunately, the long thermal time

Figure 3.8-2 General flow of information in DTCR cable model. (“STE” means “Short Time Emergency” rating, and “LTE” means “Long Time Emergency” rating.)

3-48


constant also means that there are limited temperature changes over that time. Because of the considerable heat storage capacity of underground cables, the operating power levels prior to a contingency loading have a large effect on the actual thermal behavior during emergency loading events. EPRI’s DTCR technology allows continuous monitoring and establishment of such power equipment’s actual pre-contingency thermal state. As a result, load shedding during emergencies can often be avoided and capital investment in new equipment postponed. 3.8.3

Benefit of Dynamic Ratings

The thermal rating of underground cables is traditionally calculated using worst-case seasonal loads and soil temperatures. Underground cable thermal parameters are based on manufacturer’s data, installation assump-


tions, and industry standards. Rating calculations are typically performed “off-line” using worst-case assumptions to derive seasonal limits (maximum soil temperature, worst-case loss factors). With dynamic ratings, actual soil temperatures and load data are used in place of worst-case approximations, allowing higher operating limits under most conditions and more accurate thermal modeling under all conditions. Other than cable parameters and configuration, dynamic thermal rating calculations for underground cable require soil characteristics and temperature. The equipment parameters can be verified by comparing calculated to measured equipment temperatures, which in the case of high-voltage underground cable is the earth interface temperature, or a more general comparison between a measured temperature and calculated temperature in a location near the power cables. The measured temperature from a thermocouple or DFOTS can be compared to the dynamic rating system-calculated temperature, as described in Section 3.4.7. DTCR Circuit Ratings The DTCR software allows the user to calculate realtime equipment temperatures, multiple thermal ratings, and “remaining-time” (or “Time to Temperature Overload,” TTO) during emergency loadings, given real-time load and ambient ground temperature for underground cable circuits. “Circuit” ratings, rather than “equipment” ratings, are possible by modeling all of the power equipment on a given circuit (e.g., series-connected transformers, overhead lines, cables, etc.), or in the case of cables, each unique installation section along a given route, and then letting DTCR calculate ratings for all equipment and locations on a circuit. Then, DTCR selects the lowest rating for each category (normal, LTE, STE) and reports these values as circuit ratings. Utility Implementation of Dynamic Ratings Some dynamic rating systems interface directly with monitoring hardware. This has some disadvantages:

• The hardware is probably redundant to monitoring already done by the utility.

• The hardware is sometimes very specialized, meaning that the original vendor must be recalled for maintenance and repairs, usually at a high cost.

• Telemetry for any monitoring outside of a substation is often complex, expensive, and prone to interruption. Figure 3.8-3 “Additive Wave” model for temperature tracking in underground cables.

• The computer system used to perform rating calculations, by virtue of the direct connection to the moni-

3-49



time input data file on the dynamic rating system computer through use of “Network Access calls” or other operational programs.

toring hardware, must be located in the field where weather and security are difficult to manage.

• Any changes to the hardware usually require a

• The real-time input data on the dynamic rating sys-

new custom-designed interface to collect the monitored data.

tem is read from the ASCII file created by a SCADA Network Access call.

• There is an issue of getting calculation results from

• A specific “SCADA” input file containing real-time

the remote location back to the utility’s operations center, where it can be used by engineers and operators to optimize circuit capability.

temperatures and ratings is continually updated by the dynamic rating system and made available to the utility SCADA/EMS system. This allows dissemination of the calculation results to anywhere within the utility.

For these reasons, dynamic rating systems may be interfaced to the utility SCADA system so that the SCADA system can handle all of the utility-specific telemetry issues, and the dynamic rating system can concentrate on just the rating and temperature calculations. Some favorable characteristics are as follows:

All calculations can now be performed in an engineering office or operations center environment (rather than in a substation) without the need for special monitoring device communication links. Utility operations programmers need only develop simple SCADA Network Access calls to write ASCII input data files to the dynamic rating computer, rather than spending a lot of time writing equipment-specific interface programs. Figure 3.8-4 shows the general layout of EPRI’s dynamic rating system (DTCR), which utilizes this approach.

• The preferred mode of operation is one wherein remote monitors provide data to the SCADA/EMS database using utility-specific communication links, and the dynamic rating system obtains its real-time data from that database rather than directly from the remote monitors.

• The utility SCADA/EMS system must transfer realtime monitor data from the database to a simple real-

Monitor

PC in Engineering Office or Operations Center

Modem Cell or Land Line

Monitor

Wire or Fiberoptic (RS232)

Modem

Direct Monitor Input

Monitor

Input Data File*

Direct Connect Communications Program

Input Data File*

Radio Link Communications Program

wireless

Network Access Call

Telephone Communications Program

Input Data File* Input Data File*

* File with most recent realtime data appended.

DTCR Software Product User Interface

File Handler

Real-Time Historical Data File (mmddyy.###)

File

DTCR Calculation Algorithms

Real-Time Output File (ratings, temps., etc.)

Real-Time SCADA Output File (ratings, temps, etc.)*

Network Access Call

SCADA/EMS Database Output to Engineering or Operations Center

DTCR Functional Diagram

Figure 3.8-4 Schematic overview of DTCR’s location within the utility architecture.

3-50


3.8.4

Required Monitoring

Underground cable dynamic rating systems require various monitored parameters. Some of the parameters that could be evaluated are summarized as follows: Ambient Soil Temperature The ambient temperature is a fundamental parameter to be monitored since it directly affects the allowable temperature rise from ac loading. Soil temperature monitoring should be located where it is representative of the ambient conditions imposed on the cable system. Usually, this means being at least 10 m (30 ft) away from an energized cable circuit at typical installation depths. A thermocouple tree—a series of thermocouples installed at various depths at the same location—is ideally suited for this type of monitoring, since it gives a range of temperatures that may be used for the variation in burial depth encountered along the circuit. Load The load is also an important parameter to know, even if doing quasi-dynamic ratings (described in Section 3.8.4). The load serves two purposes. First, it allows the conductor temperature to be calculated as a function of load. Second, it allows a correlation between any measured temperatures and the circuit load (see Section 3.4.7). This is important for verifying ampacity capability. Soil Thermal Resistivity Real-time monitoring of soil thermal resistivity is not common, mostly because the soil thermal resistivity does not change rapidly. Some utilities permanently install a thermal probe so that additional thermal resistivity measurements can be made to account for seasonal variations or weather effects.

As discussed in Section 3.6, thermal resistivity is a very important parameter, since earth components of thermal resistance represent more than half of the total thermal resistance to heat leaving the cable. Pipe-Type Cable Monitoring Some parameters are uniquely important to pipe-type cable dynamic ratings, particularly those that utilize fluid circulation or forced cooling. Inlet and outlet pressure to a cooling loop, fluid flow rates through the cooling loop, inlet dielectric liquid temperature, and cooling system outlet temperature all may be monitored to evaluate the performance of a pipe-type cable system with active forced cooling. The capability of the cooling plant to remove heat from the dielectric liquid is very important, since this ultimately dictates how much forced cooling can be applied to the pipe-type system.


3.8.5

Quasi-Dynamic (Real-Time) Ratings

“Quasi-dynamic ratings” utilize many of the principles of real-time ratings except they may not be done on a continuous basis. For example, a utility may have a cable circuit that is only heavily loaded two months of the year. On that basis, the cost to implement a dynamic rating system may not be justified, but the ratings during that two-month window are still critical. Quasi-dynamic ratings might be applied by monitoring load and temperatures for a period of time and then calculating what the conductor temperature might be as a result of that load. From this, the temperature of the cable conductor at rated temperature can be extrapolated for rating purposes. For example, the earth interface temperature of a cable system may be monitored with thermocouples for several months until a period of high loading occurs. At that time, the utility may download measured temperatures from a thermocouple data logger and compare measured to calculated temperatures to evaluate the assumptions used for rating models, both real-time and off-line ratings. Quasi dynamic ratings may also apply to reviewing historical load profiles using dynamic rating algorithms. The load history on a circuit for a year or two—perhaps covering high-load periods during summer months— could be run through a dynamic rating tool to evaluate peak loading periods and study loss-of-life criteria (on paper cables). 3.9


Section 3.9 describes uprating projects recently conducted at utilities. It is hoped that these case studies help to illustrate the general application of uprating techniques described in this chapter. 3.9.1

CenterPoint Energy

Description of Circuit and Summary of Rating Constraints and Utility Goals A 138-kV HPFF underground transmission line was constructed in 1969 from CenterPoint Energy’s Polk substation (located at the intersection of Polk and La Branch Streets in Houston, Texas) to CenterPoint’s Garrott Substation (located at the intersection of Garrott Street and Blodgett). The total length of this 138-kV underground transmission line is approximately 2.37 miles (12,500 ft). A 2500-kcmil, compact segmental copper, 138-kV HPFF cable with 505 mils of insulating tapes was used to construct the Polk – Garrott transmission line.

3-51


In March 2001, a loop feed to a new CenterPoint substation, Midtown Substation, was constructed by tapping into the existing Polk to Garrott underground transmission line. This loop feed to the Midtown Substation (located on La Branch Street between Taum and Drew Streets) segregated the Polk to Garrott underground transmission line into two parts with the lengths of 0.96 and 1.41 miles. CenterPoint wanted to evaluate the power transfer capabilities of the Polk-MidtownGarrott and Polk-Downtown 138-kV underground transmission lines in light of these changes and to optimize the current-carrying capacity of the circuits. The ampacity audit was based on an evaluation of recent and historical data including:

• Long-term load current, ambient soil temperatures, and cable pipe temperatures during summer operating conditions

• Distributed fiber optic temperature sensing (DFOTS) measurements performed on the circuits in February 2002 for hot spot identification

• As-built plan and profile drawings for the two cable circuits

• Cable manufacturing data CenterPoint Energy also wanted to evaluate the condition of the thirty-two-year-old Polk-Garrott HPFF cables in coordination with the ampacity analysis. Consequently, two investigations were performed for this purpose. First, Detroit Edison (DECo) performed dissolved gas analysis (DGA) and laboratory testing of cable paper tape samples obtained during construction of the loop feed to the new Midtown Substation. Power Delivery Consultants (PDC) also performed cable dissipation factor measurements at rated voltage using EPRI-developed instrumentation. A previous EPRI project (Transmission Cable Life Evaluation and Management) indicated that cable tape physical property measurements, DGA, and dissipation factor measurements are the best diagnostic tests to determine cable loss-of-life. The primary focus of the DTCR project was to examine the ratings on the Polk-Midtown-Garrott circuit. This circuit consists of two segments: 5,060 ft from Polk to Midtown Substation, and 7,440 ft from Midtown Substation to Garrott Substation. DTS measurements showed that the hotspot for the Polk-Midtown-Garrott underground line is a crossing with the Polk-Downtown 138-kV underground transmission line at the intersection of Polk and La Branch (just outside of the Polk Substation). The cable used for the Polk to Downtown 138-kV line is identical to the Polk to Garrott line. The depth of cover over the Polk-Midtown-Garrott line is approximately 11 ft-2 in. at the hot spot location, and 3-52


the vertical clearance to the Polk-Downtown line (above it) is approximately 3 ft. CenterPoint placed a thermocouple on the Polk to Garrott cable pipe near the intersection. Initially, the thermocouple temperature was monitored with a data logger, but this thermocouple is now connected directly to CenterPoint's SCADA system. A thermocouple was also placed on the PolkDowntown circuit at the location of the crossing and connected to SCADA. In 2000, CenterPoint Energy (Houston Lighting & Power) began this investigation (completed in December 2002 – EPRI Report 1007539) to increase the circuit capacity on the high-pressure fluid-filled (HPFF) pipetype cable connecting the Polk and Garrott Substations. Various studies were performed to evaluate uprating possibilities for this circuit, including the application of distributed fiber optic temperature sensing (DFOTS). Results of DFOTS revealed that a hot spot existed where another pipe-type cable (CenterPoint’s Polk-Downtown circuit) crossed over the Polk-Garrott circuit. Although an overall increase in ampacity was found for the general cable circuit, a net decrease in ampacity resulted from the modeling of the mutual heating of the two cable circuits where they cross. This was anticipated prior to beginning the project, so DTCR was implemented on the Polk-Garrott circuit in an effort to optimize available circuit capacity. The principal goal of the project was to investigate an optimized circuit rating in light of the interference temperature effects detected by DFOTS and experienced by the crossing pipes. A secondary objective was to demonstrate that, under normal loading patterns, the maximum normal temperature (85°C) of the conductor would infrequently be exceeded. Results of Uprating and Benefits to Utility The following conclusions may be reached from reviewing the application of DTCR at CenterPoint:

• The DTCR modifications and subsequent data analysis showed that CenterPoint Energy’s Polk-Midtown-Garrott and Polk-Downtown pipe-cable circuits can benefit from dynamic ratings. DTCR’s predicted load pattern assumes a typical 24-hour loss factor cycle consistent with static ratings. However, the emergency loading is a function of pre-load conditions, and DTCR accurately calculates the conductor pre-load temperature based on historical loading patterns. Also, DTCR uses the present loading to predict time to temperature overload (TTO).

• While a detailed ampacity study indicated there was effectively a reduction in the established book rating of 3.4%, applying DTCR allowed for a net increase in the normal rating of 20.7%, based on considering a


“dynamic” rating using summer 2000 load data for a “quasi-real-time” dynamic rating analysis.

• In summary, the real-time dynamic ratings of the


the harbor section. An additional goal was to consider means for increasing ampacity on the circuit.

Polk-Midtown-Garrott and Polk-Downtown underground transmission lines are expected to be significantly higher than the static ratings that were calculated under a separate project, assuming there is similar load pattern variability to that observed during the summer 2000.

Power Delivery Consultants, Inc. (PDC) was contracted in 2001 to perform a very detailed evaluation of the Bridgeport Harbor portion of UI’s 1710 and 1730 lines using sophisticated modeling and state-of-the-art technology to gather information about the installation and environment. The evaluation included several technologies:

The following conclusions are a result of the cable condition assessment testing performed on the Polk-Garrott 138 kV underground transmission line.

• Gyroscopic testing on the empty cable pipe to

• DGA testing of pipe fluid samples and laboratory

• Hydroscopic surveying of the harbor bottom to eval-

testing of a cable sample indicated that Polk-Garrott 138-kV cable offers an exceedingly long life, which is characteristic of HPFF cables.

uate the degree of siltation over the cable pipes since they were installed in 1961 and, ultimately, to determine the cable depth of cover.

• Results of the dissipation factor measurements con-

• Distributed temperature sensing (DTS) using EPRI’s

firmed that the Polk-Garrott 138-kV HPFF cables do not show any signs of insulation deterioration after more than 30 years of operation.

DTS equipment and fiber optic cable installed in the spare cable pipe

3.9.2

United Illuminating Company

Description of Circuit and Summary of Rating Constraints and Utility Goals In 1989, United Illuminating Company (UI) performed an engineering evaluation on the ampacity of the existing 1.4-mile-long UI 115-kV high-pressure gas-filled cable Circuits 1710 and 1730, which connect UI’s Pequonnock Substation to the Seaview Tap in Bridgeport, Connecticut, where the lines transition to overhead conductors. A 1600-ft section under Bridgeport Harbor, where the cables were buried approximately 25 ft under high-resistivity sediments, appeared to limit the overall circuit rating. UI’s construction records indicated that the cable configuration under the harbor consists of three pipes in a 5-ft trench, with a spare (empty) pipe centered between the two cabled pipes.

Results of the 1989 thermal tests showed that soil resistivity ranged widely, from 90º to 250º C-cm/Watt. This range of values produced a degree of uncertainty in the ratings. In addition, the degree of siltation and the actual pipe positions since the cable pipes were installed in 1961 was unknown. Because of the uncertainty of the pipes’ locations, 1989 soil tests were done at least 50 ft away from the expected pipe position to avoid possibly damaging the pipes with the soil-coring equipment. The uncertainty of some parameters from the 1989 study, the limiting of the entire circuit’s ampacity by the harbor section, combined with UI’s interest in increasing the total power transfer on the circuit, precipitated UI in undertaking a more thorough ampacity evaluation of

develop accurate cable pipe plan and profile information for the harbor crossing.

• Continuous thermocouple temperature monitoring using installed thermocouples and data loggers

• Updated soil sample testing to characterize the soils at the depths of interest

• Forced air ventilation to characterize possible uprating by removing heat from the cabled pipes An EPRI report (1007534) documents the results of these evaluations and a detailed ampacity study to determine the actual capacity of UI’s 1710 and 1730 lines under both normal and emergency ampacity conditions, and describes possible approaches for increasing the ampacity on the lines. In 2002, UI implemented two of the recommendations of the ampacity study:

• Applied forced-air cooling on the parallel cable pipe. • Implemented DTCR to monitor conductor temperature and evaluate real-time temperatures on the circuit as the result of circuit loading. Results of Uprating and Benefits to Utility The initial ampacity study resulted in several recommendations to mitigate the rating limits on UI’s cable circuits. These are summarized in Table 3.9-1. Two of the options, forced air cooling on a parallel empty cable pipe and dynamic ratings, were later implemented.

The forced-air cooling equipment is shown in Figure 3.9-1. The actual cost to install the forced-air cooling equipment was substantially higher than the initial esti-

3-53



Table 3.9-1 Summary of United Illuminating Pipe Cable Uprating Methods Forced Air Cooling Location

Reconditioning

Harbor only Harbor only

Fluid Filling

Circulation

Forced Cooling

Reconductoring

XLPE

Water Cooling

Dynamic Rating

Circuit

Circuit

Circuit

Circuit

Circuit

Harbor only

Circuit

Maximum estimated increase

4.0%a

5.6%b

<3.0%

7.8%

25–50%

18.0%

c

5.6%d

e

Additional maintenance

Minimal

None

Moderate

Moderate

High

None

None

Moderate

None

Environmental Concerns

Low

None

High

High

High

None

None

Moderate

None

Estimated Cost

$100k

$1.2M

$1.5M

$200kf

$1.5Mg

$3M

c

$500kd

$200k

a. b. c. d. e. f. g.

Based on testing in September-October 2001; small additional increase possible. Land rating becomes limiting. Not recommended for pipe-type retrofit with conventional technology. Not recommended; air-cooling could achieve same result. Rating improvements by dynamic ratings vary depending on circumstances. Increase in cost minimal after fluid filling. Assumes fluid filling already done.

mate, largely due to some complications associated with the civil works of the installation. The following conclusions and recommendations were reached based upon implementing DTCR on United Illuminating Company’s 1710/1730 circuits:

• DTCR shows that the maximum normal operating temperature of paper-insulated pipe-type cables (e.g., 85°C) is rarely exceeded, even though there are frequent occasions when the actual circuit loading exceeds the normal book ratings.

• The combined effects of circuit loading on 1710 and mutual heating from circuit loading on 1730 sometimes result in the conductor temperature on the 1730 circuit exceeding its maximum normal temperature.

As was indicated in an earlier study, this results from the typically increased load levels on the 1710 and 1730 circuits, the increased daily loss factors, and the fact that loads on the 1730 circuit are increasingly approaching the loads on the 1710 lines.

• UI may want to consider performing a long-term loss-of-life evaluation on the 1710 and 1730 circuits to see how the calculated operating temperatures on the circuits have influenced accumulated loss-of-life. Despite the occasional incursions above rated temperature, the evaluation would likely show that during a typical calendar year, the below 85°C operating temperatures for most of that time indicate that less than a calendar year of life has been consumed. This would provide increased confidence to UI that this occasional high-temperature operation should not adversely affect the future operation of the circuit. If pursued, this additional work would apply paperinsulated pipe cable aging characteristics developed during EPRI work on accelerated aging at Waltz Mill.

• From the standpoint of evaluating normal ratings, the book ratings were previously found to be 743 A (on the 1710 circuit). Real-time ratings show a range of improvements (10–25%) depending on the conditions (Table 3.9-2).

• If the 1710 and 1730 circuits are ever decommis-

Figure 3.9-1 Blower assembly for forced-air cooling on pipe-type cable circuits. 3-54

sioned, an evaluation of the paper insulation aging should be performed to determine if the typically higher operating temperatures on the 1710 cables show increased aging over the 1730 cables, since both circuits are made of similar vintage cable and have had similar in-service lives.



3.10

Table 3.9-2 Comparison of Normal “Book” Rating to RealTime and Dynamic Ratings Rating Type

Minimum

Normal Book (Previous Study)

Maximum

Tables 3.10-1 and 3.10-2 summarize the major improvements in ampacity that may be realized by the various uprating and upgrading techniques described in this chapter. The specific costs for each depend largely on the unique aspects of each installation or project, but qualitative costs, along with many other factors, are listed in the tables for reference.

743A

Real-Time Normal

621A

817A

Dynamic Normal (100% Loss Factor)

0A (722A)

877A

Dynamic Normal (with Cyclic Rating Factor)

0A (774A)

929A


• Further work on DTCR may be warranted to provide for a cyclic rating factor on emergency ratings of longer than 24 hours to fully take advantage of the “dynamic normal rating” concept.

The case studies in Section 3.9 give an indication of specific costs for one of the uprating projects.

Table 3.10-1 Summary of Uprating and Upgrading Techniques Applicable to All Cable Types Measure Soil Rho, Heat Pipes, Mitigate Hot Spots

Evaluation Criteria Rating Incremental Increasea

20%

Reliability

High

Lead Time Cost

Real Time Monitoring Thermocouples (Temp.)

Dist. Fiber Optic (Temp.)

Dynamic Ratings

Replace Conductors

Voltage Upgrading

10-20%

3-20%

66-80%

High

High

High

N.A.b High

High

Maintenance

Low

Low

Low

Low

Low

Increased, but Low

Losses

None

None

None

Low

Low

Increased, but Low

Installation

2 mos.

3 mos.c

3 mos.

2 mos.

14 mos.

24 mos.

Operating

None

Real Time

Real Time

Real Time

None

None

Installationd

Low

Low-Med

Low-Med

Low

High

High

Operating

None

Low

Low

Low

Med.-High

Med.-Highe

a. Incremental increase in ampacity over previous options. b. Monitoring the cable circuit alone, does not provide for rating improvements. Real-time monitoring, with the monitored parameters fed into rating calculations provides for optimum ampacities. c. If not done during the original installation of the cable system. d. Including material costs. e. Generally, higher voltage equipment requires more extensive and expensive maintenance. Table 3.10-2 Summary of Uprating Techniques Predominantly for Pipe-Type Cables Evaluation Criteria

Rating Incremental Increase

Cost

2%

Circulation

Forced Cooling

Slow

Rapid

Passive Heat Exchanger

21%

8%

16%

Forced-Air Heat Exchanger Refrigerated Cooling 31%

16%

Reliability

High

Medium

Medium

Medium

Low

Low

Maintenance

Medium

Medium

Medium

Medium

High

High

Losses Lead Time

Fluid Filling

None

Low

Medium

Medium

High

High

Installation

10 mos.

2 mos.

2 mos.

2 mos.

3 mos.

6 mos.

Operating

N.A.

Lowa

Lowa

Lowa

Lowa

Lowa

Installation

High

Low

Low

Medium

High

High

Operating

Low

Low

Medium

Medium

Medium

High

a. Typically less than 24 hours.

3-55


REFERENCES

The following references were used for this chapter and may be useful to the reader for additional background on the topics discussed. Anders, G. J. 1997. Rating of Electric Power Cables, IEEE Press/McGraw Hill. Bascom, III, E. C., D. A. Douglass, G. C. Thomann, and T. Aabo. 1996. “Hybrid Transmission: Aggressive Use of Underground Cable Sections with Overhead Lines.” CIGRÉ 21/22-10. Bascom, III, E. C. and J. A. Williams. 2002. “Taking Your Cable’s Temperature.” Transactions of the T&D World Expo. 7-9 May. Indianapolis, Indiana. Bascom, III, E. C. and J. A. Williams. 2002. Ampacity Evaluation and Distributed Fiber Optic Testing on PipeType Cables Under Bridgeport Harbor. Electric Power Research Institute Publication 1007534. December. Bascom, III, E. C. and J. H. Cooper. 2002. Condition and Power Transfer Assessment of CenterPoint Energy’s Polk-Garrott Pipe-Type Cable Circuit. Electric Power Research Institute Publication 1007539. December. Bascom, III, E.C. 2003. “Underground Cable Uprating and Upgrading Tutorial.” Transactions of IEEE PES Transmission & Distribution Conference. Paper 03TD0362 (Panel Session). Dallas, Texas. 7-12 September. Bascom, III, E. C., J. A. Williams, M. A. Pasha, S. M. Rahman, and W. Zenger. 2003. “Ampacity Evaluation of High-Pressure Gas-Filled (HPGF) Pipe-Type Cables Under Bridgeport Harbor.” Transactions of IEEE PES Transmission & Distribution Conference. Paper 03TD0093. Dallas, Texas. 7-12 September. CIGRÉ 1979. “The Calculation of Continuous Ratings of Forced-Cooled Cable.” Working Group 21.08. Study Committee 21. Electra. No. 66. pp. 59-84. October. CIGRÉ. 1987. “The Calculation of Continuous Rating for Forced-Cooled High-Pressure Oil-Filled Pipe-Type Cables.” Working Group 21.08. Study Committee 21. Electra. No. 113. pp. 97-120. El-Kady, M. A. and D. J. Horrocks. 1995. “Extended Values of Geometric Factor of External Thermal Resistance of Cables in Duct Banks.” IEEE Transactions on Power Apparatus and Systems. Vol. PAS-104.

3-56


EPRI. 1982. High Ampacity Terminations. EL-2233. January. EPRI. 1985. Volume 1: Calculating AC/DC Resistance Ratios for High-Pressure Oil-Filled Cable Designs Designer's Guide. EL-3977. EPRI. 1985. Volume 2: Calculating AC/DC Resistance Ratios for High-Pressure Oil-Filled Cable Designs Details of Mathematical Derivations. EL-3977. EPRI. 1992. Underground Transmission Systems Reference Book. TR-101670. EPRI. 1997. Thermal Properties Manual for Underground Power Transmission. TR108919. November. EPRI. 1998. Transmission Cable Life Evaluation and Management. TR-111712. September. EPRI. 2002. Increased Power Flow Guidebook – Overhead Transmission Lines. 1001817. December. Holman, J. P. 1997. Heat Transfer. 8th Edition. McGraw-Hill. New York. IEEE. 1988. “IEEE Guide for Application of SheathBonding Methods for Single- Conductor Cables and the Calculation of Induced Voltages and Currents in Cable Sheaths.” 575-1988. Iizuka, K. 1974. Power Cable Technology Hand Book. DenkiShoin, Tokyo. pp. 80. International Electrotechnical Commission. 1982. IEC287. “Calculation of the Continuous Current Rating of Cables (100% Load Factor).” International Electrotechnical Commission. International Electrotechnical Commission. 1989. IEC853-2. “Calculation of the Cyclic and Emergency Current Rating of Cables.” International Electrotechnical Commission. 1st Edition. Neher, J. H. and M. H. McGrath. 1957. “The Calculation of the Temperature Rise and Load Capability of Cable Systems.” Paper 57-660. AIEE Insulated Conductors Committee. June. Neher, J. H. 1963. “The Transient Temperature Rise of Buried Cable Systems.” Paper 63-917. IEEE Insulated Conductors Committee. June.



Parmar, D. and J. Steinmanis. 2003. “Underground Cables Need a Proper Burial.” Transmission & Distribution World. April. pp. 44-51.

Williams, J. A., E. C. Bascom III, B. Horgan, and T. Aabo. 1991. “Field Test Program and Results to Verify HPFF Cable Rating.” IEEE Transactions.

Purnhagen, D. W. 1984. “Designer’s Handbook for Forced-Cooled High-Pressure Oil-Filled Pipe-Type Cable Systems.” Electric Power Research Institute. EL3624. Project 7801-5. July.

Williams, J. A. and J. H. Cooper. 1998. “Distributed Fiber Optic Temperature Monitoring and Ampacity Analysis for XLPE Transmission Cables.” Electric Power Research Institute. TR-110630. June.

Stevenson, Jr., W. D. 1982. Elements of Power System Analysis, 4th Edition. McGraw-Hill. New York.

Williams, J. A. 2000. “Application of Fiber-Optic Temperature Monitoring to Solid Dielectric Cable.” Electric Power Research Institute. Publication 1000469. November.

Williams, J. A., T. R. Grave, and E. Kallaur. 1986. “Uprating of High Pressure Gas-Filled Feeders by Fluid Filling and Rapid Circulation.” IEEE Conference. Anaheim, CA. September 15-19.

3-57


APPENDIX 3.1

PIPE-TYPE AMPACITY EXAMPLE


The cable configuration is as shown in Figure A3.1-1.

This appendix contains a sample calculation of pipetype cable ampacity using the procedures outlined in this chapter and detailed in the references.

Figure A3.1-1 Cable configuration for pipe-type ampacity example.

3-58



Pipe-Type Cable Ampacity Worked Example Cables are 345kV HPFF cables with 2500kcmil segmental copper conductors, 905 mils kraft paper insulation, 0.1x0.2, 2x3in. lay stainless steel skid wires in an 10-inch cable pipe, 2 circuits, 0.62 loss factor. Cable Data: A := 2500 ρ conductor := 0.017241

Conductor area, CI ohm -meters

Electrical resistivity, copper conductor

ks := 0.39

Conductor skin effect factor, in oil

kp := 0.46

Conductor proximitty effect factor, in oil, cradled

Dc := 1.824

Diam eter of the segm ental conductor, inches

Tc := 85

Maximum normal conductor operating tem perature, °C

tcs := 0.005


ti := 0.905


tan δ := 0.0023

Values for Paper Dielectric constant of the insulation Insulation Dissipation factor of the insulation, numeric

ρ insulation := 6.00

Thermal resistivity of the insulation, C°-m/Watt

tis := 0.005

Thickness of insulation shield tapes, inches

SIC := 3.5

ρ shield := 0.7

ohm -meters

Skid W ire Size/Type

0.1in. x 0.2in., 2 x 3in. lay

ρ skidwire := 0.7

ohm -meters

f := 60

Hz

Electrical resistivity of stainless steel shield tapes

Electrical resistivity of stainless steel skidwire

LF = 0.62

Daily (24-hour) loss factor, per unit (entered below)

n := 3

Num ber of cables within pipe or conduit

N := 2 Pipe Data: Pipe is HPFF ODpipe := 10.75

Pipe outside diameter, inches

IDpipe := 10.25

Pipe inner diameter, inches

t coating := 0.07

Pipe coating (Som astic) thickness, inches

ρ coating := 3.5

Thermal resistivity of the pipe coating, C°-m/w

3-59


Installation Data: x1:= −15 burial1 := 42


x2 := 15

Horizontal location of pipe center, inches

burial2 := 42

Burial depth to pipe center, inches

Ta := 25

Ambient earth temperature, °C

f := 60

Power frequency, Hz

E := 345000× 1.05

System maximum line to line voltage, volts

ρ native := 0.9

Thermal resistivity of the native earth, C°-m/w

ρ backfill := 0.5


Width cbf := 53

Height cbf := 29


Center_Depth cbf := 39

Value for center-line depth of cbf is arbitrary

Calculate Cable Geometry: Dcs := Dc + 2tcs


Dinsulation := Dcs + 2ti


Dis := Dinsulation + 2tis


Dskidwire := Dis + 1.5 × 0.1

Diameter over 0.1" skid wires, inches

Dearth := ODpipe + 2t coating Clearance :=

IDpipe 2

− 1.366Dskidwire +

(IDpipe − Dskidwire) ⎡ 2

Dskidwire ⎞⎤ ⎛ ⎢1 − ⎜ ID ⎟⎥ ⎣ ⎝ pipe − Dskidwire ⎠⎦

0.5

Clearance in pipes, inches Dcs = 1.834 Dinsulation = 3.644 Dis = 3.654 Dskidwire = 3.804 Dearth = 10.89 Clearance = 1.992

3-60



Metric Conversion of Variables A Area conductor := 1.9735

3

2

Areaconductor = 1.267 × 10

mm

Dconductor := Dc25.4

Dconductor = 46.33

mm

Dcond_shield := Dcs 25.4


mm

Dinsulation := Din sulation25.4


mm

Dinsl_shield := Dis25.4

Dinsl_ shield = 92.812

mm

Dskidwire := Dskidwire25.4

Dskidwire = 96.622

mm

ODpipe := ODpipe 25.4

ODpipe = 273.05

mm

IDpipe := IDpipe 25.4

IDpipe = 260.35

mm

Dearth := Dearth25.4

Dearth = 276.606

mm 3



burial1 = 1.067 × 10

x1:= x125.4

x2:= x225.4

x1 = −381

mm

3

Width cb f := Width cbf25.4

Width cbf = 1.346 × 10

mm

Height cbf := Heightcbf25.4

Heightcbf = 736.6

mm

Center_Depthcbf := Center_Depthcb f25.4

Center_Depthcbf = 990.6

mm

W d = 10.741

W /m/phase

Calculate the dielectric losses: 2

E⎞ −9 ⎟ tanδ10 3 ⎝ ⎠ ⎛ Dinsulatio n ⎞

2πf SIC⎛⎜ Wd :=

18 ln ⎜



ρ conductor Areaconductor

RdcT := RdcT1.025

RdcT := Rdc20⎡⎢

−5

Rdc20 = 1.361 × 10

⎥ ⎣ 20 − ( −234.5) ⎦

Assume 2.5% Stranding of Conductor

−7

Xs :=

Tc − ( −234.5) ⎤

8πf( ks ) 10

−7

Xp :=

RdcT

Ohms/meter

8πf(kp ) 10 RdcT

2

Ycs :=

Xs

192 + 0.8Xs

2

S := Dskidwire

2 2 ⎞ ⎛ Dco ndu ctor ⎞ 2⎡⎢ ⎛ Xp ⎛ Dconductor ⎞ ⎜ ⎟ Ycp := ⎜ ⎟ 0.312⎜ ⎟ ... ⎜ 192 + 0.8Xp2 ⎟ ⎝ S S ⎠ ⎢ ⎝ ⎠ ⎝ ⎠ ⎢ 1.18 + ⎢ 2 ⎞ ⎛ Xp ⎢ ⎜ ⎟ + 0.27 Racc := RdcT⎡⎣ 1 + 1.5(Ycs + Ycp )⎤⎦ ⎢ ⎜ 2⎟ ⎣ ⎝ 192 + 0.8Xp ⎠

Ycs = 0.056

⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦

Ycp = 0.061

3-61



Calculate the shield and skidwire loss increments: Area of shield tape is width of tape times thickness. Resistance of shield tape is the area times the helical length times the resistivity divided by the area. Shield tape thickness is 0.005in stainless steel, with 1/8" lapped, with typical tape width of 7/8". Assume there are 2 tapes. 7 widthshield _tape := 25.4 8

area shield _tape := thickness shield _tape width shield _tape Rshield :=

⎛ πDinsl_shield ⎞ 1+ ⎜ ⎟ ⎝ lay shield ⎠

ρ shield area shield _tape

1 lapshield := 25.4 8

thickness shield _tape := 0.005 × 25.4

layshield := width shield _tape − lapshield

2

Rshield = 3.804

Ohms/meter

Skid wire resistance Area of elipse is pi * major_radius * minor_radius. Area of skid wire is half this. Skid wire is 0.1 x 0.2, 3-inch lay, 2 wires. Material is stainless steel. minor_radius := 0.1 × 25.4

major_radius := 0.2

25.4

area skidwire :=

2

π 2

minor_radius major_radius

layskidwire := 3 × 25.4 Length of a helix is (1 + (pi*D/Lay)^2)^.5 Rskidwire :=

ρ skidwire

1+

area skidwire

⎛ πDskidwire ⎞ ⎜ ⎟ ⎝ lay skidwire ⎠

2

1

Rs :=

1

1

+

Rskidwire

Rskidwire

+

1 Rshield

+

1

Rskidwire = 0.284

Ohms/meter

Rs = 0.132

Ohms/meter

Rshield

Calculate Mutual Reactance (assume cradled configuration) −7

Xm := 2( 2πf) 10 Ysc :=

Rs

⎛ 2.3Dinsl_shield ⎞ ⎟ ⎝ Dskidwire ⎠

ln⎜

−5

Xm = 5.977 × 10

Ohms

1

Racc

−3

2

Ysc = 1.314 × 10

⎛ Rs ⎞ 1+ ⎜ ⎟ ⎝ Xm ⎠ Racs := RdcT ⎡⎣ 1 + 1.5( Ycs + Ycp + Ysc) ⎦⎤

Calculate the pipe loss increments to AC resistance: Yp :=

0.0438Dskidwire + 0.0226IDpipe

Yp = 0.578

6

RdcT 10

Racp := RdcT ⎡⎣1 + 1.5( Ycs + Ycp + Ysc) + Yp⎤⎦ −5

Racc = 2.06 × 10 Qs :=

3-62

Racs Racc

Qp :=

−5

Racs = 2.063 × 10 Racp Racc

Qs = 1.002

−5

Racp = 3.075 × 10 Qp = 1.493

Ohms/meter AD/DC resistance ratios



Calculate Cable Thermal Resistances Ri :=

ρ insulatio n 2π

⎛ Dinsl_shield ⎞ ⎟ ⎝ Dcond uctor ⎠

ln ⎜

U := 0.26

V := 0

Ri = 0.663 Y := 0.0026

Tmoil = 66.827 Roil :=

Constants for HPGF Estimate of m ean temperature in duct

nU

Roil = 0.175

1 + 0.1( V + YTmoil) Dinsl_shield2.15

Rpipe_coating :=

ρ coating 2π

⎛ Dearth ⎞ ⎟ ⎝ ODpipe ⎠

n ln⎜

Rpipe_coating = 0.022

Calculate External Thermal Resistances Calculate geometric correction factor for backfill envelope: x := Height cbf

x=short dimension of backfill

y := Width cbf

y=long dim ension of backfill

⎤ ⎡⎢⎛ 1 ⎞ ⎛ x ⎞ ⎛ 4 x ⎞ ⎛⎜ y 2 ⎟⎞ ⎜ ⎟ ⎜ ⎟ ⎜ − ⎟ ln 1+ 2 + ln( x)⎥ ⎢⎝ 2 ⎠ ⎝ y ⎠ ⎝ π y ⎠ ⎜ x ⎟ ⎥ ⎝ ⎠ ⎦ Db := e ⎣

Db = 985.973

Lb := Center_Depth cbf

Lb = 990.6

⎛ 2L + 4L 2 − D 2 ⎞ ⎜ b b b ⎟ Gb := ln ⎜ ⎟ Db ⎝ ⎠

Gb = 1.322


α soil :=

6.71 × 10

(ρ nativ e100)

Dx := 1.02 α soil24 Rearth :=

ρ back fill 2π

2

Thermal diffusivity of native soil 0.8

mm

hour Diam eter beyond which 24 hour average losses apply, mm

⎛ ⎛ 2burial1 + 4burial1 2 − D 2 ⎞ ⎞ ⎜ ⎛ Dx ⎞ ⎜ earth ⎟ ⎟ n ⎜ ln ⎜ + LFln ⎟ ⎜ ⎟⎟ D D x ⎝ ⎝ earth ⎠ ⎝ ⎠⎠

3

α soil = 1.834 × 10

Dx = 213.978 Earth thermal resistance for AC losses at loss factor Rearth = 0.381

Rearth' :=

ρ back fill 2π

⎛ ⎛ 2burial1 + 4burial1 2 − D 2 ⎞ ⎞ ⎜ ⎛ Dx ⎞ ⎜ earth ⎟ ⎟ n ⎜ ln ⎜ + ln ⎟ ⎜ ⎟⎟ D D x ⎝ ⎝ earth ⎠ ⎝ ⎠⎠

Earth thermal resistance for dielectric losses at 100% loss factor Rearth ' = 0.652

3-63



Mutual thermal resistance between two pipes (just for normal ampacities) d'12 := ⎡⎣ ( x1 − x2) + (burial1 + burial2)

2⎤

d 12 := ⎡⎣ ( x1 − x2) + (burial1 − burial2)

⎦

2

2

F12 :=

d'12

Rmutual :=

d12

Rmutual' :=

Rcor rection := LF

Rcor rection ' :=

⎦

2⎤

ρ backfill 2π

(ρ native − ρ backfill) 2π

(ρ native − ρ backfill)

Distance between one cable pipe and image of other cable pipe

.5

Distance between one cable and the other

n LFln( F12)

ρ backfill 2π

.5

Rmu tual = 0.161

n ln ( F12)

Rmu tual' = 0.26 Thermal resistance correction for native soil for AC losses Rcor rection = 0.313

n N Gb

Thermal resistance correction for native soil for dielectric losses

n N Gb

2π

Rcor rection' = 0.505 Calculate Normal Ampacity on primary cable ∑RacRth := Racc Ri + Racs Roil + Racp ( Rpipe_coating + Rearth + Rmutual + Rcorrection)

LF ≡ 0.62

⎞ ⎛ Ri + Roil + Rpip e_coating + Rearth' + Rmutual' + Rcorrection '⎟ ⎝2 ⎠

ΔTd := W d⎜

ΔT := Tc − ΔTd − Ta Irated :=

ΔT = 39.104

ΔT

Adjust "iterated" values below until they equal "calculated".

Irated = 940.2

∑RacRth

Itotal := 2Irated

ΔT d = 20.896

Itotal = 1880.4

Tc calc := Irated ⎡⎣ Racc Ri + Racs Roil + Racp (Rpip e_coating + Rearth + Rmu tual + Rcor rection) ⎤⎦ ... + ΔTd + Ta 2

Tc calc = 85 2

Tshield calc := Tc calc − Irated Racc Ri − W d

Ri 2

Toil calc := Tshield calc − ⎛⎝ Irated Racs + W d ⎞⎠ 2

Roil 2

T earth_interface := Toilcalc − ⎛⎝ Irated Racs + W d ⎞⎠ 2

Roil 2

Tshield calc = 69.357

Tshield ≡ 69.357

Toil calc = 66.827

Tmoil ≡ 66.827

− ⎛⎝ Irated Racp + W d ⎞⎠ Rpip e_coating 2

T earth_interface = 63.477

3-64


APPENDIX 3.2

EXTRUDED AMPACITY EXAMPLE

This appendix contains a sample calculation for a crosslinked polyethylene (extruded) cable ampacity using the


procedures outlined in this chapter and detailed in the references. The cable configuration is as shown in Figure A3.2-1.

Figure A3.2-1 Cable configuration for extruded ampacity example

3-65



Extruded Dielectric Cable (XLPE) Ampacity Worked Example The ampacity calculation is for a 230kV 1750 kcmil segmented copper conductor circuit, with 866mils XLPE insulation, and lead metallic sheath, 2 circuits installed in a vertical duct bank and 0.60 loss factor. The sheath is cross bonded to minize circulating current. Cable Data: A := 1750

Conductor area, CI

ρ conductor := 0.017241

ks := 0.435

Conductor skin effect factor, dry segmental

kp := 0.6

Conductor proximitty effect factor, dry segm ental

Dc := 1.416

Diam eter of the segmental conductor, inches

Tc := 90

Maximum allowable norm al conductor operating temperature, C

tcs := 0.0787


ti := 0.866


tis := 0.0984

Thickness of insulation semiconducting shield, inches

tms := 0.125

Thickness of lead moisture barrier / metallic sheath

tj := 0.125

Jacket thickness, inches

SIC := 2.3

Dielectric constant of the insulation

tan δ := 0.001

Dissipation factor of the insulation, num eric

Duct Data: ODduct := 6.625

PVC Duct outside diameter, inches

IDduct := ODduct − 2⋅ 0.28

IDduct = 6.065

Duct inside diameter, inches

Installation Data: Burial := 42

Depth to center of top conduit, inches

d phases := 10

Distance between adjacent phases, inches

d circuits := 20

Distance between adjacent circuits, inches

Ta := 20

Earth am bient temperature summer, °C

f := 60

Power frequency, Hz

LF := 0.60

24 hour loss factor

E := 230000

System line to line voltage, volts

n := 1

Num ber of conductors per duct

N := 6

Num ber of occupied ducts

Thermal Resistivities: ρ insulation := 3.50 ρ jacket := 3.50

Thermal resistivity of the jacket, C°-m/w

ρ duct := 6.00

Thermal resistivity of the duct, C°-m/w

ρ native := 1.00

Thermal resistivity of the native earth, C°-m /w

ρ backfill := 0.50


Width cbf := 33

3-66

Thermal resistivity of the insulation, C°-m/w

Height cbf := 33


ohm -meters



Calculate Cabl e Geometry: Dcs := Dc + 2⋅ tcs


Dcs = 1.573

Dinsulation := Dcs + 2⋅ ti


Dinsulation = 3.305

Dis := Dinsulation + 2⋅tis


Dis = 3.502

Dms := Dis + 2⋅tms

Diameter over the metallic shield/moisture barrier, inches

Dms = 3.752

Mean metallic shield diameter, inches

Dmms = 3.627

Djacket := Dms + 2⋅ tj

Diameter over jacket, inches

Djacket = 4.002

Clearance := IDduct − Djacket

Clearance in conduit, inches

Clearance = 2.063

Dmms :=

Dis + Dms 2

Metri c Conversion of Variabl es A Areaconductor := 1.9735

2

Areaconductor = 886.749

mm

Dconductor := Dc⋅25.4

Dconductor = 35.966

mm

Dcond_shield := Dcs⋅ 25.4


mm

Dinsulation := Dinsulation⋅ 25.4


mm

Dinsl_shield := Dis⋅ 25.4

Dinsl_shield = 88.956

mm

Dmean_shield := Dmms⋅25.4

Dmean_shield = 92.131

mm

Dmet_shield := Dms⋅ 25.4

Dmet_shield = 95.306

mm

tms = 3.175

mm

tms := tms⋅ 25.4 Djacket := Djacket⋅ 25.4

Djacket = 101.656

ODduct := ODduct⋅ 25.4

ODduct = 168.275

mm mm

IDduct := IDduct⋅ 25.4

IDduct = 154.051

mm

Burial := Burial⋅ 25.4

Burial = 1.067× 10

mm

dphases := dphases⋅ 25.4

d phases = 254.000

mm

dcircuits := dcircuits⋅ 25.4

d circuits = 508.000

mm

3

Calculate the dielectric losses: 2⋅ π⋅f⋅ SIC⋅⎛⎜ W d :=

2

E ⎞ −9 ⎟ ⋅ tanδ⋅ 10 ⎝ 3⎠ ⎛ Dinsulation ⎞

Wd = 1.144

W/m

18⋅ ln ⎜


3-67




ρ conductor

−5

Rdc20 = 1.944 × 10

Areaconductor

Rdc90 := Rdc20⋅⎛⎜

234.5 + Tc ⎞

ohms/meter

−5

⎟ ⎝ 234.5 + 20 ⎠

Rdc90 = 2.479 × 10

ohms/meter

Assume 2.5% Stranding of Conductor −5

Rdc90 := Rdc90⋅1.025

Rdc90 = 2.541 × 10

ohms/meter

−7

Xs :=

8⋅ π⋅ f⋅ ( ks) ⋅ 10

Xs = 2.581

Rdc90 2

Ycs :=

Xs

Ycs = 0.034

2

192 + 0.8⋅ Xs

−7

Xp :=

8⋅ π⋅ f⋅ ( kp) ⋅ 10

Xp = 3.561

Rdc90

2 2 ⎛ ⎞ ⎛ Dconductor ⎞ 2 ⎡⎢ Xp ⎛ Dconductor ⎞ ⎜ ⎟ Ycp := ⋅⎜ ⎟ ⋅ 0.312⋅ ⎜ d ⎟ ... ⎜ 2 ⎟ ⎝ d phases ⎠ ⎢ phases ⎠ ⎝ 192 + 0.8 ⋅ Xp ⎝ ⎠ ⎢ 1.18 ⎢+ 2 ⎞ Xp ⎢ ⎛⎜ ⎟ + 0.27 ⎢ ⎜ 2⎟ ⎣ ⎝ 192 + 0.8⋅ Xp ⎠

Racc := Rdc90⋅ (1 + Ycs + Ycp)

−5

Racc = 2.638 × 10

⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦

−3

Ycp = 4.468× 10

ohms/meter

Calculate the shield losses: Assume that the conductors will lie in a flat (vertical) configuration for purposes of calculating shield losses. The metallic sheath consists of lead, and the bonding scheme is cross-bonded, so there will be no circulating current and only eddy current losses. −8

ρ lead := 21.4⋅ 10

Sheath material is lead Areasheath := π⋅

2 2⎞ ⎛D ⎝ met_shield − Dinsl_shield ⎠

4

2

Areasheath = 918.965

mm −6

Areasheath := Areasheath⋅10 Rsheath :=

ρ lead

−4

Rsheath = 2.329 × 10

Areasheath

Estimated sheath temperature: Rsheath := Rsheath⋅

3-68

Tmshield − (−236.0) 20 − ( −236.0)

Tmshield = 73.856 −4

Rsheath = 2.819 × 10

2

m



Eddy current loss increm ent −7

m :=

2⋅ π⋅ f⋅ 10

m = 0.134

Rsheath

⎛ m2 ⎞ ⎡⎢⎡ ( Dmean_shield)⎤ 2⎤⎥ ⎟⋅ YSe0 := 6⋅ ⎜ ⎢ 2⋅ d ⎥⎥ ⎜ 2⎟ ⎢ phases ⎦ ⎦ ⎝ 1 + m ⎠ ⎣⎣ YSe1 := 0.86⋅ ( m)

3.08

⎛ Dmean_ sh ield ⎞ ⋅⎜ ⎟ ⎝ 2⋅ dphases ⎠

−3

YSe0 = 3.468× 10

1.4⋅ m+ 0.7

−4

YSe1 = 3.852× 10

2

8⋅ π ⋅ f

β 1 :=

β 1 = 47.050

7

ρ lead⋅ 10

1.74

tms −3 ⎛ ⎞ ⎛ ⎞ ⎜D ⎟ ⋅ ⎝ β 1⋅ Dmean_shield⋅ 10 − 1.6⎠ ⎝ mean_ shield ⎠ ⎡ (β 1⋅ tms ) 4 ⎥⎤ ⎛ Rsheath ⎞ ⎢ Yse := ⎜ ⎟ ⋅ gs ⋅ YSe0⋅ (1 + YSe1) + 12 ⎥ ⎝ Racc ⎠ ⎢⎣ 12⋅ 10 ⎦ g s := 1 +

Ysc := 0

g s = 1.008

Yse = 0.038

Single point bonded so no circulating currents

Racs := Rdc90⋅ ( 1 + Ycs + Ycp + Ysc + Yse)

−5

Racs = 2.734× 10

Calculate Cable Therm al Resistances Ri :=

Rj :=

ρ insulation 2⋅ π ρ jacket 2⋅ π

⎛ Dinsl_shield ⎞ ⎟ ⎝ Dconductor ⎠

⋅ ln⎜

⎞ ⎟ ⎝ Dmet_sh ield ⎠ ⎛

Djacket

⋅ ln⎜

Tmduct = 67.629 Rcable_to_du ct :=

Rduct :=

ρ duct 2⋅ π

Ri = 0.504

Rj = 0.036

Estimate of mean temperature in duct 5.2

1 + 0.1⋅ ( 0.91 + 0.01⋅ Tmduct)⋅ (Djacket)

⎛ ODduct ⎞ ⎟ ⎝ IDduct ⎠

⋅ ln⎜

Rcable_to_du ct = 0.304

Rduct = 0.084

3-69



Calculate External Thermal Resistances Calculate geometric correction factor for backfill envelope: x := Width cbf

x := x⋅ 25.4 x = 838.200

y := Height cb f

y := y⋅ 25.4

y = 838.200

⎡⎢⎛ 1 ⎞ ⎛ x ⎞ ⎛ 4 x ⎞ ⎛⎜ y 2 ⎟⎞ ⎤ + ln( x)⎥ ⎜ ⎟ ⋅ ⎜ ⎟ ⋅ ⎜ − ⎟ ⋅ ln 1+ ⎢⎝ 2 ⎠ ⎝ y ⎠ ⎝ π y ⎠ ⎜ x2 ⎟ ⎥ ⎝ ⎠ ⎦ Db := e ⎣

Db = 921.455

Lb := Burial + dphases

Lb = 1.321 × 10

3

⎛ 2⋅L + 4⋅ L 2 − D 2 ⎞ ⎜ b b b ⎟ ⎟ Db ⎝ ⎠

Gb := ln⎜

Gb = 1.714


α n :=

2

6.71⋅ 10

( ρ native⋅100)

Thermal diffusivity of native soil

3

α n = 1.685 × 10

hour

0.8

Dx := 1.02⋅ α n⋅ 24

mm

Diameter beyond which 24 hour average losses apply, mm

Dx = 205.148

The self and mutual earth thermal resistances each consist of two terms. The first term assumes that the concrete resistivity applies everywhere, the second term corrects for the excess of the native earth resistivity over the concrete resistivity. 3

L := Burial + dphases

L = 1.321 × 10

⎛

⎛

ρ backfill ⎜ ⎛ Dx ⎞ ⎜ 2⋅ L + ⋅ ⎜ ln⎜ + LF⋅ ln⎜ Rearth := ⎟ 2⋅ π ⎝ ⎝ ODdu ct ⎠ ⎝

Middle phase has highest total thermal resistance

mm 2

2⎞⎞

4⋅ L − ODduct ⎟ ⎟

⎟⎟ ⎠⎠

Dx

Rearth = 0.171 Earth thermal resistance for AC losses

⎛

Rearth' :=

⎛

ρ backfill ⎜ ⎛ Dx ⎞ ⎜ 2⋅L + ⋅ ⎜ ln⎜ + ln ⎜ ⎟ 2⋅ π ⎝ ⎝ ODduct ⎠ ⎝

Rco rrection := LF⋅

Rco rrection ' :=



⋅ n⋅ Gb

2

2 ⎞⎞

4⋅ L − ODdu ct ⎟ ⎟ Dx

⎟⎟ ⎠⎠

Rearth' = 0.274 Earth thermal resistance for dielectric losses

Rco rrection = 0.082 Correction for native backfill thermal resistance for AC losses

⋅ n ⋅ Gb

Rco rrection ' = 0.136 Correction for native backfill thermal resistance for dielectric losses

3-70



Mutual Heating

⎛ 2⋅ Burial + d phases ⎞ ⎛ 2⋅ Burial + 3⋅ d phases ⎞ F1 := ⎜ ⎟ ⋅⎜ ⎟ d phases d phases ⎝ ⎠⎝ ⎠

⎡ ⎢ ⎡⎣⎡⎣2⋅ (Burial + F21 := ⎢ ⎣

2 2 d phases )⎤⎦ + d circuits ⎤⎦

d circuits

.5⎤

⎥ ⎥ ⎦

.5 ⎤ ⎡ .5 ⎤ ⎡ ⎢ ⎡⎣( 2⋅ Burial + d ph ases) 2 + d circuits2⎤⎦ ⎥ ⎢ ⎡⎣(2⋅ Burial + 3⋅ d ph ases) 2 + d circuits2⎤⎦ ⎥ F22 := ⎢ ⎥ ⋅⎢ ⎥ .5 .5 2 2⎞ 2 2⎞ ⎢ ⎥⎢ ⎥ ⎛d ⎛ ⎣ ⎝ circuits + d ph ases ⎠ ⎦⎣ ⎝ d circuits + d phases ⎠ ⎦ 4 F = 1.262 × 10

F := F1⋅ F21⋅ F22 Mutual thermal resistance for AC losses:

(

)

ρ native − ρ backf ill ρ backf ill ⋅ LF⋅ ln ( F) + ( N − 1) ⋅ n ⋅ LF⋅ ⋅ Gb 2⋅ π 2⋅ π

Rmutual :=

Mutual thermal resistance for dielectric losses: Rmutual' :=

(

)

ρ native − ρ backf ill ρ backf ill ⋅ ln ( F) + ( N − 1) ⋅ n ⋅ ⋅ Gb 2⋅ π 2⋅ π

Rmutual = 0.860

Rmutual' = 1.434

Calculate temperature ris e from dielectric heating 1 ΔTd := W d⋅ ⎛⎜ ⋅ Ri + Rj + Rcable_to_duct + Rdu ct + Rearth' + Rmutual' + Rcorrection'⎟⎞ ⎝2 ⎠

ΔTd = 2.884

Calculate the Ampacity −5 ΣRacRthermal= 5.533 × 10

ΣRacRthermal:= Racc⋅ Ri ... + Racs⋅ Rj ... + Racs⋅ Rcable_to_duct ... + Racs⋅ Rdu ct ... + Racs⋅ Rearth ... + Racs⋅ Rco rrection ... + Racs⋅ Rmutual

C° / A^2

ΔTcond := Tc − ΔTd − Ta Irated :=

ΔTcond = 67.116

ΔTcond ΣRacRthermal

Ito tal := 2⋅ Irated

Am pacity per phase group, amperes:

Irated = 1101.4

Total am pacity, amperes

Itotal = 2202.8

Check and adjust the estimated shield and duc t air temperatures: 2 Loss at the conductor, w/m Wc := Irated ⋅ Racc T's := Tc − Wc ⋅ Ri

Wc = 32.003

Check tempe rature of shield which was estim ated at T's = 73.856 Tmshield ≡ 73.856

2 Ws := Irated ⋅ Racs

⎛ ⎝

T'm := T's − Ws ⋅ ⎜ Rj +

Ws = 33.169 Rcable_to_ duct⎞ 2

⎟ ⎠

Check m ean tem perature between cable surface and T'm = 67.629 inside of duct w hich was esti mated at: Tmduct ≡ 67.629

3-71


CHAPTER 4

Power Transformers

4.1

INTRODUCTION

Power transformers are a crucial link in the electric power system. Power transformer failures can result in extremely high financial losses, both in lost revenue and the capital expenditure of unit itself. Therefore, it is essential that power transformers be operated in a safe and prudent manner. In addition, given the high equipment cost, power transformers must be operated in a manner to give a reasonable service life in order to realize a positive return on investment. Power transformers represent a significant portion of capital investment costs. Under existing conditions in the industry, utility budgets are reduced and networks are being forced to support greater power transfer over existing transmission circuits than ever before. As such, there is increased interest in safely utilizing all available capacity of power transformers. The thermal design of power transformers is based on an assumed daily average ambient temperature of 30°C, with a maximum of 40°C. It is also based on continuous loading at the rated maximum current. These assumptions are essential to the specification and design of power transformers; however, they are probably never realized in service. In most cases, these assumptions result in very conservative thermal ratings for liquid-filled power transformers. Safe utilization of this “latent capacity” is the subject of this chapter. In general, transformer load capacity is limited by equipment (winding and oil) temperatures. Industry standards (IEEE C57.12.00 in the U.S.) specify a maximum average winding rise that defines the rated load. In other words, when operating at rated nameplate current, the average winding rise shall not exceed the given value. For newer transformers with thermally upgraded insulation, manufactured starting in the late 1960s, this maximum average winding rise is 65°C. Combined with the 30°C ambient and a 15°C gradient between the winding hottest spot temperature and the average winding temperature, the peak temperature in the winding is 110°C. This temperature represents a somewhat arbitrary benchmark temperature that gives a reasonable life expectancy based upon the collective experience of the industry. Earlier transformers built before the introduction of thermally upgraded insulation were based upon a rated average winding rise of 55°C, or a hot spot of 95°C.

4-1


Chapter 4 includes seven sections:

• Section 4.2, Transformer Design, describes the general construction of power transformers, types of cooling, losses generated by transformers, and factory testing.

• Section 4.3. Risks of Increased Loading, outlines short- and long-term risks related to the loading of transformers.

• Section 4.4, Thermal Modeling, provides an overview of heat transfer mechanisms and describes the four most prevalent thermal models.

• Section 4.5, Thermal Ratings, discusses factors behind thermal ratings, including ambient air temperature, load, and maintenance considerations.

• Section 4.6, Winding Temperature Measurement, describes methods of measuring and monitoring winding temperature.

• Section 4.7, Modest Increases in Capacity from Existing Transformers, outlines methods of increasing cooling.

• Section 4.8, Examples, provides two examples of increasing capacity. 4.2

TRANSFORMER DESIGN

4.2.1

General Construction

Power transformers are commonly categorized into two main construction configurations: core form and shell form. These two categories are clearly defined in the case of three-phase power transformers. The definition becomes less distinct in the case of single-phase transformers, especially in the smaller sizes. In this range, the distinction is of minor importance, however. Core-Form Construction A core-form power transformer is constructed with windings that are in the general form of concentric cylinders (Figures 4.2-1 and 4.2-2). The magnetic core consists of stacks of laminated grain-oriented silicone steel sheets. The width of these sheets is varied so that, as stacked, the cross section of each leg conforms as nearly as practical to the circular form of the innermost wind-

Figure 4.2-1 Typical core-form construction (front view).

4-2


ing. With very few exceptions, the winding assemblies and core legs are assembled with their axis in a vertical or upright plane. The magnetic circuit is completed with yoke assemblies that bridge the three legs at the top and bottom. On some of the larger transformers, part of the required cross section of the yokes might be provided by outer legs at each end. These are referred to as “fifth legs” and allow a reduction in the vertical dimensions of both the top and bottom yokes. This reduction is often an important factor in meeting shipping clearances since core form power transformers are shipped with the coils and core legs in an upright or vertical position. The legs and yoke assemblies are joined with mitered interfaces that have alternating steps that overlap to provide good magnetic coupling. Modern practices are to use laminations of 0.009-in. thickness with at least five overlapping steps. This pattern is repeated across the entire build of the core assembly. The legs and yokes are maintained as an independent assembly by banding the legs with a nonconducting material such as fiberglass and in some cases, metallic bands that must be provided with an insulating gap to prevent circulating currents to flow around the band. Ducts for the flow of cooling oil are provided between concentric winding sections and sometimes within winding sections if required by the thermal characteristics of the design (Figures 4.2-3 and 4.2-4). Cooling ducts may also be required in the core legs and/or yokes (Figures 4.2-5 and 4.2-6). These ducts are formed by providing spacers between laminations at discrete intervals determined by the dimensions of the core. These ducts between laminations are usually mirrored in the top and bottom yokes.

Figure 4.2-2 Typical core-type internal assembly.



In a core-form transformer, the winding design permits cooling oil to flow vertically through the concentric windings and the core leg ducts (Figure 4.2-7).

Figure 4.2-3 Core-type winding assembly with concentric cooling ducts.

Figure 4.2-6 Cross section of core form construction.

Figure 4.2-4 Cooling duct being assembled on winding.

Figure 4.2-7 Oil flow in core-type winding.

Figure 4.2-5 Inner winding assembled on core (note oil ducts in core and below windings).

Shell-Form Construction In shell-form power transformers, the windings consist of phase assemblies produced by winding individual sections in a flat plane on a winding machine (Figures 4.2-8 and 4.2-9). These windings are initially assembled flat with insulation and cooling ducts between sections. Complete phase assemblies are then clamped and oriented in a vertical direction so that the plane of the individual sections are upright. The core laminations are inserted through and around the windings in the final 4-3


assembly process. The core and coil assembly is not designed to be lifted as a unit in most cases. In shell-form construction, the oil flows vertically through the ducts between individual winding sections (Figure 4.2-10). The spacers in these ducts are positioned to direct the oil across the width of each winding section.


Directed Flow Designs When forced oil cooling is employed, the transformer internal assembly may be designed with oil manifolds that direct the incoming cool oil to the lower part of the core and windings. In a nondirected flow transformer, the incoming cool oil is pumped into the bulk oil of the lower tank and moves through the core and windings in much the same manner as normal convection currents but with greater velocity (Figures 4.2-11 and 4.2-12). A directed flow design is normally used with larger sizes of transformers equipped with heat exchangers rather than radiators (Figures 4.2-13 and 4.2-14).

Figure 4.2-8 Typical shell-form construction (plan view).

Figure 4.2-10 Shell-form phase assembly under construction (cooling ducts are assembled between sections).

Figure 4.2-9 Shell-form transformer.

4-4

Figure 4.2-11 Core-form transformer designed for directed flow.



4.2.2

Types of Cooling

Oil-immersed power transformers are cooled by four different cooling configurations, each with unique heat transfer. They are as follows:

• ONAN (OA) – Also referred to as self-cooled, no pumps are used to circulate oil, and no fans are used to increase airflow over the radiators. Oil circulates upward through the windings and down through the radiators by natural thermosiphon flow.

• ONAF (FA) – No pumps are used to circulate the oil. Fans are used to force air over the radiators to increase heat transfer from the bulk oil to the surrounding air. As with ONAN, oil circulates upward through the windings and down through the radiators by natural thermosiphon flow.

• OFAF (Non-directed FOA) – Pumps are used to cirFigure 4.2-12 Directed oil flow in core-form construction.

culate the oil. Fans are used to force air over the radiators. The forced circulation of the oil increases the convective heat transfer from the windings to the oil. The forced air increases the convective heat transfer from the oil to the air. With OFAF, there are no ducts to direct the oil over the winding. In general, the bulk of the forced oil flow passes upward between the winding and the tank, bypassing the windings. Natural convection is still the predominant mode of heat transfer from the windings to the adjacent oil.

• ODAF (Directed FOA) – Pumps are used to circulate

Figure 4.2-13 Heat exchangers assembled on transformer.

the oil. Fans are used to force air over the radiators or heat exchangers. The forced circulation of the oil increases the convective heat transfer from the windings to the oil. The forced air increases the convective heat transfer from the oil to the air. With ODAF, ducts are added to direct the oil over the winding. This forces a significant portion of the forced oil to flow upward through the vertical winding ducts. Washers may also be employed in a zig-zag fashion to force the oil to flow back and forth between disk sections of a disk winding, further increasing the convective heat transfer from the winding to the oil. 4.2.3

Figure 4.2-14 Radiators assembled on transformer.

Losses

As with all electrical apparatus, transformers generate losses. These losses are manifested in the form of heat. This heat increases the temperature of the transformer components, and therefore limits the load capacity. Therefore, it is essential to discuss losses when discussing loading. The losses in a transformer are due to several different mechanisms, but are generally lumped into two categories: load losses and no-load losses (Figure 4.2-15). Load losses are losses that vary with load current, but not with excitation. No-load losses are losses that do not vary with load current, but rather vary with excitation or voltage.

4-5



ment of the magnetic domains produces losses. These losses are termed hysteresis losses.

Figure 4.2-15 Transformer equivalent circuit.

Load losses and no-load losses may be further broken down. Load losses consist of three components: winding I2R losses, winding eddy losses, and stray losses. Winding I2R losses are the Ohmic losses due to the load current flowing in the windings. Skin effect is generally ignored, but would be included in the I 2 R losses. Depending upon the conductor dimensions, the increase in winding I2R losses may or may not be negligible. In addition to the intended load current, unintended eddy currents flow within the winding conductor due to the presence of leakage flux, or flux that does not flow within the core. These eddy currents result in additional Ohmic losses in the winding conductors. The eddy losses can be reduced by using a stranded conductor, breaking the path for eddy current flow into smaller regions. If parallel strands or conductors are used, circulating currents between parallel sections can flow due to differing amounts of flux linkage. These losses can be reduced by transposing the cable, as in the cases of CTC (continuously transposed cable) or transposing the winding conductors at various points along the winding. Stray losses comprise the remainder of the load losses. Stray losses are losses due to currents induced in various metallic structures of the transformer, including the winding clamping structure, tie plates, core bolts, etc. Stray losses are parasitic in nature, and difficult to calculate. In some cases, the losses can result in high localized temperatures of various metal components. Often, in larger power transformers and GSUs (generation step ups), this is a serious concern and must be carefully examined during design and construction. No-load losses are composed mainly of losses in the steel core. The steel that comprises the core contains many microscopic regions of like magnetic polarity, called magnetic domains. When magnetic flux passes through the core, these domains shift to orient their magnetic poles in the direction of the flux. Since the flux varies sinusoidally, the domains must change direction as the flux changes direction. This continuous move-

4-6

Like the winding conductors, the flux passing through the steel core, which is electrically conductive, induces a current flow around the core. The magnitude of these induced currents is reduced by dividing the core cross section into thin sheets or laminations. Each sheet is coated with an insulating film. This reduces the total eddy current, and therefore the eddy loss, in the steel core. The core losses in any transformer are dependent on the core flux density. The core flux density is determined by the magnitude and frequency of the primary voltage and the cross-sectional area of the core leg according to Equation 4.2-1.

BM =

225 V × × 10 − 3 fA T

4.2-1

Where: Bm = maximum flux density in Tesla. f = operating frequency. A = cross-sectional area of core in mm2. V = primary voltage (RMS) per phase. T = number of primary winding turns per phase. The flux density, and therefore the principal core losses, are thus independent of load. There may be some localized heating of the outer core laminations or the core support structure by stray flux due to winding current that will be exacerbated by overloads. These losses are usually of little consequence to either short-term or long-term reliability of the transformer because they are removed from the winding insulation and affect the oil only in the local area involved. If a transformer has displayed a tendency, in normal service, to produce methane or ethane close to or in excess of condition #1 as described in ANSI C57.104, dissolved gas analyses should be performed at daily intervals when overloading to a level that has not been previously experienced. Continued operation at that level may normally be considered safe from this point of view if gas accumulation rates do not exceed condition #2 as detailed in ANSI C57.104. 4.2.4

Factory Testing

Little information on a particular power transformer is available to the user. Generally, the only information a user has on a unit is the information given on the factory test report and on the nameplate. Combined, these reports give the user key performance characteristics needed to operate the transformer. Included in this information is the heat run data, giving the temperature rises of the windings and the oil at the benchmark loading of the nameplate rating, and the loss data. In order



to interpret the data given on a factory test report properly, at least a passing understanding of the underlying test is necessary. This understanding will assist the reader in interpreting the numbers and any remarks that may be associated with the test values.

20°C plus the rated average winding rise. For 55°C or 55/65°C transformers, the reference temperature is generally 75°C. For 65°C rise transformers, the reference temperature is generally 85°C. This should be explicitly specified on the test report.

Factory Loss Tests

The I2R losses vary with temperature in a predictable fashion. The difficulty is in determining the appropriate temperature for an operating condition since the temperature variation between parts of a winding can be considerable.

No-Load Loss Testing No-load loss testing is performed with one winding open-circuited and rated voltage applied to the other winding. For practical reasons, voltage is usually applied to the low-voltage winding. This results in full excitation on the transformer, with only the exciting current flowing through the excited winding (Figure 4.2-16). Load Loss Testing The load losses in an operating transformer consist of:

•

I2R

losses in the current carrying components due to load current in all active windings.

• Joule losses caused by circulating currents in winding conductors due to impedance inequalities in parallel conductors.

• Eddy currents in winding conductors due to radial gradients in the induced voltages.

• Stray losses due to induced currents in the tank walls

ANSI standards require reporting of transformer losses at a reference temperature of 85°C for 65°C transformer ratings and 75°C for 55°C transformer ratings. For copper, these I2R losses are corrected to an operating temperature (T) as shown in Equation 4.2-2. PR(T) = PR(Tm ) (234.5 + T)/(234.5 + Tm )

4.2-2

Where: Pr(T) = I2R loss due to load current at operating temperature T (°C). Tm = reference temperature of the test report losses. PR(Tm) = test report I2R losses at Tm.

and internal support structures. Load losses are measured by short-circuiting either the high-voltage or low-voltage winding and then applying a voltage to the other winding that results in rated current flowing through the windings (Figure 4.2-17). The power loss measured, as measured by the wattmeter, is then the load loss at the temperature of the windings during the test. Since losses are dependent upon temperature, the load losses must be corrected to a standard reference temperature.

(The test report will give total load losses at the reference temperature and the measured winding resistances corrected to this temperature. The tested I2R can be calculated using the test report resistance at the reference temperature and rated winding current. Note that the test report resistance values for each winding are equal to the sum of the three phases as required by ANSI standards. Use of rated winding phase current with the test report resistance allows calculation of the threephase I2R loss for each winding.)

Prior to the test, the transformer is allowed to sit deenergized long enough for the oil temperature to stabilize. The temperature of the windings is then assumed to be equal to the average oil temperature. The load losses are corrected to a standard reference temperature of

The stray and eddy losses vary inversely with temperature. For copper, these losses are corrected as shown in Equation 4.2-3.

Figure 4.2-16 Basic circuit for no-load loss testing.

Figure 4.2-17 Basic circuit for load loss testing.

Ps(T) = Ps(Tm) (234.5 + Tm)/(234.5 + T)

4.2-3

4-7


Where: Ps(T) = stray losses at operating temperature T (°C) Tm = reference temperature of the test report losses Ps(Tm) = test report load losses at Tm minus PR(Tm) calculated above. The load losses at operating temperature T are the sum of PR(T) and Ps(T). Factory Temperature Rise Tests The basis for all practical transformer thermal models used in the evaluation of transformer loading is the factory heat run. The factory heat run provides a direct measurement of the thermal performance of a transformer at a particular benchmark, the nameplate rating. Given the temperature rises at this benchmark loading, it is possible to estimate the temperature rises under other loading conditions. Therefore, to understand the thermal models and their application to transformer loading and rating calculations, one must know the basic principles behind the factory heat run. This knowledge will prove invaluable when interpreting the data presented on the certified test report.

This test must be performed on the tap position and winding connection that gives the highest winding temperature as required by ANSI standards. The temperature rises over ambient should be given in the certified test report for each winding—along with the tap position, total losses, and line currents. The calculated winding hot spot temperature rise over ambient should given for the maximum transformer rating. Two methods are used to perform factory heat runs: the “short-circuit” method and the “loading-back” method. Of these two methods, the short-circuit method is by far the most common and will be covered in the greatest depth here. In addition to these two methods, it is also possible that a heat run may be performed by connecting the transformer to a load and loading the transformer at rated voltage and current simultaneously. This method is generally only practical for small power transformers and is not often used. Short-Circuit Method The short-circuit method, also sometimes referred to as loss injection, consists of two segments. In both segments of the test, one winding is short-circuited and a voltage is applied to the other winding. In this manner, each winding temperature can be checked. For transformers with multiple windings, the test load levels are usually agreed upon before hand, and each winding is tested with the other windings short-circuited.

4-8


For the initial segment of the test, one winding is shortcircuited and a voltage is applied to the other winding such that the active power supplied equals the total losses (load losses plus no-load losses) previously measured by other means (refer to IEEE C57.12.90 or IEC 76-1). Note that temperature rise tests are usually performed at the combination of taps that gives the highest losses. The power is applied continuously to bring the oil temperatures up to their steady-state values. Steadystate is defined in the respective test standards, but usually is such that the average oil temperature has not increased more than 1°C (or 2.5%, whichever is greater) for three consecutive hours. The purpose of this segment of the test is to establish the oil temperature rise over ambient. The second segment of the test is to measure the winding temperature rises. Once a steady-state average oil temperature has been reached, the applied voltage is reduced such that rated current flows in the windings under test. This load is held continuously for one hour. At the conclusion of one hour, the winding resistance is measured shortly after the windings have been disconnected, allowing just enough time for the inductance effects to dissipate. The winding resistance is measured several different times after shutdown, recording the resistance and time after shutdown each time (Figure 4.2-18). These points are then used to extrapolate the winding resistance back to the instant of shutdown. With this winding resistance and the cold winding resistance (measured prior to the heat run with the windings at a known ambient temperature), the average winding rise at the instant of shutdown can then be determined. This procedure may have to be repeated for each winding unless the available test equipment and transformer design allow simultaneous resistance readings on all windings. After completion of the above procedures, the oil temperature rises and average winding rises for each winding are known, given the test conditions. Since it is not

Figure 4.2-18 Example winding cooldown curve illustrating extrapolation of resistance measurements to shutdown.



always possible to maintain the exact loadings required to give the total loss or rated current, the raw results obtained above must be corrected to the rated losses and loads. This is done using simple empirical equations as shown in Equations 4.2-4 and 4.2-5. For oil temperatures:

θ o,corr

⎛P = θ o, meas ⎜ t, rated ⎜P ⎝ t, meas

⎞ ⎟ ⎟ ⎠

m

4.3.1 4.2-4

For winding temperatures:

⎛ I w , rated ⎜I ⎝ w , meas

θ w, corr = θ w , meas ⎜

⎞ ⎟ ⎟ ⎠

term degradation of the insulation paper and short-term reduction in dielectric strength due to bubble formation. Understanding these risks and their mechanisms is essential to any discussion on transformer loading. Users must be aware of the risks, take steps to assess these risks, and develop a methodology for maintaining risks at acceptable levels.

2n

4.2-5

Where: θo,corr = oil temperature corrected to rated losses. θo,meas = oil temperature measured during the heat run. Pt,rated = total losses at rated load. Pt,meas = total losses applied during oil rise portion of the heat run. m = oil rise exponent (0.8 for ONAN, ONAF, OFAF; 1.0 for ODAF). θw,corr = average winding rise corrected to rated load. θw,meas = average winding rise measured during test. Iw,rated = rated winding current. Iw,meas = winding current measured during the winding rise portion of the test. n = winding rise exponent (0.8 or ONAN; 0.9 for ONAF; 1.0 for OFAF, ODAF). Loading-Back Method This method is rarely used, and as such will not be described in any great detail here. For more information, consult the relevant test standards, IEEE C57.12.90 and IEC 76-2.

Short-Term Risks

Risks classified as “short-term” are those that would result in the immediate failure of the transformer. Reduction in dielectric strength due to gas evolution from the winding conductor insulation is the principal short-term risk. Additional short-term risks include gas evolution from lead conductors, gas evolution from wood and cellulose materials adjacent to metallic hot spots from stray flux heating, delamination of phenolic resin tap boards, and reduction of short-circuit withstand capability in epoxy-bonded CTC. Some of these risks will not result in failure in and of themselves, but when combined with an abnormal transient voltage or throughfault, may result in failure. Bubble Evolution Through destructive testing of model coils, researchers have discovered that under certain loading conditions, a significant decrease in dielectric strength of the winding assembly occurs. In the transformers considered here, specially refined petroleum oil is used as an electrical insulation material and, concurrently, as a heat transfer fluid. Gas-filled bubbles can be formed in the transformer oil in units in service. The electrical breakdown strengths of these gases are significantly lower than that of the transformer oil surrounding these bubbles. Bubbles that find their way into an electrically stressed oil gap can significantly reduce the breakdown voltage of the gap and interfere with the functioning of a transformer (Figure 4.3-1). Sixty-Hertz Breakdown Voltage in Percent of 25C Strength 100

90

80


Any energized transformer has a finite risk of failure. This risk of failure is generally very low. Loading transformers above the nameplate rating results in higher risks, eventually reaching the extreme where failure would be certain. The challenge is to determine loading levels that represent an acceptable level of risk, given the circumstances.

70 Breakdown Voltage, %

4.3

Paper Insulated Cable - Dry (<0.5%)

Paper Insulated Winding Conductor Dry (<0.5%)

60

50

40 Paper Insulated Winding Conductor Wet (3%)

30

20

10

0 0

50

100

150

200

250

300

Hot Spot Temperature, C

There are several risks related to the loading of transformers. The most significant of these risks are long-

Figure 4.3-1 Example of 60-Hz breakdown vs. temperature illustrating bubble formation.

4-9



Henry’s Law states that the concentration, Ci, of a single ideal gas, i, dissolved in a liquid is proportional to the partial pressure of that gas, Pi, over the liquid:

Ci = Ki * P i

4.3-1

At equilibrium, the drive of the dissolved gas to escape is balanced by the drive of the gas over the liquid to enter the liquid. Ki is a constant dependent on temperature, T, in a typical exponential manner:

Ki ~ exp (Bi /T)

4.3-2

The magnitude of Ki and its dependence on temperature reflect the particular intermolecular interactions of a given gas – liquid combination and are unique to that combination. Bi can be either positive or negative algebraically; it is negative for gases whose solubility increases as the temperature decreases. If, at constant temperature, the partial pressure of the gas over a liquid is decreased, the liquid will be supersaturated and gas will vaporize in order to reach a new equilibrium concentration as defined by Henry’s Law. Likewise, if the temperature changes so that Ki becomes smaller while the pressure of the gas over the liquid is held constant, additional gas will make its escape. In the reverse of these happenings, gas will dissolve. When the reduction in pressure of the gas over the liquid is slow or the local mass transport processes are relatively fast, the dissolved gas will diffuse through the liquid to and across the gas-liquid interface. The gas will “steam” away. The escape of the gas tracks the slow decrease in the external partial pressure. If, however, the pressure of the gas over the liquid drops so rapidly that dissolved gas does not have time to move to the surface, local supersaturation can occur and bubbles can nucleate. The bubble presses aside the surrounding liquid, and continues to grow as it absorbs supersaturating gas from the liquid. A bubble will grow so long as the pressure within the bubble exceeds the external pressure. The primary constraint to bubble growth is the pressure of the atmosphere over liquid. The effect of surface tension of the liquid at the bubble surface and the hydrostatic pressure of the liquid over the site of bubble growth are minor. An example – warm beer bubbles and foams when the bottle cap is removed and the pressure of carbon dioxide (CO 2 ) in the neck of the bottle is suddenly released. Colder beer bubbles and foams less, in part because the pressure to be released in the neck of the bottle is less, but also because CO 2 is more soluble in cold water (BCO2 is algebraically negative).

4-10

Oil in transformers normally contains more than one gas. Some transformers are designed to allow access of air to the interior. The gases dissolved in the oil are those present in air: nitrogen, oxygen, carbon dioxide, and traces of other gases. Other transformers are sealed and evacuated and then filled with nitrogen. The primary gas dissolved in the oil is nitrogen. Only small amounts of oxygen and traces of carbon dioxide remain. In general, gases dissolved in transformer oil behave as ideal dilute solutions in that the solubility of one gas is independent of the presence of any other gas; e.g., KN2 is the same whether CO2 is present or not, and CN2 is not affected by P CO2 . However, in forming bubbles, gases behave collectively. Each gas dissolved in the oil contributes to the internal pressure of the bubble according to Henry’s Law, shown in Equation 4.3-3. Pbubble = ∑ Pi = ∑ (C i / K i ) > Patm

4.3-3

A bubble forms when the sum of the partial pressures resulting from local concentrations of gases in the liquid exceeds the pressure over the surface of the liquid phase – Patm. The major solid electrical insulation in typical transformers is cellulose in the form of paper and press board impregnated with transformer oil. Water is absorbed by the cellulose. It distributes itself between the bulk oil and paper so that the concentrations of water in the solid and liquid media are in equilibrium with the water vapor pressure over the insulation system. Unlike nitrogen and oxygen, water vapor is a condensable gas. A very high percentage of the total mass of water in the system is contained in the paper. In most transformers the amounts of free oil and impregnated cellulose are comparable. In a subsystem containing equal volumes of paper (with 0.5% moisture content by weight) and transformer oil and equilibrated at 80°C, the paper will contain approximately 99.9% of the total weight of water. In effect, the paper in a transformer acts as an almost infinite reservoir supplying additional water to the oil at the higher internal temperatures occurring during operation. Water will re-absorbed on the paper when the electrical load on the transformer is reduced and will again be available for desorption when the transformer is next loaded. Desorption of water from the cellulose in the oil/paper insulations system is an example of a physical reaction that can increase the local concentration of gases in the oil to produce bubbling. Local concentrations can also change as a result of chemical reactions within the system.



Thermal decomposition of cellulosic insulation can occur in an operating transformer. The decomposition reaction can increase the local concentration of gases in the oil. The primary products of thermal decomposition of cellulose are water vapor, CO2, and CO. Decomposition of the oil/paper insulation at a sufficiently high temperature generates gases more rapidly than they can diffuse away into the surrounding oil. Again, the local concentration of gases builds to the point where the summation of partial pressures exceeds the pressure in the transformer and a bubble forms. To summarize, formation of bubbles in transformer oil reflects a complex interplay of variables in an operating transformer. Bubbles result from an abrupt departure from equilibrium between dissolved gas and oil – resulting from some change in pressure and/or local temperature in a transformer. Bubbles form when a local increase in gas concentration results in a local pressure that exceeds the pressure over the oil. Evaluation of bubble formation is difficult. The mechanisms are complex and dependent upon local conditions. The most influential factor is the moisture content of the paper. The temperature at which bubbles form is highly dependent upon moisture content, as illustrated in Figure 4.3-2. Note that this plot is for an example loading condition, and therefore, the values depicted are not to be taken as absolute truths. Given the importance of moisture in the determination of bubble evolution risk, accurate determination of moisture content would be necessary to use any sort of analytical model. Currently, there are no means of determining the moisture content distribution throughout an operating transformer with the required precision. Moisture content in oil is often related to moisture content in the paper using equilibrium curves. This,

however, has two problems. First, the moisture distributes throughout the winding inversely proportional to temperature. The moisture in oil could only give an average content of the entire bulk insulation. Second, the paper-oil system is rarely at equilibrium. The time constant of moisture diffusion is on the order of several days or weeks. Without any practical means to precisely assess the risk of bubble evolution, we must fall back on general guidelines that have been proven by experience. The general consensus in the industry is that bubble evolution does not occur at hot spot temperatures up to 140°C. This is probably valid for moisture contents up to 1.5–2%. Newer, dryer transformers could probably be safely loaded to temperatures approaching 160°C. Transformers in service for less than 6 months should be limited to temperatures of 120°C. Oil Expansion As with any fluid, oil expands as temperature increases. Specifically, the coefficient of expansion for oil is 0.000756, or the oil expands 0.08% for every degree C rise in temperature. This expansion is anticipated, and transformers are equipped with devices to handle oil expansion to some degree. IEEE C57.12.10, the IEEE standard for power transformers below 230 kV, requires that a transformer be capable of operating with temperature to 105°C. If the oil temperature exceeds 105°C, the oil may expand beyond the capacity of the gas space or conservator tank, resulting in operation of the mechanical pressure relief device and the expelling of oil. Not only does this present a maintenance and environmental headache, this can cause problems if enough oil is expelled such that upon cooling the oil level drops to a level exposing the active parts. This could result in a dielectric failure. 4.3.2

Long-Term Risks

200

Aging of Cellulose and Oil in Transformers For liquid-immersed transformers, the insulation system consists of the paper and pressboard solid insulation (cellulose) and the oil liquid insulation. Both the cellulose and liquid insulation are adversely affected by heat. However, while the liquid insulation can be replaced or reprocessed relatively easily, the properties of the solid insulation cannot be easily or effectively restored, nor can the insulation be economically replaced. Therefore, the loss of the paper insulation life is of utmost importance when considering transformer load capability.

190

Gas Evolution Temperature (deg C)

180

170

160

150

140

130

120

110

100 0

0.5

1

1.5

2

2.5

3

Moisture Content (% dry weight)

Figure 4.3-2 Gas evolution temperature vs. moisture content for example conditions.

3.5

Oil Aging Oils in transformers are mainly mineral oils. The oils can be grouped in two types: inhibited oils, which are heavily refined, reducing the amounts of aromatics and

4-11


polyaromatics, and then inhibited with an antioxidant to reduce oxidation, and the uninhibited oils, where natural aromatics and polyaromatics are natural inhibitors. When oils are subjected to oxygen and heat, they start to oxidize: the aldehydes, ketones, and finally carboxylic acids, presumably with a high molecular weight, are formed. The neutralization value and loss factor of the oil gradually increase, and the interfacial tension is reduced. At an even later stage, sludge may form. The oxidation rate increases with increasing temperature. For an inhibited oil, first the inhibitor is consumed (the period this takes is called the induction period). When it is fully consumed, the oils quickly start to oxidize. Before the inhibitor is gone, one may re-inhibit the oil, but the induction period is now be shorter, unless the oil is reclaimed. The main risk from the oil aging is sludge formation and clogging of cooling channels. The oil aging is not governed by the oxygen concentration but by catalytic processes, where hydroxyl radicals are formed via interaction with active metals like copper and iron. The oil condition may be followed by several diagnostic markers: Neutralization value, interfacial tension, loss angle, inhibitor content, and sludge measurement. It is important to take maintenance precautions before the condition becomes too severe.

Cellulose Aging Paper and pressboard are made from cellulose fibers (Figure 4.3-3). They contain 93% cellulose, with molecules that are long, straight polysaccharide chains, which may form crystalline regions. The average number


of cellulose molecules, called the degree of polymerization (DP), describes the length of the cellulose molecule. The cellulose also contains 5-6% hemicelluloses, which are polysaccharide chains with branches that do not easily crystallize, and lignin, which is a large branched molecule. The last two act as a thermoplastic. When cellulose ages, the cellulose chains are cut in a process called chain scission, reducing the average length of the cellulose chains and resulting in shorter fibers. The number of chain scissions (η) is defined as η= DPnew/DPold –1, where the DP value is taken before and after the aging period. Paper may be chemically modified to allow for operation at higher temperatures (thermally-upgraded paper). Upgraded paper is paper that is chemically changed by different chemical additives that reduces the aging rate compared to untreated kraft paper. A paper is considered “thermally upgraded” if it meets the life criteria as defined in ANSI/IEEE C57.100—50% retention in tensile strength after 65,000 h in a sealed tube at 110°C. However, upgrading can be done in various ways, so it is not a uniform group and may react differently to chemical aging accelerators. To retard aging, one can thermally upgrade the paper by linking bulky substituents such as cyanoethyl ether groups to the HO-groups in the cellulose and hemicellulose; or add weak, organic bases such as dicyandiamide, urea, or melamine (a cyclic trimer of urea) so as to neutralize acids produced by oxidation of the oil and paper. Beginning in the late 1960s, transformers in the U.S. were manufactured using thermally-upgraded paper, whether specified or not. Cellulose degrades at any temperature. The rate of degradation is very slow at room temperature. At elevated temperatures, however, the rate of degradation increases exponentially, effectively doubling for approximately every 8°C increase in temperature. Management of insulation degradation is necessary to maintain a reasonable life expectancy for the transformer. The shortening of the cellulose chains results in a reduction of the mechanical properties of paper and board, such as tensile, bursting, and folding strength. It is well known that the aging rate increases with increasing temperature; Montsinger states that the aging rate doubles (or life is halved) by every 6-8 oC temperature increase (Montsinger 1930).

Figure 4.3-3 Graphic depiction of cellulose chain (light gray is carbon, dark gray is oxygen, white is hydrogen).

4-12

The insulation aging rate has been studied extensively, and several mathematical models have been proposed. The most accepted of these models for insulation aging is that given in IEEE C57.91-1995 (IEEE 1995b), which



expresses insulation aging as an Arrhenius reaction rate equation. The equation is as shown in Equation 4.3-4. FAA = e

⎛ ⎞ A A ⎜ ⎟ − ⎜θ ⎟ ⎝ HS , R + 273 θ HS + 273 ⎠

(IEEE 1995b, Section 5.2, Equation 2) 4.3-4 Where: FAA is the insulation aging rate. A is a constant equal to 15,000 for most insulation types. θHS,R is the reference hot spot temperature for the insulation. θHS is the hot spot temperature at which aging is evaluated. The IEEE insulation model requires two parameters, the constant A and the reference hot spot temperature. For all cases, it is safe to assume that A is 15,000. The reference hot spot temperature varies depending upon whether the insulation is thermally upgraded and what standard is applied. For 55°C insulation, the reference hot spot temperature is 95°C. For 65°C insulation, the reference hot spot temperature is 110°C. Equation 4.3-4 can also be expressed in a form for per unit life: B

PerUnit Life = At e T

Hot

− 273

transformer condition on aging is hard to find. It is all about getting information about the At factor.

Chemical Description of Aging For the purposes of insight, aging considerations can be based not on changes of a functional property like tensile strength, but on changes of the chemical properties of the paper—the degree of polymerization. A disadvantage of doing this is that the link is lost to the directly relevant mechanical properties, though only applicable on laboratory aged samples. The main advantages are that the approach uses a property that can be measured from samples from service-aged transformers and that it is closer to considerations on the chemical kinetic processes taking place. If the aging analyses are based on DP changes, a correlation between the functional critical tensile strength and the DP, as shown in Figure 4.3-4, is needed. One usually considers aging under normal conditions (nameplate conditions and specified overload) to be due either to hydrolysis or to oxidation, and that a third process (pyrolysis) may take place under failure conditions (thermal defects). The aging due to one kinetic mechanism follows Equation 4.3-6 −E

1 1 − = Ae R⋅(T + 273) ⋅ t DPold DPnew

4.3-6

4.3-5

Where: B describes how sensitive the ageing is to temperature (15,000 in C57.91). THot is the hotspot temperature of the transformer. At is a factor describing the influence of the environment on the change in tensile strength (9.8 x 10-18 in C57.91).

where the DP is given before and after an aging period ( t ) at a temperature T. E is the so-called activation energy, which describes the sensitivity to the temperature, A depends on the chemical environment, and R is the molar gas constant. Note that this is of the same form as the Arrhenius reaction rate equation first proposed by Dakin in 1948 (Dakin 1948). Usually the paper has a DP around 1000 in a transformer after

The base of all this is a definition of a material test where the criterion is that paper aged under a certain condition (e.g., T Hot = 110 o C) should not lose more than a certain percentage of its functional property (tensile strength) within the period. This is referred to as the expected life of a transformer (e.g., 30 years) at nominal load under specified ambient conditions where the hotspot condition has to be mastered. The dependence of aging on temperature is fairly well known; However, the big problem for a utility when managing an aging transformer population is that Equations 4.3-4 and 4.3-5 are based on experiments under optimum clean conditions for the paper, and that quantitative information on the importance of the

Figure 4.3-4 Correlation between tensile index and DP value for nonthermally upgraded kraft paper.

4-13



vapor phase drying, and often a DP of 200 is used as an end-of-life criterion. We can rearrange and change the equation to: −E

⎤ 1 ⎡ DPnew − 1⎥ = Ae R ⋅(T + 273) ⋅ t ⎢ DPnew ⎣ DPOld ⎦

4.3-7

and further to

1 ⋅η = k ⋅ t DPnew

4.3-8

where η is the chain scissions and k the aging rate. We can see that the aging rate depends on temperature (T), the activation energy (E), and the environment (A). For a first-order single process, this dependence can be described by an Arrhenius plot, plotting the natural logarithm of the rate versus the inverse absolute temperature (T + 273) as shown in Figure 4.3-5. The principle here is that, if the points end along a straight line, this aging can be described by one single aging process. Thus far, focus has been on the temperature dependence. Recent investigations indicate that the environment may be of even greater importance. Let us first consider non-upgraded kraft paper.

The other major mechanism of paper aging is hydrolysis. The significance of water content is paramount: a humidity of 3-4% may increase the degradation rate of paper by a factor of 10 or more, compared to dry paper. In addition, it is commonly acknowledged that a high acidity in the oil accelerates aging but in a nonspecific way. Lately, models have been developed outside the power engineering community (Lundgaard et al. 2004). It is now understood that the hydrolysis is specific-acid catalyzed and unimolecular. This means that it is catalyzed exclusively by hydrogen ions from dissociated acids; undissociated carboxylic acids do not depolymerize cellulose. It is the hydrogen ion activity (or “pH”) that matters, not the total (undissociated) acid concentration. It also means that water does not participate in the rate-controlling step. Water does, however, affect the acidity by causing carboxylic acids to dissociate, and in this way it exerts a profound influence upon the aging process. During this process, carboxylic acids (like formic, acetic, and laevulinic acids) are produced, which makes the process auto-acceleratory. These acids mainly reside in the cellulose and may to a large degree be extracted from oil and paper using water extraction. This applies to kraft paper. The processes for thermallyupgraded papers are more complicated. It is likely that the activation energy of oxidation is different and lower than for hydrolysis, and that for pyrolysis, it is even higher than for hydrolysis. This can be illustrated by the plot in Figure 4.3-6, where lines with different slopes are plotted for the different mechanisms.

ln (reaction rate)

Kraft Paper One major mechanism of paper aging is oxidation. The oxidizing agent in this environment is oxygen from air ingress. The ultimate end products of oxidation are the same as for combustion—i.e., water and carbon dioxide. The mechanism of low-temperature oxidation is quite different from that of combustion, though. The oxygen

concentration is, of course, an important parameter to determine the rate of oxidation. However, most experimental studies show that the aging rate is not so strongly influenced by oxygen content. Typically, the overall degradation rate no more than doubles in experiments with oxygen present, compared to when oxygen is totally excluded. We can, therefore, say that the importance of oxygen is limited.

H2O

Figure 4.3-5 Arrhenius plot and significance of parameters for kraft paper at 0.5% (dry) and 3% (wet) moisture.

4-14

O2

1/T

Figure 4.3-6 Total aging as a sum of several mechanisms.


Thermally Upgraded Paper Upgraded paper is paper that is chemically changed by different chemical additives that reduce the aging rate compared to untreated kraft paper. A paper is considered “thermally upgraded” if it meets the life criteria as defined in ANSI/IEEE C57.100—50% retention in tensile strength after 65,000 h in a sealed tube at 110°C. However, upgrading can be done in various ways, so it is not a uniform group and may react differently to chemical aging accelerators. To retard aging, the paper can be thermally upgraded by linking bulky substituents such as cyanoethyl ether groups to the HO-groups in the cellulose and hemicellulose, or weak, organic bases such as dicyandiamide, urea or melamine (a cyclic trimer of urea) can be added so as to neutralize acids produced by oxidation of the oil and paper. In one study it was found that the aging rate for one upgraded paper type (Insuldur from Avery Dennison) showed both lower reaction rates at a specific temperature, and that the acceleration due to presence of water was lower, as shown in Figure 4.3-7 (IEEE 1995c). In another study on an upgraded paper (Rotherm) from Tullis Russel, a similarly reduced sensitivity to water was observed (Schroff 1985). The different sensitivity to water indicates that the acid catalyzed hydrolysis is suppressed. In (Lundgaard et al. 2004), the experimental results indicated that aging for oxygen-rich oil could increase by a factor of about seven in the temperature range below 90oC, while water (3%) increased it around 3 times as shown in Figure 4.3-7. Plastic Deformation and Winding Slackness The transformer winding is clamped with a pressure strong enough to give friction forces between windings that may withstand the forces from a short-circuit current. The cellulose can undergo plastic deformation;

Figure 4.3-7 Arrhenius plots of aging rate for standard Kraft paper and thermally-upgraded insuldur paper (IEEE 1995c).


water will in this context act as a plasticizer. Changes in pressure may result from the following reactions:

• Increased moisture will cause swelling and increase the pressure.

• Drying may cause shrinking of the insulation and reduced pressure.

• Thermal cycling will cause expansion and retraction of the materials, cyclic pressure variation, and loss of pressure. Diagnostics of the Cellulose Accurately diagnosing the condition of the cellulose, and therefore the remaining useful life of the transformer, is a most difficult, if not impossible, task. The only way of accurately determining the condition of the cellulose insulation system is to take samples from various places throughout the transformer and measure the DP. This is impractical for several reasons. First and foremost, this involves disturbing the solid insulation in areas of high electrical stress. Additionally, many areas are simply inaccessible. A limited sampling can be done by taking paper from relatively accessible areas. This, however, involves draining all of the oil, physically breaching and entering the tank, collecting the sample while avoiding contamination, and refilling the unit under vacuum. Breaching the tank introduces the possibility of contamination by particulates or moisture and carries a finite risk. Without entering the tank, the only remaining alternative for measurement is to draw an oil sample and measure the level of a chemical marker indicative of cellulose aging. Fortunately, several furanic compounds, measurable by High-Performance Liquid Chromatography, are produced during the aging process. By measuring the levels of these compounds in the oil, the average condition of the entire insulation system can be estimated. This method, however, carries with it several drawbacks. First, the measurement represents only the average of all of the cellulose in the unit. In reality, only a small percentage of the cellulose is subject to high temperatures during overload. It is this cellulose, and in particular the cellulose that is exposed to high temperatures and high electrical stress, that is important. In addition, furan analysis is incapable of discerning localized defects that result in high heating in a small area. Furan production is also a function of the paper-to-oil ratio of a transformer, which varies widely depending upon winding construction, BIL, and rating. Finally, if the oil is replaced or reclaimed, the aging information derived from furan analysis up to that point is lost. A final method of estimating the condition of the cellulose is to simply examine the typical loading and ambient

4-15



air temperatures over the transformer’s service life and approximate the cumulative insulation aging by the standard thermal models and insulation aging models. While not precise, this method is remarkably simple and gives a general feel for the serviceability of a particular unit. Concluding Remarks on Thermal Aging of the Insulation Historically, too little attention has been given to the changes in thermal performance of a transformer due to changes in the condition of the insulation system. Depending on the materials used, the acceleration of aging due to chemical contamination may exceed that from increased temperature. Together with a poor condition of the transformer, a long-term temperature increase may result in a very short life. The life may be estimated using the formulae below. The life expectancy of the solid insulation is difficult to define precisely. The “end-of-life” of any device or system is when the system can no longer perform its intended function. In the case of electrical insulation, this is when the insulation no longer provides sufficient dielectric strength to prevent dielectric breakdown. In the case of cellulose insulation, such as that used in power transformer, the electrical properties of the paper do not significantly degrade until well after the mechanical properties become unworkable. The paper will became extremely brittle and crack or tear at the slightest mechanical disturbance. If this were to occur in an operating transformer, the loss of solid insulation by displacement could detrimentally weaken the insulation structure. Therefore, the mechanical strength of the paper is the defining evaluation criterion with respect to aging.

Several different mechanical strength properties have been used by various investigators to quantity the degradation of cellulose. The burst strength, fold strength, elongation to break, abrasion resistance, and tensile strength have all been used as indicators of mechanical strength. In addition, degree of polymerization (a measure of average polymer chain length of the cellulose molecule) has been used. Degree of polymerization, DP, varies nearly proportionally to reduction and mechanical strength. Of these measures, tensile strength and DP are used most commonly to define end-of-life criteria. Table 4.3-1 lists several different end points for insulation thermal life based upon 50% tensile strength retention, 20% tensile strength retention, and a degree of polymerization value of 200 (McNutt 1992). Also illustrated in this table are the detrimental effects of moisture and oxygen. Since there are many different valid end-of-life criteria, it is ultimately up to the user to select a criterion. The recommendation of this guide is that the DP of 200 end point be used when evaluating life consumption. As an alternative, the user could forgo the definition of an insulation life end point and instead consider aging in relative terms—i.e. per unit aging rate (FAA) or equivalent aging hours. However, the question still remains of when to remove a unit from service. The failure risk of transformers has often been represented by the “bathtub” curve, so named for its shape (Figure 4.3-8). This curve represents the failure risk over time for a particular transformer, with all else constant. External factors, such as loading, throughfault fre-

Table 4.3-1 Insulation Thermal Life Expectancies for Various Endpoint Criteria, Moisture Contents, and Oxygen Levels (McNutt 1992) Basis

50% Tensile

20% Tensile

200 D.P.

4-16

Moisture in Paper (%)

Oxygen Level

Life (hrs)

0.5%

Low

65,020

1.0%

Low

32,510

2.0%

Low

16,255

0.5%

High

26,000

1.0%

High

13,000

2.0%

High

6,500

0.5%

Low

152,000

1.0%

Low

76,000

2.0%

Low

38,000

0.5%

High

60,800

1.0%

High

30,400

2.0%

High

15,200

0.5%

Low

158,000

1.0%

Low

79,000

2.0%

Low

39,500

0.5%

High

63,200

1.0%

High

31,600

2.0%

High

15,800


quency, and maintenance (or lack thereof) all shift portions of the curve in some fashion. If the failure rate with time is represented by a bathtub curve, the time axis can be viewed as a “cumulative thermal aging” rather than actual age of the unit. As the insulation system ages thermally, the system approaches the “wear out” portion of the curve, where failure risk increases, although failure is not necessarily imminent. The transition point from a relatively flat failure risk to an increasing failure risk is the thermal end-of-life, in rough terms. Of course, this is only approximate and varies with several factors, including condition, design, vintage, etc. One major point of confusion and misunderstanding when performing loading calculations and making loading decisions is the discussion of percent loss-of-life (in percent total life expectancy) and of the end-of-life or life remaining. In rough terms, the “end of life” for an insulation system is the point at which the insulation no longer performs reasonably. For electrical insulation, this means the point at which the insulation system no longer maintains a majority of its original dielectric strength. As insulation ages, the dielectric strength of the paper does not decrease significantly until well after the paper has become brittle. Given the need for transformer insulation to withstand mechanical forces, especially during throughfault, the point at which the paper loses enough strength to withstand the mechanical forces is the practical end of life for the insulation system. Given this, a precise definition becomes difficult because this is dependent upon the application of the material, both electrically and mechanically. Therefore, general measures of mechanical strength have been historically


used. Some criteria include 50% tensile strength retention, 20% tensile strength retention, and more recently, a degree of polymerization of 200. In addition, functional life testing has been performed on distribution transformers subjected to impulse voltages and shortcircuits. Each of these criteria gives a different life end point, ranging from 65,000 hrs to 180,000 hrs. These values are largely artificial. A transformer that is not subject to high throughfault duty may operate reliably well after the 180,000-hr end point. Therefore, if %loss of life (LOL) is discussed, the value for a given temperature can vary by a factor of three. It is well known that insulation aging rates increase with the presence of increased moisture and oxygen. The original equations in the IEEE Loading Guide (IEEE 1995b) are based mostly upon sealed tube aging tests with moisture contents less than 0.5% and presumably lower oxygen contents. This does not reflect the reality of operating transformers and misleads the user on the actual aging rate. The importance of keeping transformers dry and oxygen free are not reflected in the guide, and are best addressed by including quantitative estimates of the effects of moisture and oxygen in the aging equation. It is proposed that this be done by applying multiplying factors to the “Age Acceleration Factor” calculated as shown in Equation 4.3-9. F AA = kH O kO e Θ 2

2

B o+

B 273 Θ HS + 273

4.3-9

Where: FAA is the insulation aging rate. A is a constant equal to 15,000 for most insulation types. θHS,R is the reference hot spot temperature for the insulation. θHS is the hot spot temperature at which aging is evaluated. kH2O and kO2 are determined from Tables 4.3-2 and 4.3-3, respectively Table 4.3-2 Aging Rate Correction Factor for Moisture in Paper Moisture Content in Paper (roughly)

kH2O

Dry (< 0.5%)

1

Moist (0.5-2.5%)

2

Wet (> 2.5%)

4+

Table 4.3-3 Aging Rate Correction Factor for Oxygen Content of Oil Oxygen Content

Figure 4.3-8 Example bathtub curve demonstrating thermal end-of-life.

kO2

Low

1

High

3-5

4-17



The factors developed in the tables were derived from data published by Emsley, Lundgaard and McNutt (Emsley and Stevens 1994; Lundgaard et al. 2004; and McNutt 1992). They are approximations. However, insulation aging calculations, as a whole, are gross approximations. By applying these factors directly in the equation, users are well aware of the importance of moisture and oxygen, and are given a method for evaluating the impact of moisture and oxygen, as well as estimated life consumption for transformers with moisture contents in paper greater than 0.5% and with increased oxygen levels. % LOL =

FAA ⋅ t Expected Life

4.3-10

Where: t is the number of hours at the hot spot temperature. Expected life is a value selected from Table 4.3-1. 4.3.3

Additional Risks

Ancillary Components Following insulation loss of life and bubble formation, the most significant risk associated with transformer overload is damage to the ancillary components, such as bushings, on-load tap changers (LTCs), off-load tap changers (DETCs), and current transformers (CTs). This risk is often overlooked as a rating consideration. Generally, these components are oversized due to their relative cost when compared to the transformer itself. However, it is possible that some limitation on the overload capability of a particular transformer may be due to an ancillary component.

Bushings Oil-impregnated, paper-insulated, capacitance-graded bushings are designed with 105°C bushing hot spot limit at rated load and 95°C top oil temperature average over 24 hrs. Overload, based upon the rated bushing current, is possible. Overload risks of bushings include:

• • • •

Pressure build-up due to oil expansion. Deterioration of gaskets and seals. Thermal deterioration of paper insulation. Increase in dielectric loss, possibly resulting in thermal runaway.

• Gas evolution at extreme hot spots. Overload limits, as specified in C57.19.100-1995:

4-18

• • • •

40°C ambient temperature 110°C transformer top oil temperature 2x rated bushing current 150°C bushing hot spot temperature

The bushing hot spot is usually located adjacent to the central conductor in the area of the mounting flange. It is here that the insulation is the thickest and the external heating, via the bulk oil, is highest. The hot spot temperature of the bushing conductor may be calculated as shown in Equation 4.3-11 (IEEE 1995c). Δθ HS = K1I n + K 2 ΔθO

4.3-11

Where: ΔθHS is the bushing hot spot temperature. K1 is a bushing-specific constant, typically ranging from 15 to 32. K2 is a bushing-specific constant, typically ranging from 0.6 to 0.8. n is a bushing-specific constants, typically ranging from 1.6 to 2.0 with 1.8 typical. I is the bushing current in per unit of the rated bushing current. Δθ O is the bushing immersion oil temperature (transformer top oil). The transient temperature rise may then be calculated as shown in Equation 4.3-12. Δθ HS ,2 = Δθ HS ,1 + ( Δθ HS ,U

Δt ⎛ − τB ⎜ − Δθ HS ,1 ) 1 − e ⎜ ⎝

⎞ ⎟ ⎟ ⎠

4.3-12

Where: ΔθHS,2 is the bushing hot spot rise at time t1 + Δt. ΔθHS,1 is the bushing hot spot rise at time t1. ΔθHS,U is the steady-state temperature given in the previous equation. τB is the bushing time constant. The determination of the constants is the greatest obstacle to the use of these equations. Accurate determination can only be made through tests on duplicate bushings. These tests are not performed routinely by the bushing manufacturer. This infor mation may be requested from the manufacturer. If the data is not available, however, typical default values can be used without a significant sacrifice in accuracy. The paper used in paper-insulated bushings is not thermally-upgraded, unless otherwise specified. As such, the standard loss-of-life model given in C57.91-1995 for 65°C rise insulation systems should not be used to cal-



culate the loss-of-life for bushing insulation. Instead, Equation 4.3-13 should be used: 15,000

FAA = e

368

−

Δθ C = Δθ C , R I n

15,000

θ HS + 273

4.3-13

Where: FAA is the aging acceleration factor. Percent loss-of-life and cumulative aging can be calculated as outlined in C57.91-1995. The above method may be applied to resin-bonded or resin-impregnated bushings. The above method does not apply to draw-lead connected bushings. Draw-lead connected bushings are limited by the temperature rise of the draw-lead. Therefore, the bushing temperature is determined by the size and construction of the drawlead. Accurate determination of draw-lead current carrying capability would require detailed information on the lead and its application. However, in a properly designed application, the draw-lead does not limit the thermal rating of the transformer. On-Load Tap Changers (LTCs) The critical component of an on-load tap changer, from a thermal standpoint, is the contacts. LTCs are properly designed with a contact rise over oil of less than 20°C at 1.2 times rated load (rated load here is the rated load of the LTC, not the transformer itself). In addition, LTCs are designed to break twice rated current at least 40 times without detrimental degradation of the contacts. In some instances of high overloads, it may also be advisable to switch an LTC to manual control and minimize or eliminate operation. Overload risks of LTCs include:

• Increased contact wear and ablation with increased load during break operations

• Increased contact temperature increases probability and rate of coking of contacts (>120°C)

• Higher overloads result in prolonged arcing during break operation. Dragging the arc across the contacts could result in short-circuiting the regulating winding. Overload limits, as specified in C57.131-1995 (IEEE 1995a):

• 120°C contact temperature (higher is OK, but may result in greater maintenance).

• 2x LTC rated load current (limit breaking operations at high load level to few times/year).

The temperature rise of the contacts is calculated as shown in Equation 4.3-14 (IEEE 1995c) 4.3-14

Where: ΔθC is the LTC contact temperature rise over oil. ΔθC,R is the LTC contact temperature rise over oil at rated load. I is the LTC current in per unit of the rated LTC current. n is an exponent that varies from 1.6 to 1.85, with 1.8 as the default.

θ C = θ A + Kθ TO + Δθ C

4.3-15

Where: θC is the total contact temperature. θA is the ambient air temperature. θTO is the transformer top oil temperature. K is a constant to account for the difference between transformer top oil temperature and LTC compartment oil temperature. This is typically around 0.8. It is important to note that the main difficulty associated with elevated temperatures in LTCs is the increased tendency toward contact coking. Since coking increases the electrical resistance across the contact assembly, coking can result in even higher temperatures and possible thermal runaway. If frequent high loading periods are expected, the temperature differential between the main tank oil and the LTC compartment oil should be checked, if possible. In addition, the LTC oil should be clean oil with high interfacial tension (IFT) and low acidity. Reduced Capacity Taps The load dependent losses, and therefore the heating of the transformer windings, is a function of the winding current. Often the transformer load is expressed in terms of apparent power, or MVA, since this number is essentially the same for all windings (neglecting losses). However, in the case of rated MVA when taps are present, the rated current varies inversely proportional to the voltage. The consequence for loading is that, for lower voltage taps, the rating in MVA for a given size conductor decreases.

Often, to maintain the same MVA load capability for all taps, the conductors are sized according to the current at the lowest voltage time. However, occasionally, to reduce cost, the transformer may be specified with reduced capacity taps. In this case, the conductors are sized for the rated current at the neutral position. For higher-voltage taps, the transformer is capable of carrying full rated MVA. However, for lower voltage taps, the

4-19



transformer is capable of carrying only a reduced MVA, corresponding to the rated current at the neutral tap. Transformers with reduced capacity taps can easily be identified by referring to the table of tap positions, voltages, and rated currents on the nameplate. Transformers with reduced capacity taps have the same rated current for all taps at voltages below neutral. An example of this is shown in Table 4.3-4.

It is important to examine the nameplate when determining the load capability of a particular transformer to determine if the unit was designed with reduced capacity taps. If it was designed with reduced capacity taps, and the unit is operated at taps below neutral, the load capability in MVA will be lower than the nameplate MVA.

Table 4.3-4 Nameplate Showing Tap Positions, Voltages, and Currents CONNECTIONS CRT LOAD TAP CHANGER WINDING

“H” VOLTAGE WYE


VOLTAGE

MAXIMUM FOA AMPERES

PCS

P1 TO

P3 TO

R TO

120175

432

16L

11

11

3

119495

435

15L

11

10

3

118610

437

14L

10

10

3

118130

440

13L

10

9

3

117445

442

12L

9

9

3

116765

445

11L

9

8

3

116080

448

10L

8

8

3

115395

450

9L

8

7

3

114715

453

8L

7

7

3

114030

456

7L

7

6

3

113350

458

6L

6

6

3

112665

461

5L

6

5

3

111980

464

4L

5

5

3

111300

467

3L

5

4

3

110615

470

2L

4

4

3

109935

473

1L

4

3

3

109250

476

NEUT

11

11

11

108565

476

1R

11

10

11

107885

476

2R

10

10

11

107200

476

3R

10

9

11

106520

476

4R

9

9

11

105835

476

5R

9

8

11

105150

476

6R

8

8

11

104470

476

7R

8

7

11

103785

476

8R

7

7

11

103105

476

9R

7

6

11

102420

476

10R

6

6

11

101735

476

11R

6

5

11

101055

476

12R

5

5

11

100370

476

13R

5

4

11

99690

476

14R

4

4

11

99005

476

15R

4

3

11

98325

476

16R

3

3

11

NO LOAD TAP CHANGER

4-20


WINDING

VOLTAGE

AMPERES

A

B

“X” VOLTAGE WYE

59000

753

2

1 TO 19

13 TO 15

06000

787

1

1 TO 18

13 TO 14

POS


Bushing or Internal CTs Detailed evaluation of bushing CTs is difficult, if not impossible. The location of the CT can be in the bushing adapter or “turret,” or mounted on the active assembly in the tank. Bushing CTs are usually limited by transformer top oil temperature. Maintaining a top oil temperature of less than 110°C should avoid excessive temperatures. Aging rates should be lower than that of the winding insulation over the average of the loading conditions. De-Energized Tap Changers (DETCs) De-energized tap changers are similar, in a thermal sense, to on-load tap changers, albeit much simpler. The same general considerations and risks apply to DETCs as to LTCs. Coking may become a greater problem for DETCs, as they are seldom operated. It may be advisable to periodically operate the DETC over the range of taps to “wipe” the contacts clean of any deposits. Lead Heating Internal connecting leads may be a concern. The same hot spot limits, and associated risks, apply for leads as for windings. In general, it is impossible to evaluate lead heating without detailed design data. In a properly designed transformer, the connecting leads should not limit the overload capability. However, lead hot spots have been a limitation in the load carrying capability of many transformers because of lack of attention in the design stage or manufacturing practices that permitted or even encouraged liberal application of insulating tape at lead connection points.

Evaluation of lead heating problems outside of the factory is rather difficult. Even with dimensions of the leads and construction details, it is difficult to assess the oil flow conditions in the vicinity of the lead. The best method for assessing lead heating problems is by examining the DGA records for the unit for any hint of heating gases involving cellulose decomposition, particularly CO and CO2 , and eventually CH4 and C 2 H6 . If these gases are present in significant quantity or have a generation rate that increases sharply with load, load should be reduced immediately. At the earliest convenience, an internal inspection should be performed to locate the source of the gassing. In addition to DGA, partial discharge detection and perhaps Furan analysis may also yield useful information. Stray Flux Heating Heating of non-current carrying metal components by the leakage flux of the windings and leads is termed “stray flux heating.” The leakage flux induces eddy current in any conducting material that it passes through. This includes the steel clamping structure, tie rods or tie plates, metal core bands, and the tank wall itself. Since


leakage flux varies proportionally with load current, the stray flux heating increases roughly with the square of winding current. For larger power transformers and GSUs in particular, the problem of stray flux heating can be substantial. Special design measures must be taken to reduce the induced currents. The most common areas of stray flux heating problems are tie plates, used to connect the upper and lower core yoke clamping structure, and bushing penetrations. As with lead heating, evaluation of stray flux heating potential is difficult. The best method for assessing stray flux heating problems is by examining the DGA records for the unit for any hint of hot metal gases, specifically methane and ethane. Should either of these gases exceed 120 ppm or 65 ppm, respectively, high loading should be discontinued and the source of the gases investigated. In addition, sudden increases in these gas levels concurrent with increased loading should be considered additional cause for alarm. In addition to DGA, stray flux heating in the tank wall can be evaluated by examining the transformer with an infrared camera. Particular attention should be paid in the area of bushing penetrations and bushing adapters. A visual examination for discolored paint could also reveal stray flux heating. 4.4

THERMAL MODELING

Given the extreme complexities of heat transfer within a transformer, as well as the lack of information typically available, drastic simplifications must be made. It is important to recognize the simplifications and to know the areas in which these simplifying assumptions are not sufficiently accurate. Therefore, this section begins with a brief and somewhat academic overview of the various heat transfer mechanisms involved. Following this, the section describes available thermal models. 4.4.1

Mechanisms of Heat Transfer

In a power transformer, two heat transfer mechanisms are predominant: radiation and convection. Conduction plays a smaller role and will not be described at length here. It should also be noted that even the most modern treatments of the subject are largely empirical. This initial discussion parallels that of Montsinger in (Montsinger 1951), with additional emphasis on variables that may not be constant. Radiation All bodies at a temperature above their surroundings radiate heat energy to the surroundings. The mathematical relationship between heat lost due to radiation and

4-21



the temperature rise are fairly well known, as shown in Equation 4.4-1 (Cengel 1997)

Qrad = εσA(Tb − Ta ) 4

4

4.4-1

This relationship can be simplified to a simple power relationship of the form shown in Equation 4.4-2.

Qrad = KΔθ x

4.4-2

This relationship, for a given exponent x, is generally valid over a limited temperature range (Figure 4.4-1). The curve fits in Figure 4.4-1 are generally valid from a 0°C rise to about a 70°C rise. The exponents vary from 1.133 for a 0°C ambient to 1.117 for a 40° C ambient. Note that the emissivity will change the multiplicative constant but not the exponent. This relationship could also be expressed inversely as: m Δθ = CQrad

4.4-3

where m = 1/x. For the ranges of x derived above, m varies from 0.883 for a 0 ° C ambient to 0.895 for a 40 ° C ambient. The absorption rate in the infrared region for transparent liquids such as transformer oils is relatively high. Therefore, the radiant energy from transformers windings is absorbed by even a thin layer of oil, and is therefore negligible. Air, on the other hand, has a negligible absorption rate, and radiant energy loss must be considered when determining the heat loss from the tank, and therefore the oil.

Forced Convection When heat is transferred from a solid to a moving fluid medium, the adjacent fluid is heated by conduction. Since the fluid medium is moving, the heated fluid is quickly replaced by cooler fluid. This results in an increased rate of heat transfer than would occur by conduction alone. The heat loss due to convection can be expressed by Newton’s Law of Cooling, as shown in Equation 4.4-4 (Cengel 1997).

Q = hA(Tc − Ta ) 4.4-4 Where: Q is the rate of heat loss. h is the heat transfer coefficient. Tc is the temperature at the surface of the object (solid). Ta is the temperature of the surrounding fluid.

For cross-flow over a cylinder or similar-shaped object (Cengel 1997): ⎛ ρVD ⎞ k ⎟⎟ h = C ⋅ Re Pr ⋅ = C ⋅ ⎜⎜ D ⎝ μ ⎠ m

n

m

⎛ μC p ⎜ ⎜ k ⎝

⎞ ⎟ ⎟ ⎠

n

4.4-5

Where: C is a constant. Re is the Reynold’s Number. Pr is the Prandtl Number. k is the thermal conductivity of the fluid. D is the characteristic length of the immersed object (diameter of cylinder). ρ is the density of the fluid. V is the velocity of the fluid. μ is the viscosity of the fluid (varies with temperature). Cp is the specific heat of the fluid. m, n are constants. From this, it can be seen that h is a function of several parameters, including geometry, fluid velocity, and fluid viscosity. The exponent n is typically 1/3. The exponent m, determined empirically, ranges from about 0.3 to 0.8, depending upon the geometry. Note that if the exponents are equal, the viscosity cancels out and is no longer a factor. Summarizing, the heat loss can be expressed by: Q = KΔθ

4.4-6

or, solving for the temperature rise: Δθ = KQ Figure 4.4-1 Radiative heat transfer at various ambient temperatures.

4-22

4.4-7

Natural Convection Natural convection is slightly more complex than forced convection. The heat transfer is still a function of the



velocity of the fluid, as described above. However, now the velocity of the fluid is the result a varying fluid density with temperature. This is known as thermosiphon flow. The basic relationship is the same as for forced convection. Q = hA(Tc − Ta )

4.4-8

However, h is now a function of the temperature rise as well. For natural convection along a vertical plate (also applicable to a vertical cylinder), h is given by: h =C ⋅

k k m ⋅ (Gr ⋅ Pr ) = C ⋅ L L

⎛ gρ β (Tc − Ta )L μC p ⎞ ⎟ ⋅⎜ ⋅ ⎜ k ⎟⎠ μ2 ⎝ 2

3

forced convection, the viscosity is generally not a factor. For natural convection, the temperature rise is a function of viscosity as follows: 1 ( m + 1) Δθ = KQ nat ⋅ μ −m

4.4-14

Transient Formulation For any temperature rise, the temperature at any time, t, can be determined by equating the heat input to the sum of the change in heat storage and the heat loss:

Heat generated = Change in heat storage + Heat loss.

m

Q gen = mC p

dθ + KΔθ x dt

4.4-15

4.4-9

m varies from 1/3 to 1/4. Note that h is also a function of viscosity, μ, to the -m power.

Combining the temperature component of h with the equation for convection heat transfer: Q = KΔθ m + 1

4.4-10

Taking the inverse to solve for the temperature rise: 1 ( m + 1) Δθ = KQ nat

4.4-11

Since m varies from 1/3 to 1/4, the exponent in Equation 4.4-11 varies from 0.75 to 0.80. Combined Heat Transfer Summarizing the above discussion, the temperature rise (or, conversely, the heat loss) for a particular mechanism of heat transfer can be expressed in the following form:

Δθ = KQ x

4.4-12

or Q = K Δθ

1

x

4.4-13

Where: Δθ is the temperature rise above the surrounding medium. K is a constant. Q is the heat loss (or gain). x is an exponent that varies with mechanism as shown in Table 4.4-1. The constant K is generally constant over the range of temperatures and materials considered in transformer thermal modeling. The only variable that changes appreciably with temperature is the viscosity of oil. For

Traditionally, transient temperatures have been calculated by approximating an instant of time as a stepchange in load and calculating the temperature at the end of the time step as follows: − Δt ⎛ ⎞ Δθ = Δθ i + (Δθ u − Δθ i )⎜1 − e τ ⎟ ⎜ ⎟ ⎝ ⎠ 4.4-16 Where: Δθ is the calculated temperature at time t + Δt. Δθi is the initial temperature at time t. Δθu is the ultimate steady-state temperature. Δt is the time step. e is the time constant.

This closed form solution to the transient differential equation has several drawbacks. First, it is difficult to correct for the change in losses with temperature. The losses at the ultimate temperature rise are a function of the ultimate temperature. The ultimate temperature is, of course, a function of these losses, requiring an iterative calculation at each time step to find the ultimate temperature rise. In addition, the closed form solution above is only truly correct for heat transfer function with an exponent of 1.0 (i.e., forced convection). A more robust approach is to solve the differential equation using a finite difference approach, as taken by Pierce (Pierce 1994) and Lesieutre (Lesieutre et al. 1997) Table 4.4-1 Exponents for Radiation, and Forced and Natural Convection Mechanism

Exponent

Radiation

0.883-0.895

Forced Convection

1.0

Natural Convection

0.75-0.8

4-23



Referring to the differential equation above, the difference equation would take the form:

Q gen,2 = mC p 4.4.2

θ 2 − θ1 Δt

+ KΔθ x

temperature, the hot spot temperature, is located at the top of the winding. This hot spot temperature represents the hottest temperature endured by the insulation and therefore the highest aging rate (1995b).

4.4-17

Top Oil Model (IEEE C57.91-1995, Clause 7)

The following is an outline of the temperature calculation methods presented in Clause 7 of IEEE C57.911995 (IEEE 1995b) (Figure 4.4-2). The thermal mechanisms of a transformer are extremely complex and difficult to model. To reduce complexity, the transformer is analyzed as a lumped system, and several assumptions are made. The transformer is essentially reduced to two systems, the bulk oil and the winding, with an additional “hot spot” temperature located at the top of the winding.

The IEEE top oil method relates the steady-state oil temperature rises to the total losses by a power function. The steady-state winding rises are also related to the winding current by a power function. In addition, certain corrections are made to account for additional considerations such as increased mixing due to forced-oil cooling systems and change in winding resistance with temperature. The following is an outline of the temperature calculation method presented in IEEE C57.91-1995, Clause 7. Symbols:

C

The oil temperature is presumed to be lowest at the bottom of the winding. As the oil rises upward along the winding, the oil adjacent to the winding is heated at a constant rate. Therefore, the oil temperature is assumed to increase linearly from the bottom of the winding to the top of the winding, with the highest oil temperature located at the top of the winding. At rated load, the winding temperature distribution is assumed to be higher than the oil temperature distribution by a constant value, Δw, and thus parallel to the oil temperature distribution. Due to stray flux concentration near the top of the winding, a further increase in

is the thermal capacity (Watt-hours/deg C).

WCC is the weight of the core and coils (kg). WTank is the weight of the tank and fittings in contact with the oil (kg). VFluid is the volume of oil (L). τO

is the oil thermal time constant (min).

τw

is the winding time constant (min).

t

is the time (min.).

Δt

is the calculation time step (min).

ΔθTO is the top oil rise over ambient temperature (deg C).

Figure 4.4-2 Graph of temperature rises vs. height for IEEE Clause 7 Model. 4-24



ΔθHS is the hot spot rise over the top oil temperature (deg C). PT

is the total loss (W).

K

is the load (per unit of the nameplate rating).

R

is the ratio of load loss to no-load loss at the nameplate rating.

m

is the winding temperature rise exponent.

n

is the oil temperature rise exponent.

θHS

is the hot spot temperature (deg C).

θA

is the ambient temperature (deg C).

A combined thermal capacity can be calculated by combining the specific heats of the various component materials with the component weights. However, the components are not at a uniform temperature. The oil temperature varies from the bottom of the tank to the top. For OA (ONAN) and FA (ONAF), the assumption has been made that the mean oil temperature is 76% of the maximum top oil temperature. In addition, 2/3 of the tank weight is used. For OA and FA (ONAN and OFAF), the thermal capacity, C, equals:


4.4-19

Subscripts:

For DFOA and NDFOA (ODAF and OFAF), the thermal capacity, C, equals:

R

indicates a rated quantity.

i

indicates an initial quantity.

U

indicates an ultimate or steady-state quantity.



Oil Thermal Time Constant:

In order to calculate the transient response of the bulk oil, it is necessary to calculate an oil thermal time constant. The thermal time constant of the bulk oil at rated temperature equals:

τO,R = C * ΔθTO,R / PT,R 4.4-18 Where: τO,R is the oil thermal time constant at rated load (min). C is the combined thermal capacity of the transformer (W-min/lbs-C). Δθ TO,R is the measured oil temperature rise over ambient at rated load (C). PT,R is the total loss at rated load (W). The thermal capacity, C , is the combined thermal capacity of all transformer components in contact with the bulk oil. This includes the core, windings, tank and fittings, and the oil itself. The specific heat for each component material is shown in Table 4.4-2.

τ O = τ O, R

⎛ Δθ TO ,U ⎜ ⎜ Δθ ⎝ TO , R ⎛ Δθ TO ,U ⎜ ⎜ Δθ ⎝ TO , R

⎞ ⎛ Δθ TO , i ⎟−⎜ ⎟ ⎜ Δθ ⎠ ⎝ TO , R 1

⎞ n ⎛ Δθ TO , i ⎟ −⎜ ⎜ Δθ ⎟ ⎝ TO , R ⎠

Table 4.4-2 Specific Heat for Copper, Steel, and Oil Specific Heat (W-min/lbs-C)

Copper

0.05

Steel

0.06

Oil

14.6

⎞ ⎟ ⎟ ⎠ 1

⎞n ⎟ ⎟ ⎠

4.4-21


The following equations are used to calculate the initial temperatures based upon the assumption that the load prior to the calculation period was constant long enough for the temperatures to reach their steady-state limits. This assumption is reasonable if the load is fairly constant for a period of time prior to the overload equal to two to three times the oil thermal time constant.

(

)

⎡ K 2R + 1 ⎤ Δθ TO , i = Δθ TO , R ⎢ i ⎥ ⎣⎢ (R + 1) ⎦⎥ Δθ HS , i = Δθ HS , R ⋅ K i2 m

Material

4.4-20

n

4.4-22

Transient Temperatures:

The following equations are used to calculate the transient temperature rises based upon the oil time constant calculated above, the user-determined winding time constant, load, losses, and initial and ultimate temperature rises. For a graphical representation of the various temperature rises, see Figure 4.4-2.

4-25



For all cooling modes: The top oil rise at time t2 = t1 + Δt is given by the following: Δθ TO ,U

(

)

⎡ K 2R +1 ⎤ = Δθ TO , R ⎢ U ⎥ ⎢⎣ (R + 1) ⎥⎦

Δθ TO ,2 = (Δθ TO ,U

n

4.4-23

Δt ⎛ − − Δθ TO ,1 )⎜1 − e τ ⎜ ⎝ O

⎞ ⎟ + Δθ TO ,1 ⎟ ⎠

4.4-24

The hot-spot rise over top oil at time t2 = t1 + Δt is given by the following: Δθ HS ,U = Δθ HS , R ⋅ K U2 m Δθ HS ,2 = (Δθ HS ,U

4.4-25

Δt ⎛ − τ ⎜ − Δθ HS ,1 ) 1 − e ⎜ ⎝ W

⎞ ⎟ + Δθ HS ,1 ⎟ ⎠

4.4-26


θ HS ,2 = θ A,2 + Δθ TO ,2 + Δθ HS ,2

4.4-27


Bottom Oil Model (IEEE C57.91-1995, Annex G)

This model was originally developed by Linden Pierce with GE in the early 1990s based upon detailed temperature measurements on a model coil (Pierce 1992, 1994). The model was included in the 1995 revision of IEEE C57.91 as Annex G (IEEE 1995b). In the top oil model, the hot spot temperature consisted of three components: ambient temperature, top oil rise over ambient, and hot spot rise over top oil (Figure 4.4-3). In the bottom oil model, which is the approach that will be developed here, the hot spot temperature consists of four components: ambient temperature, bottom oil rise over ambient, top-of-duct oil to bottom oil gradient, and hot spot rise over top of duct oil. These components are shown schematically below. In addition to these components, the average winding rise over average duct oil needs to be developed, as the winding losses are a function of this temperature and not the hot spot temperature.

θ HS = θ A + Δθ BO + Δθ DO / BO + Δθ HS / DO

4-26

Average Winding Rise over Average Duct Oil It will be assumed that the temperatures of the winding and the duct oil vary linearly from bottom to top, and both are parallel. This results in a winding temperature rise over adjacent duct oil that does not vary over the height of the winding, and a constant heat flux from the winding to the duct oil. In line with the finite difference transient formulation described above, a heat balance will be developed for the winding-duct oil system.

The heat generated by the winding at time t2 = t1 + Δt is given by: Q gen,W = L2 (PI 2 R ⋅ K W + PE K W )

4.4-29

Where: Qgen,W is the average heat generated by the windings. L is the winding current, in per unit rated. PI2R is the Ohmic losses in the windings due to the winding current at rated current. is the eddy losses in the windings at rated PE current.

⎛ θW ,1 + θ K ⎞ ⎟ KW = ⎜ ⎜θ ⎟ + θ K ⎠ ⎝ W,R 4.4-30 Where: θW,1 is the average winding temperature calculated at the previous time step, t1. θW,R is the average winding temperature at rated load. θK is 234.5°C for copper windings and 225°C for aluminum windings. The heat lost by the windings to the duct oil is dependent upon the mechanism of heat transfer. For ONAN, ONAF, and OFAF, the predominant mode of heat

θDO θHS

θBO

θA

Figure 4.4-3 Components of bottom oil model. 4.4-28



transfer is natural convection. As outlined above, the heat loss for natural convection can be expressed by: m +1

m

⎛ θW ,1 − θ DO,1 ⎞ ⎛ μW , R ⎞ ⎟ (PI 2 R + PE ) ⎟ ⎜ Qloss ,W = ⎜ ⎟ ⎟ ⎜μ ⎜θ θ − DO , R ⎠ ⎝ W ,1 ⎠ ⎝ W ,R 4.4-31 Where: Qloss,Wis the average heat lost by the windings to the average duct oil. θW,1 is the average winding temperature at the previous time step. θDO,1 is the average duct oil temperature at the previous time step. θW,R is the average winding temperature at rated current. θDO,R is the average duct oil temperature at rated current. μW,R is the oil viscosity at a temperature equal to the average of the average winding temperature and average duct oil temperature at rated load. μW,1 is the oil viscosity at a temperature equal to the average of the average winding temperature and average duct oil temperature at the previous time step. m is a constant, usually between 1/3 and 1/4. For ODAF transformers (directed forced oil), the predominant mode of heat transfer is forced convection. The heat loss for OFAF can then be expressed by:

⎛ θW ,1 − θ DO,1 Qloss,W = ⎜ ⎜θ ⎝ W , R − θ DO, R

⎞ ⎟(PI 2 R + PE ) ⎟ ⎠

4.4-32

Note that it is assumed that the effect of the change in oil viscosity with temperature is negligible for this case. Completing the heat balance, the heat absorbed by the windings is given by:

Qabs ,W = mW C P ,W

(θ

W ,2

− θW ,1 )

Δt 4.4-33 Where: Qabs,W is the heat absorbed by the winding during incremental time step, Δt. mW is the mass of the windings. CP,W is the effective specific heat of the windings. θW,1 is the average winding temperature at time t1. θW,2 is the average winding temperature at time t2 = t1 + Δt. Δt is the incremental time step.

constant calculated from the winding cooldown curves taken during the factory heat run. From the definition of a thermal time constant:

mW C P ,W =

τ W (PI 2 R + PE ) (θW , R − θ DO, R )

4.4-34

Summing the three terms of the heat balance and solving for θW,2:

θW , 2 =

(Q

gen,W

− Qloss ,W )Δt

mW C P ,W

+ θW ,1 4.4-35

Duct Oil Gradient over Bottom Oil The oil entering the winding ducts is at a temperature equal to the bottom oil temperature. The oil is then heated as it rises up the winding duct, either by forced oil flow or natural thermosiphon flow. The temperature at the duct exit, for a constant heat flux along the duct, is dependent upon the mass flow rate, as follows:

Te = Ti +

q s As

ρVAcC P

4.4-36

Where: Te is the temperature of the fluid exiting the duct. Ti is the temperature of the fluid entering the duct. qs is the constant heat flux along the duct. As is the surface area of the duct. ρ is the density of the fluid. V is the fluid velocity (average). Ac is the cross-sectional area of the duct. Cp is the specific heat of the fluid. For ODAF, the mass flow rate through the duct remains essentially constant for varying load levels. For ONAN, ONAF, and OFAF, the oil flow through the duct is by natural thermosiphon flow. The flow rate through the duct in these cases is a complex function of the temperature rise in the duct, the temperature drop through the radiators, and the relative height of the windings and the radiators. The temperature rise in the duct, in turn, is a function of the mass flow rate through the duct (Figure 4.4-4). Lacking sufficient data, the following simple approach will be taken, relating the temperature rise through the vertical ducts (top-of-duct oil – bottom oil) to the loss by an exponent, y, as follows:

Δθ DO / BO,2 = H HS ⋅ Δθ TDO / BO, R * L2 y

4.4-37

Where: ΔθDO/BO is the duct oil rise over bottom oil.

The term mWCP,W is usually not known directly. Instead, this term can be calculated from a winding thermal time 4-27



that, for ONAN, ONAF, and ODAF, this value is equal to the rated top oil rise. For OFAF, Pierce suggests using the average winding rise. These recommendations appear to be based upon the tests of the model coil in (Pierce 1992). Hot Spot Rise over Top Duct Oil By following a development similar to the average winding rise over average duct oil, only considering an incremental portion of the winding at the hot spot (top of winding), the hot spot temperature rise over top duct oil can be calculated.

The heat generated by the winding at the hot spot at time t2 = t1 + Δt is given by: Figure 4.4-4 Oil flow throughout the duct.

Q gen, HS = L2 (PI 2 R ⋅ K HS + PE K HS )

4.4-38

is the height of the winding hot spot in per unit of the winding height (1.0 = top). ΔθTDO/BO,R is the top-of-duct oil rise over bottom oil at rated load (see discussion below). L is the per unit load. y is an exponent.

Where: Qgen,HS is the heat generated by the windings at the hot spot. L is the winding current, in per unit rated. PI2R is the Ohmic losses in the windings due to the winding current at rated current. PE is the eddy losses in the windings at rated current.

In almost all cases, it can be assumed that the hot spot is at the top of the winding, and hence adjacent to the top duct oil temperature, making HHS equal to 1.0. The data from tests done on model coils in Pierce (1994) suggests that, for most cases, the hot spot is within the top 10% of the winding. When the increased eddy loss at the top of the winding is factored in, the hot spot should be even closer to the top, most often within a few turns or disc sections. However, HHS has been included to allow the engineer to assume a hot spot position below the top of the winding.

⎛ θ HS ,1 + θ K ⎞ ⎟ K HS = ⎜ ⎟ ⎜θ + θ HS , R K ⎠ ⎝ 4.4-39 Where: θHS,1 is the winding hot spot temperature calculated at the previous time step, t1. θHS,R is the winding hot spot temperature at rated load. θK is 234.5°C for copper windings and 225°C for aluminum windings.

HHS

The exponent, y, is as yet undetermined. Lacking measured data, the values given by Pierce (1994) can be used. For ONAN, ONAF, and OFAF, y is given as 0.5. For ODAF, y is given as 1.0. Since the mass flow rate does not change for ODAF over varying loads and the heat flux is proportional to the losses, the exponent of 1.0 for ODAF should be correct. For the other cooling modes, however, the mass flow rate is a function of both the oil temperatures within the duct and the oil temperatures in the bulk oil and radiators. Therefore, a more complex relationship is needed. The temperature of the oil exiting the ducts, expressed as the rise over bottom oil ΔθDO/BO, at rated load is difficult to determine. It cannot be measured easily. Even when measurements are made, the values vary considerably for the various vertical ducts around the circumference of the winding (Pierce 1992). Pierce (1994) suggests

4-28

The heat lost by the windings to the duct oil is dependent upon the mechanism of heat transfer. For ONAN, ONAF, and OFAF, the predominant mode of heat transfer is natural convection. As outlined above, the heat loss for natural convection can be expressed by: Qloss , HS

⎛ θ HS ,1 − θ DO,1 =⎜ ⎜θ ⎝ HS , R − θ DO, R

⎞ ⎟ ⎟ ⎠

m +1

⎛ μ HS , R ⎜ ⎜μ ⎝ HS ,1

⎞ ⎟ ⎟ ⎠

m

(PI 2R

+ PE ) 4.4-40

Where: Qloss,HS is the heat lost by the winding hot spot to the top duct oil. θHS,1 is the winding hot spot temperature at the previous time step. θDO,1 is the duct oil temperature at the previous time step. θHS,R is the winding hot spot temperature at rated current.



θDO,R is the duct oil temperature at rated current. μHS,R is the oil viscosity at a temperature equal to the average of the winding hot spot temperature and top. μHS,1 is the oil viscosity at a temperature equal to the average of the winding hot spot temperature and top duct oil temperature at the previous time step. m is a constant, usually between 1/3 and 1/4.

For ODAF transformers (directed forced oil), the predominant mode of heat transfer is forced convection. The heat loss for OFAF can then be expressed by: ⎛ θ HS ,1 − θ DO,1 Qloss, HS = ⎜ ⎜θ ⎝ HS , R − θ DO, R

⎞ ⎟(PI 2 R + PE ) ⎟ ⎠

4.4-41

Note that it is assumed that the effect of the change in oil viscosity with temperature is negligible for this case. Completing the heat balance, the heat absorbed by the windings is given by: Q abs, HS = mW C P ,W

(θ

HS ,2

− θ HS ,1 ) Δt

4.4-42

Where, Qabs,HS is the heat absorbed by the winding during incremental time step, Δt. mW is the mass of the windings. CP,W is the effective specific heat of the windings. θHS,1 is the average winding temperature at time t1. θHS,2 is the average winding temperature at time t2 = t1 + Δt. θt is the incremental time step. Summing the three terms of the heat balance and solving for θHS,2:

θ HS ,2 =

(Q

gen , HS

)

− Qloss, HS Δt

mW C P ,W

+ θ HS ,1

The heat generated by the active assembly (core and coils) at the hot spot at time t2 = t1+ Δt is given by: Q gen, O = L2 (PI 2 R ⋅ K W + (PE + PS ) K W ) + PC

4.4-44

Where: Qgen,O is the heat generated within the transformer. L is the winding current, in per unit rated. PI2R is the Ohmic losses in the windings due to the winding current at rated current. PE is the eddy losses in the windings at rated current. PS is the stray loss. PC is the core (no-load) loss. ⎛ θW ,1 + θ K ⎞ ⎟ KW = ⎜ ⎜θ ⎟ + θ W , R K ⎝ ⎠ 4.4-45 Where: θW,1 is the average winding temperature calculated at the previous time step, t1. θW,R is the average winding temperature at rated load. θK is 234.5°C for copper windings and 225°C for aluminum windings.

The heat loss is given by: Qloss , AO

⎛ θ AO ,1 − θ A,1 =⎜ ⎜θ ⎝ AO, R − θ A, R

⎞ ⎟ ⎟ ⎠

1

y

PT 4.4-46

Where: Qloss,AO is the heat lost by the bottom oil to the surrounding air. θA,1 is the ambient temperature at the previous time step. θA,R is the ambient temperature during the heat run. θAO,1 is the average oil temperature at the previous time step. θAO,R is the average oil rise at rated load. y is an exponent equal to 0.8 for ONAN, 0.9 for ONAF and OFAF, 1.0 for ODAF.

4.4-43

Bottom and Top Bulk Oil Rise Pierce (1994) calculates the average oil rise and then applies a top-to-bottom oil gradient to that average oil rise. This gradient is calculated as a function of the losses raised to an exponent. This exponent is given by Pierce (1994) as 0.5 for ONAN and ONAF, and 1.0 for OFAF and ODAF.

Completing the heat balance, the heat absorbed by the bulk oil is given by: Qabs , AO = ∑ mC P

(θ

AO ,2

− θ AO ,1 )

Δt 4.4-47 Where: Qabs,AO is the heat absorbed by the average bulk oil during incremental time step, Δt. θAO,1 is the average bulk oil temperature at time t1. θAO,2 is the average bulk oil temperature at time t2 = t1 + Δt. Δt is the incremental time step.

4-29



The value ΣmCP is a sum of product of the masses of the transformer in contact with the oil, as well as the oil itself, and the specific heat of those components:

∑ mC

P

4.4.4

The IEC 354-1991 (McNutt 1992) model is similar to the IEEE Clause 7 model (Figure 4.4-5). The two models differ in a few important respects. First, the calculation of the rated hot spot rise is done by applying a “hot spot factor” to the average winding rise over average oil temperature gradient. This “hot spot factor” is a design specific constant that generally varies between 1.0 and 1.4, with 1.2 being typical for power transformers.

= C P , steel (WC & C + WTank ) + C P , fluidW fluid 4.4-48

Summing the three terms of the heat balance and solving for θAO,2:

θ AO ,2 =

(Q

gen , O

− Qloss, AO )Δt

∑ mC P

+ θ AO ,1

Note: The winding temperature rise exponent in this document differs slightly from that described in IEC 354. The equations listed below apply a multiple of 2 to this exponent, whereas in IEC 354, this multiple is included in the exponent definition. Therefore, the winding temperature rise exponent listed here is equal to half of the winding temperature rise exponent in IEC 354.

4.4-49

Once the average bulk oil temperature has been determined, a top-to-bottom bulk oil gradient must be calculated. This is done by the following equation:

θ TO / BO = (θ TO , R

⎛ Qloss , AO ⎞ ⎟ − θ BO , R )⎜ ⎜ Q gen, O Δt ⎟ ⎠ ⎝

z

Oil Thermal Time Constant: 4.4-50

Where, θTO/BO is the top-to-bottom bulk oil gradient, C. θTO,R is the top oil rise at rated load, C. θBO,R is the bottom oil rise at rated load, C. Δt is the incremental time step. z is an exponent (0.5 for ONAN, ONAF; 1.0 for OFAF, ODAF). The top and bottom oil temperatures are then solved for by adding and subtracting, respectively, half of the topto-bottom bulk oil gradient:

θ TO = θ AO +

θ BO = θ AO −

θ TO / BO 2

4.4-51

θ TO / BO 2

IEC Model (IEC 354-1991)

In order to calculate the transient response of the bulk oil, it is necessary to calculate an oil thermal time constant. Since IEC 354 does not include this information, the IEEE C57.91-1995 equations can be offered as an option:

(

0.1 ) 1.108

For OA and FA (ONAN and OFAF), the thermal capacity, C, equals: C = 0.0272 * WCC + 0.01814 * WTank + 5.034 * VFluid (1) (IEEE Clause 7) 4.4-53

For DFOA and NDFOA (ODAF and OFAF), the thermal capacity, C, equals: C = 0.0272 * WCC + 0.0272 * WTank + 7.305 * VFluid (2) (IEEE Clause 7) 4.4-54

4.4-52

Figure 4.4-5 Diagram illustrating assumed temperature profile within transformer for IEC model. 4-30



The thermal time constant of the bulk oil at rated temperature equals: τO,R = C * ΔθTO,R / PT,R (3) (IEEE Clause 7)

4.4-55


τ O = τ O, R

⎛ Δθ TO ,U ⎜ ⎜ Δθ ⎝ TO , R

⎞ ⎛ Δθ TO , i ⎟−⎜ ⎟ ⎜ Δθ ⎠ ⎝ TO , R 1

⎛ Δθ TO ,U ⎞ n ⎛ Δθ TO , i ⎟ −⎜ ⎜ ⎜ Δθ ⎟ ⎜ Δθ ⎝ TO , R ⎝ TO , R ⎠ (4) (IEEE Clause 7)

⎞ ⎟ ⎟ ⎠ 1

⎞n ⎟ ⎟ ⎠

The top oil rise at time t2 = t1 + Δt is given by the following:

(

)

n

⎡ K 2R +1 ⎤ Δθ TO ,U = Δθ TO , R ⎢ U ⎥ ⎢⎣ (R + 1) ⎥⎦ (8) (IEC 2.4.1, Equation 1) Δt ⎛ − τO ⎜ Δθ TO ,2 = (Δθ TO ,U − Δθ TO ,1 ) 1 − e ⎜ ⎝ (9) (IEC 2.5)

4.4-60

⎞ ⎟ + Δθ TO ,1 ⎟ ⎠ 4.4-61

The hot-spot rise over top oil at time t2 = t1 + Δt is given by the following: 4.4-56


Δθ HS ,U = Hg R ⋅ K U2 m

(10) (IEC 2.4, Equation 1+2)

The following equations are used to calculate the initial temperatures based upon the assumption that the load prior to the calculation period was constant long enough for the temperatures to reach their steady-state limits. This assumption is reasonable if the load is fairly constant for a period of time prior to the overload equal to two to three times the oil thermal time constant. ⎡ K 2R + 1 ⎤ Δθ TO , i = Δθ TO , R ⎢ i ⎥ ⎢⎣ (R + 1) ⎥⎦ (5) (IEC 2.4.1, Equation 1)

(

)

n

⎡ K R +1 ⎤ Δθ BO , i = Δθ BO , R ⎢ ⎥ ⎣⎢ (R + 1) ⎦⎥

)

n

(

2 i

4.4-57

(6) (IEC 2.4.2, Equation 2)

In addition, for DFOA (ODAF) cooling modes a correction factor is applied to account for the change in winding Ohmic losses due to temperature as follows:

θ HS ,U ′ = θ HS ,U + 0.15(θ HS ,U − θ HS , R ) (11) (IEC 2.4.3, Equation 3)

4.4-63

For other types of cooling, the change in winding Ohmic losses is negligible. Note that the IEEE method neglects the change in winding resistance with temperature for all cases, assuming that this change is always offset by the change in oil viscosity with temperature. The transient hot spot rise is then:

4.4-58

Δθ HS , i = Hg R ⋅ K i2 m

(7) (IEC 2.4, Equation 1+2)

4.4-62

Δθ HS ,2 = (Δθ HS ,U

4.4-59

g is difference between average winding and average oil temperatures. H is a multiplier that equals 1.3.

Hg is the hot spot rise above top oil. Transient Temperatures:

The following equations are used to calculate the transient temperature rises based upon the oil time constant calculated above, the user-determined winding time constant, load, losses, and initial and ultimate temperature rises. For a graphical representation of the various temperature rises, see Figure 4.4.5. For OA and FA (ONAN and ONAF) cooling modes:

Δt ⎛ − τW ⎜ − Δθ HS ,1 ) 1 − e ⎜ ⎝

(12) (IEC 2.5)

⎞ ⎟ + Δθ HS ,1 ⎟ ⎠ 4.4-64

The equation form is the same as IEEE if the hot spot rise over top oil term is calculated with the IEC method. Note that the IEC method calculates the hot spot rise over top oil temperature at rated load through the use of a multiplier, H, applied to the difference between the average winding temperature from test and the average top oil temperature from test. For power transformers, H is typically approximately 1.3. The hot-spot temperature at time t2 = t1 + Δt is given by:

θ HS ,2 = θ A,2 + Δθ TO ,2 + Δθ HS ,2 (13) (IEC 2.4.1, Equation 1)

4.4-65

4-31



For NDFOA and DFOA (OFAF and ODAF) cooling modes: For forced-oil cooling modes, the increased mixing introduced by the forced circulation of the oil increases the complexity of the model. The top oil temperature leaving the winding is greater than the measured top oil. Therefore, the top oil temperature leaving the winding is calculated using the sum of the ambient temperature, the bottom oil temperature rise, and the difference between the top oil and the bottom oil rises. Note that this differs from the IEEE methodology. The IEEE method assumes that the measured top oil temperature is equal to the temperature of the oil leaving the top of the winding for all cooling modes. The bottom oil rise at time t2 = t1 + Δt is given by:

(

)

Rather than taking an analytical approach to the problem, as had been taken by Pierce with the IEEE Annex G model, the authors of the model took the approach of applying corrective factors and multiple time constants. The constants would be adjusted empirically to fit measured temperature data. Like the IEEE Clause 7 model, the revised IEC model lumps the hot spot temperature into a top oil rise over ambient and a hot spot rise over top oil.


4.4-71

n

⎡ K R +1 ⎤ Δθ BO ,U = Δθ BO , R ⎢ ⎥ ⎢⎣ (R + 1) ⎥⎦ (14) (IEC 2.4.2, Equation 2) Δt ⎛ − τO ⎜ Δθ BO ,2 = (Δθ BO ,U − Δθ BO ,1 ) 1 − e ⎜ ⎝ (15) (IEC 2.5) 2 U

this new model recognized that the hot spot temperature increases more rapidly initially than is currently predicted with traditional equations. This is commonly attributed to an increase in the duct oil that occurs more quickly than the increase in bulk oil. This phenomenon they have dubbed the "hot spot bump" (see Figure 4.4-6).

4.4-66

⎞ ⎟ + Δθ BO ,1 ⎟ ⎠ 4.4-67

The top-to-bottom oil rise at time t2 = t1 + Δt is given by the following: Δθ T − BO ,U = Δθ T − BO , R K U2 m

The computation of the constituent rises is a complex arrangement of factors and time constants. The intent of these factors is to simulate the “hot spot bump” by inclusion of an additional exponential term in the calculation of the hot spot rise over top oil. The calculation of the top oil temperatures proceeds in a similar fashion to the IEEE Clause 7 model. First, the ultimate top oil temperature for the given load level is calculated: x

(16) (IEC 2.4.2, Equation 2)

4.4-68

⎛ − Δθ T − BO ,2 = (Δθ T − BO ,U − Δθ T − BO ,1 )⎜1 − e τ W ⎜ ⎝ (17) (IEC 2.5)

Δt

⎞ ⎟ + Δθ T − BO ,1 ⎟ ⎠ 4.4-69

The hot-spot rise above top oil, ΔθHS, is calculated using the same equations as used for OA and FA cooling modes described above.

⎡ K 2 R + 1⎤ Δθ TO ,U = Δθ TO , R ⎢ ⎥ ⎣ R +1 ⎦ 4.4-72 Where: ΔθTO,U is the ultimate top oil temperature rise, C. ΔθTO,R is the rated top oil temperature rise, C. K is the per unit load. R is the ratio of load losses to no-load losses. x is a constant exponent.


θ HS ,2 = θ A,2 + Δθ BO ,2 + Δθ T − BO ,2 + Δθ HS ,2 (18) (IEC 2.4.2, Equation 2)

4.4-70


Proposed IEC Model

The proposed IEC model (IEC 1991) takes a bit of a radical departure from the earlier models. The authors of 4-32

Figure 4.4-6 Example of “hot spot bump.”



The transient top oil rise is then calculated by the following equation (note the additional constant applied to the time constant): Δθ TO ,2 = Δθ TO ,1 + (Δθ TO ,U

− Δt ⎛ k 11τ O ⎜ − Δθ TO ,1 ) 1 − e ⎜ ⎝

⎞ ⎟ ⎟ ⎠

The hot spot rise over top oil is then calculated. The ultimate hot spot rise over top oil is calculated in the traditional manner: 4.4-74

Where: ΔθHS/TO,U is the ultimate hot spot rise over top oil, C. ΔθHS/TO,R is the rated hot spot rise over top oil, C (IEC defines this as H*g, where H is a hot spot factor between 1.1 and 1.5 and g is the average winding to average oil gradient). K is the load in per unit. y is a constant exponent. The most significant difference between this new IEC model and more traditional calculations is in the transient formulation of the hot spot rise over top oil. The new IEC model breaks the rise into two components with different time constant, one on the order of the winding time constant and the other on the order of the oil time constant. The transient hot spot rise over top oil is calculated as follows for increasing load: Δθ HS / TO ,2 = Δθ HS / TO ,1 + (Δθ HS / TO ,U − Δθ HS / TO ,1 ) − Δt ⎡ ⎛ ⎢k21 ⎜1 − e k 22τ W ⎢ ⎜ ⎣ ⎝

− Δt ⎞ ⎛ ⎟ − (k − 1)⎜1 − e τ O / k 22 21 ⎟ ⎜ ⎠ ⎝

⎞⎤ ⎟⎥ ⎟⎥ ⎠⎦

ONAN

ONAF

OFAF

Oil exponent, x

0.8

0.8

1.0

1.0

Winding exponent, y

1.3

1.3

1.3

2.0

4.4-75

Where: ΔθHS/TO,2 is the hot spot rise over top oil at the current time step, C. ΔθHS/TO,1 is the hot spot rise over top oil at the previous time step, C. k21 & k22 are transformer specific constants. Δt is the time step, minutes. τW is the winding thermal time constant, minutes. τO is the oil thermal time constant, minutes. For decreasing loads, the effects of thermal capacity are ignored, and the hot spot rise over top oil is taken as the

ODAF

Constant k11

0.5

0.5

1.0

1.0

Constant k21

2.0

2.0

1.3

1.0

Constant k22

2.0

2.0

1.0

1.0

Oil Time Constant (min)

210

150

90

90

Winding Time Constant (min)

10

7

7

7

4.4-73

Where: ΔθTO,2 is the top oil temperature rise at the current time step, C. ΔθTO,1 is the top oil temperature rise at the previous time step, C. Δt is the time step, minutes. k11 is a transformer specific constant. τO is the oil thermal time constant, minutes.

Δθ HS / TO ,U = Δθ HS / TO , R K y

Table 4.4-3 Suggested Values for Constants in Revised IEC Model

ultimate hot spot rise over top oil. The individual terms are then summed to give the hot spot temperature:


4.4-76

The various k-constants and the exponents x and y are transformer specific. The recommended method for determining these values is via extrapolation from the heating curves of a prolonged factory heat run test. This information would not be available for existing transformers, and it is unclear whether it could even be derived using standard factory heat run procedures. In lieu of measured values, Table 4.4-3 provides suggested values. 4.5

THERMAL RATINGS

To this point, this chapter has examined the risks of increased loading and determined ways to predict the pertinent equipment temperatures. Now a method for maintaining reasonable risk levels under everyday operation must be developed. The manner in which transformer ratings are calculated and communicated varies from utility to utility, depending upon operating procedures. Thermal ratings are used for various purposes, ranging from planning to operation. The form and complexity of the presentation of calculated ratings vary with the preference of the user. The loading of transformers is ultimately an economical decision. The increased risk of failure and reduced usable life must be balanced with the capital investment of the unit and, to a smaller degree, increased maintenance costs. In addition, the impact of the loss of the unit on the integrity of the system must be factored in. Therefore, the ultimate decision on rating limits is up to the individual utility. Presented here are general recommendations. Ratings can be viewed as a function of several factors:

• Ambient temperature —magnitude —diversity

• Load Shape (diversity) • Pre-Load 4-33


• Rating Duration Power transformer ratings are traditionally calculated over a 24-hour period. The general procedure is to calculate the temperatures and loss-of-life over the 24-hour period and compare these to pre-selected limits. The load is adjusted accordingly such that none of the limits is exceeded and one or more limits are met. This is then the definition of the rating. The steps to calculating the rating are as follows: 1. Determine initial temperatures. Since transformers have a significant thermal capacity, the initial temperatures prior to the rating become an important factor, particularly with rating durations less than twice the oil thermal time constant. Therefore, the initial operating temperatures of the transformer must be estimated by some means. The initial temperatures can be estimated directly (possibly from measured temperatures) or calculated by calculating the temperatures at the end of a 24-hour period of assumed loading. 2. Calculate equipment temperatures and loss-of-life for rating period. Using any available means, such as those outlined in Section 4.4, the operating temperatures, principally hot spot and top oil, are calculated throughout the rating period. In addition, loss-of-life is calculated. 3. Compare maximum temperatures and loss-of-life from Step 2 to selected limits. 4. Adjust load level and return to Step 2. 4.5.1

Ambient Air Temperature Obviously, the ambient air temperature is a major factor in the load capacity of a power transformer (Figure 4.5-1). Each degree that average 24-hour air temperature is below 30°C represents additional capacity. Therefore, seasonal variations in air temperature can be used to give higher thermal ratings for cooler periods.


Seasonal Variation Depending upon geographical location, the temperature can vary widely between seasons. This allows for increased capacity during cooler months. Depending upon the nature of the load, this can be a significant advantage, especially in cooler climates. If the load is largely heating and lighting loads, then the peak system loading tends to occur in the winter, when ambients are the lowest and thermal capacity the highest. On the flip side, in areas with summer peaking loads, the peak load coincides with the peak ambient temperatures and consequently the minimum capacity periods.

Often times, users produce thermal ratings based upon seasonal peak or average ambients. This allows the user to take advantage of the additional capacity during periods where the ambient is below the rated ambient. Ratings of this kind are simple and safe. Significant additional capacity can be realized without even exceeding the rated hot spot temperature of 110°C. Diurnal Variation Diurnal variations in ambient temperature are often predictable. Due to the thermal capacity of the transformer, cyclic variations in ambient temperature can be used to advantage. Measurement Ambient temperature should be measured as close as possible to the transformer. Ideally, one would want the temperature of the air in the vicinity of the radiators or heat exchangers. This is generally not practical. Temperatures measured within the substation should be sufficient. Weather bureau data may be used with the understanding that temperatures can vary significantly over a short distance.

For transformers located in any sort of enclosure such as a kiosk or vault, temperatures should be used that are measured in the vicinity of the transformer. If this is not possible, an offset should be added to the ambient temperature to account for the increased local temperatures. 4.5.2

Load

Pre-load For transient ratings, the thermal mass of the transformer makes the rating dependent upon the initial temperatures at the start of the rating period. These initial temperatures are governed by the loading for the previous 24 hours. Therefore, for rating durations less than approximately twice the oil thermal time constant, preload is a significant factor. An illustration of this is shown in Figure 4.5-2. Figure 4.5-1 Example plot of rating vs. air temperature for various durations with pre-load = 0.7 PU. 4-34

Load Shape Also due to the long thermal time constant of the transformer, load shape can be a factor in rating calculations.



A load shape that is flat will achieve higher temperatures than a diverse (large difference between minimum and maximum) load shape for a given peak magnitude. This can often be used to advantage if the loading on a particular unit is cyclic and predictable.

length of the oil time constant makes this definition a bit unclear given the cyclic variation in load and air temperature. For the sake of discussion and throughout this chapter, a long-term emergency rating is defined as a rating greater than 4 hours in duration.

4.5.3

Short-Term Emergency As with LTEs, the definition of short-term emergency ratings (STE) varies. Short-term ratings are usually defined as extremely short duration ratings that take advantage of the thermal capacity of the equipment. These ratings range from a few minutes in duration to a few hours. In this document, STEs are defined as ratings 4 hours and less. An example of a 4-hour STE rating is shown in Figure 4.5-3, demonstrating the pre-load, rating period, and post contingency period.

Rating Type and Duration

A thermal rating is a statement of the load capability of a transformer under a given set of conditions. These conditions represent various typical operating scenarios that a system operator may run into. The system operator then selects the rating scenario that most represents the current operating scenario to determine the load capability of the transformer for the current operating scenario. Depending upon the application of the transformer, the system conditions impacting the transformer, and company operating policies, various rating scenarios may be developed. However, these rating scenarios can generally be lumped into three categories: - Long-term emergency (LTE)

It is important to note here that short-duration ratings are highly sensitive to the inaccuracies in the transient temperature modeling of transformers. Therefore, caution should be exercised when calculating ratings less than 1 hour in duration.

- Short-term emergency (STE)

4.5.4

Normal Life-Expectancy Loading Normal life-expectancy loading represents the normal operating state of the transformer. A transformer represents a large capital investment, and therefore it makes good business sense to get a full life expectancy out of the unit. Increased temperatures result in accelerated aging rates, and therefore a lower return on investment. The “normal rating” represents the load limit for continuous operation.

As a guideline, the following procedure for initial rating or re-rating of a transformer is proposed.

- Normal life-expectancy loading

Long-Term Emergency The definition of a long-term emergency rating (LTE) varies within the industry. Typically, it denotes a rating where the thermal capacity of the equipment does not greatly impact the rating. For power transformers, the

Figure 4.5-2 Example plot of rating vs. pre-load for various rating durations.

Rating Procedure

1. Gather information Information essential to the loading calculations must be gathered. This information must include, at minimum, the factory test report and the nameplate drawing. It is highly recommended that maintenance history (DGA, oil quality, etc.) and loading history be obtained. Outline drawings may be of use as well. 2. Assess condition The full scope of this step is beyond this guide; however, it is important to recognize the importance of condition. Guidelines for condition assessment with regard to loading are given below.

Figure 4.5-3 Example 4 Hr STE rating.

4-35



3. Examine long-term risks When considering a particular loading event, the first things examined are the long-term risks. This mainly consists of evaluating the loss of insulation life outlined above. This is an economic decision, balancing the cost benefit of the increased load levels with the decreased return on capital investment. If the loading is short duration, the loss of life may be negligible, and therefore the only concern is avoiding immediate failure. 4. Examine short-term risks If the increased life consumption is acceptable, the concern then shifts to avoiding immediate failure. This means limiting operating temperatures, particularly hot spot temperature. 5. Check auxiliary equipment Most of the attention when presented with a potential overload scenario is on the oil and winding temperatures. However, the auxiliary equipment (bushing, LTCs, etc.) should not be neglected. While these should be sized properly to avoid limiting the transformer rating, this is not guaranteed. Before proceeding with increased loading, it is often advisable to verify the thermal capability of these devices. 6. Follow-up post loading Once the decision has been made to permit with increased loading, any significant overload events should be followed up with a site inspection and oil analysis. This should be done to verify that there were no unintended consequences of the increased loading event and to determine suitability for future overload. 4.5.5

Condition-Based Loading

Rather than proposing a static set of limits for various loading situations, a condition-based methodology is presented here. Limits are first given for healthy transformers. These are to be viewed as maximum limits.

These maximum limits are then reduced based upon the assessed condition of the unit. Conditions necessitating the reduction of the temperature limits include:

• • • •

moisture content of bulk insulation oxygen content gassing history criticality of service

For this guide, three condition categories are proposed: Good, Moderate, and Marginal. Transformers are placed in each category using the several different criteria outlined above. The lowest category for any particular criterion is the category for the unit. For example, if a unit has an Ethylene content of less than 36 ppm, but has a moisture content of 2%, the unit falls in the “Marginal” category (Table 4.5-1). Once the unit has been placed in a condition category, the criticality of service, or the impact of failure, should be considered. If the unit is crucial to system integrity, or is the only GSU for a generation plant with no spare, it may be advisable to use the rating limits for a “Moderate” or “Marginal” unit, even if the condition suggests “Good.” The rating limits for each condition category are given in Table 4.5-2. These should be taken as guideTable 4.5-1 Criteria for Condition Categories Used to Determine Rating Limits Good

Moderate

Moisture

< 0.5%

0.5%-1.5%

Marginal > 1.5%

Oxygen

< 3% TDG

3%-5% TDG

> 5% TDG

Methane

< 120 ppm

120-400 ppm

> 400 ppm

Ethane

< 65 ppm

65-100 ppm

> 100 ppm

Ethylene

< 50 ppm

50-100 ppm

>100 ppm

Table 4.5-2 Condition-Based Rating Limits for Transformers Condition

GOOD

MODERATE

MARGINAL

4-36

Normal

LTE (> 4 hrs)

Top Oil

95

105

STE (< 4 hrs) 110

Hot Spot

120

140

160

LOL (hrs)

24

-

STE (< 4 hrs)

Normal

LTE (> 4 hrs)

Top Oil

95

105

105

Hot Spot

120

130

140

LOL (hrs)

24

-

-

Normal

LTE (> 4 hrs)

STE (< 4 hrs)

Top Oil

95

100

100

Hot Spot

110

120

120

LOL (hrs)

24

-

-


lines and not necessarily as God-given rules. Each user has different policies and risk tolerances. 4.5.6

Maintenance Considerations

Given the multitude of unknowns in loading power transformers, it is essential that increased vigilance be exercised. The reasons for this are twofold. First, the assumptions made in evaluating the risks of loading need to be verified. Second, the unit must be maintained in top working order to prevent conditions that may be exacerbated by increased loading. Throughout the thermal rating process, assumptions are made to turn a problem of enormous complexity into a manageable process. This is what distinguishes engineering from science. The most important of these assumptions are the location of the ther mally limiting temperature near the top of the winding, adequately sized and applied leads, and proper construction and design. These assumptions need to be verified in some manner. Direct measurement of the temperatures of the winding is impossible unless fiber optic probes had been installed during manufacture. Even with the probes installed, this does not preclude the existence of an unintended hot spot elsewhere in the transformer. Increased Preventive Maintenance One often neglected consideration in the loading of transformers is the need for increased maintenance. The cooling equipment must be maintained in top working order. Loss of even partial cooling could be disastrous. If a unit were loaded to the nameplate rating of the highest cooling mode of an OA/FA/FA and all cooling fans were lost, the unit would be overloaded by roughly 66%, resulting in temperatures exceeding 200°C. In addition, various components will age or wear more quickly.

Prior to initial re-rating or increased load, a field inspection should be scheduled. At this time, the unit should be subjected to careful scrutiny. In particular, the following should be checked:

• Make sure all pumps and fans are operational. Manually switch the cooling on and off to ensure proper operation. Listen to the pumps, if possible, for sounds of cavitation. Occasionally, phases on the pumps are reconnected in the wrong phase order, causing the pump to run in reverse. Note the position of all radiator valves. If a radiator or bank of radiators is valved off, do not open the valve. Make a note of this, and derate the unit accordingly.


• Calibrate and check all gauges. This is particularly important if the cooling equipment is switched on/off by the temperature gauges. Oil temperature should be double-checked by placing a handheld thermocouple on the tank wall as close to the thermal well as safety allows. Once the oil gauge has been calibrated, the estimated hot spot temperature should be calculated for the measured top oil temperature and the given load. The ratio of the CT feeding the heating element of the analog WTI (winding temperature indicator) (if equipped) should be adjusted until the gauge reads the calculated value. Finally, check that all snap switches or setpoints for cooling switching and alarms are properly set. Be sure the alarm and trip settings coincide with appropriate rating limits. Calculated ratings do no good if the unit will trip at lower temperatures!

• Check the oil level. Make sure the oil is at the level specified in the operating manual for the measured oil temperature. As mentioned previously, oil will expand with increasing temperature. Too much oil will result in operating of the pressure relief device and expulsion of oil. Too little oil could result in exposing the active assembly upon cooling.

• Check all gasketed surfaces for leaks. Specifically, check the bushings, both at the tank cover and at the top of the bushing, and any other tank penetrations. Gaskets in particular will harden and become brittle more rapidly than at normal operating temperatures. As this happens, the gaskets can begin to leak, resulting in reduced oil levels and ingress of moisture and oxygen. Should this occur, the unit must then be taken out of service at some point to replace the gaskets. If this occurs with sufficient frequency, it may be advisable to replace the gaskets with a higher temperature material such as Viton.

• Check the tank wall for discolored paint. Areas of high temperatures due to stray flux heating in the tank wall may result in noticeable discoloration of the paint. Pay close attention to bushing penetrations.

• Check conservator and gas blanket systems. Make sure the oil conservator, if equipped, is filled to the proper level and all piping is leak free. Make sure any desiccant canisters are filled with a suitable desiccant. If equipped with an inert gas blanket system, make sure that the pressure regulator is operating properly and that sufficient gas quantity is available in the canister. Gas over-pressure can cause supersaturation of the oil at high temperatures. Upon cooling, the gas would come out of solution and free bubbles would form.

• Check the LTC for proper operation, if equipped. If possible, measure the temperature of the LTC compartment oil. If the differential between the LTC oil

4-37


and the main tank exceeds 15°C, consider scheduling an outage to investigate the cause. If system conditions permit, consider cycling the LTC throughout the tap range, in particular exercising the reversing switch.

• Draw an oil sample for DGA and oil quality. Safe overloading requires the oil to be in good condition. In addition, DGA provides a useful tool for spotting lead heating or stray flux heating problems, or any other unknown thermal conditions. In addition, units with possible incipient problems should never be considered for overload. If an evaluation of insulation condition with respect to thermal aging is desired, Furan analysis could be performed as well. The above checks should be repeated as part of a preventive maintenance program at the usual scheduled interval. If a unit is frequently loading near or above nameplate, and increased preventive maintenance schedule should be considered. In addition, following more severe emergency overloads, a site inspection should be scheduled at the earliest convenient time to ensure that no damage was done and that the unit is operating normally. 4.6

WINDING TEMPERATURE MEASUREMENT

Temperature monitoring and measurement is an important tool in loading power transformers. It provides feedback on the cooling performance of the transformer, confirmation of calculated temperatures, and a reliable assessment of the current operating condition of the transformer. That said, accurate temperature measurement is difficult and can be expensive. Depending upon the technology, it may not be economical for smaller units. Simulated WTI Simulated WTIs (winding temperature indicators) are by far the most common devices for measuring winding temperatures (Figure 4.6-1). In reality, however, these devices do not actually measure the winding temperature. They simply measure the temperature of a specially calibrated heating element that is immersed in the top bulk oil near the tank wall. These devices simulate the actual winding temperature.

These most common analog devices consist of a brass tube, or well, that is mounted on the side of the tank, such that it is immersed in the top oil. A separate heating element is the placed in the tube, and a current proportional to the winding current is passed through the heating element. This current produces a temperature rise that, at rate load, equals the expected hot spot temperature.

4-38


Since these devices do not directly measure the winding temperature, they are inherently inaccurate. The thermal characteristics of the devices do not exactly match that of the transformer windings. At higher loads, the error can be significant. In addition, these devices have a longer time constant, making them inaccurate during transient shifts in load (Teetsel 2003). This can be significant, especially if the cooling equipment is switched by the WTI temperature. Fiber Optic Temperature Measurement First introduced in the early 1980s, use of fiber optic temperature probes provides a method for direct temperature measurement of a point on the surface of the winding insulation. This is possible due to the inherent dielectric strength of the silica fiber optic material. There are essentially two viable competing technologies in this area: fluoroptic thermometry and abortion shift of GaAs semiconductor.

Fluoroptic thermometry probes utilize a phosphor coating at the tip. When the coating is excited with a pulse of light sent down the fiber optic, the coating fluoresces. The rate of decay of this fluorescence is temperature dependent. Therefore, by measuring the rate of decay at the far end of the fiber optic, the temperature of the probe tip can be determined. GaAs semiconductor devices utilize a GaAs semiconducting wafer topped with a reflective coating at the end of the probe. A pulse of white light is sent down the fiber, passing through the GaAs wafer. Some of the light is absorbed by the GaAs, while the remainder passes through and reflects off the reflective coating. The light then returns down the fiber where the magnitude of the received light is measured for the various wavelengths of the spectrum of the light pulse. Light at different wavelengths is absorbed by the GaAs, with the magnitude at a particular wavelength a function of temperature of the GaAs semiconductor. Therefore, the absorption spec-

Figure 4.6-1 Schematic drawing of winding temperature indicator.



trum is a function of the temperature of the GaAs. The characteristic curve of the absorption spectrum shifts toward higher wavelengths with increasing temperatures. By measuring the shift in the absorption spectrum, the temperature of the probe is determined.

• retrofit radiators or heat exchangers with higher cool-

Regardless of the technology used, fiber optic temperature probes have a few significant disadvantages. First, these probes must be installed during manufacture. The probes must be inserted in the winding at the expected hot spot location. Since this location is difficult to pinpoint, several probes at different locations must be used. In addition, hot spot locations can move with differing oil flow regimes, making precise hot spot determination impossible. These probes are also extremely delicate. Even with the newer, ruggedized probes, breakage often occurs. The manufacturer must take extra precautions during winding and final assembly not to break the fibers. This in turn increases the cost of manufacture for the unit as a whole. The measuring units for reading the probes are also rather expensive, making them economical only for larger, critical units.

All of the methods listed above increase the heat transfer from the oil to the surrounding environment. The effect would then be to decrease both the average oil rise and the top-to-bottom oil gradient. In non-directed flow designs, this reduction in oil temperature increases the thermal pressure of the natural thermosiphon flow through the windings. Assuming that the duct size is not limiting the oil flow in the area of the hot spot, the hot spot temperature is then decrease.

4.7

MODEST INCREASES IN CAPACITY FROM EXISTING TRANSFORMERS

When additional capacity is required, and higher temperatures are not practical or acceptable, there are limited options for increasing the rating of a transformer by adding additional cooling. This can be effective to some extent, but care must be taken to ensure that the winding hotspot is not excessive. There are essentially two ways to reduce transformer temperatures: reduce the losses or increase the heat transfer. The former would require a redesign and rewind of the transformer and is therefore not economical unless the unit is already being rewound following a failure. Even then, other design constraints will limit the amount of additional capacity. The only viable option is, therefore, to increase the heat transfer. To be cost effective, any cooling upgrades must be installable in the field. This precludes any internal modifications. Additional pumps and fans may be added, with limited increase in capacity. There is a practical maximum to pump flow rates or fan capacities, above which there will be no increase in heat transfer. For units employing heat exchangers, larger heat exchangers may be added if the cost of the retrofit is justified by the increased capacity. Methods of increasing the cooling capacity include:

• addition of fans, or higher flow rate fans, to radiators or heat exchangers

ing capacity units

• water spray cooling over radiator fins • retrofit with oil-water heat exchangers

However, this leads to a major caveat in the application of supplemental cooling: the drop in oil temperature does not necessarily give a corresponding drop in the hot spot temperature. In other words, if the oil temperature is reduced 10°C, the hot spot temperature will be reduced somewhere between 0 ° and 10 ° C. Without detailed design data or embedded fiber optics, it is impossible to determine the actual decrease in hot spot temperature. Therefore, the excess capacity, if any, gained by applying supplemental cooling should not be relied upon for planning or operating purposes unless the manufacturer has reviewed the application. 4.8

EXAMPLES

Example 1:

This first example will illustrate a simple 6 hr transient rating with a flat preload and load cycle, followed by a 6 hr transient rating with a cyclical preload and load cycle. The unit is a 220/69-kV autotransformer rated at 224 MVA with directed forced-oil cooling (DFOA). For this unit, the bottom oil temperature rise at rated load is known, so the more accurate IEEE Annex G model is used. The parameters for the thermal calculation are as shown in Table 4.8-1. As mentioned previously, the preload and load cycles are flat. A flat preload enforces a conservative assumption that the transformer temperatures have reached steady-state (and therefore the maximum) prior to the onset of the contingency. The contingency onset is assumed to occur at 12 pm to coincide with the peak ambient. The load shape during the contingency is also assumed to be flat, again giving a conservative answer (Figure 4.8-1). The ambient temperature used for the calculation is a representative peak day for the summer months measured at the substation. This represents the worst-case 4-39



scenario where the contingency occurs on the hottest day of the season (Figure 4.8-2). This particular unit was manufactured in 1997 and is in good working order. Therefore, the temperature limits Table 4.8-1 Parameters for Example 1 MVA Base for Loss Data

200

Temperature Base for Loss Data

75

C

525072

W

Winding I2R Losses

MVA

Winding Eddy Losses

0

W

Stray Losses

0

W

Core Losses

54560

W

Cooling Mode Type

ODAF

Nameplate MVA

224

MVA

Guaranteed Average Winding Rise

65

C

Rated Average Winding Rise

50.6

C

Rated Hot Spot Rise

62.2

C

Rated Top Oil Rise

32.2

C

Rated Bottom Oil Rise

29.2

C

30

C

Rated Ambient Temperature Winding Conductor

Copper

Per Unit Eddy Loss at Winding Hot Spot

0

Winding Time Constant

5

Per Unit Winding Height to Hot Spot

1

min

Weight of Core & Coils

225500

lbs

Weight of Tank & Fittings

102600

lbs

Fluid Type

Mineral Oil

Oil Volume

21696

for this LTE rating shall be set at 140 hot spot temperature and 110 ° C top oil temperature. Given the above load and air temperature cycles and the temperature limits, the load over the 6 hour rating interval is increased until either the hot spot temperature or the top oil temperature meets the temperature limit. This is demonstrated in Figure 4.8-3. The 6 hr LTE rating for this specific scenario is 278 MVA. In the above scenario, the conservative approximation of assuming a flat preload and load cycle was used. Where the load follows a predictable cyclical pattern, increased capacity can be safely realized by using the actual load shapes. Recalculating the rating above utilizing the preload and load cycles, shown in Figure 4.8-4, reveals a slight increase in the rating from 278 MVA to 291 MVA. Note that the preload in this example peaks higher at 0.88 pu than the flat preload of 0.7 pu assumed above. However, the preload is below 0.7 the majority of the 24 hour cycle, with an average load of 0.53. Given the thermal time constant of the transformer bulk oil, the operating temperatures with a diverse load shape will be fractionally less than the temperatures with a flat load shape (Figure 4.8-5).

gals

Load (Per Unit)

Load 1.4 1.2 1 0.8 0.6 0.4 0.2 0 0

10

20

30

40

50

60

Time (hrs)

Figure 4.8-3 Calculated transformer temperatures for Example 1.

Figure 4.8-1 Preload and load cycle for Example 1. Load 35

Load (Per Unit)

Ambient Temp (deg C)

Ambient Temperature 30 25 20 15 10 5

1 0.8 0.6 0.4 0.2 0 0

0

10

20

30

40

50

60

Time (hrs) 0

10

20

30

40

50

Time (hrs)

Figure 4.8-2 Air temperature cycles for Example 1.

4-40

1.4 1.2

60

Figure 4.8-4 Preload and load cycles for Example 1 with cyclical load.



Example 2

This second example will answer a question: A substation transformer is feeding a circuit in parallel with two other transformers. One of the three transformers must be removed from service for 48 hours. Can the remaining two units handle the increased load safely? The unit in this example is a 220/138-kV autotransformer rated at 180/240/300MVA OA/FA/FA. Again, the Annex G model is used with the parameters shown in Table 4.8-2. The predicted load for the days of the outage is shown in Figure 4.8-6. The lower curve shows the predicted load with all units in service. The upper curve shows the load with two units in service. Figure 4.8-7 shows the

predicted air temperatures in the vicinity of the substation for the 48 hour period under question. Figure 4.8-8 reveals that the hot spot temperature peaks at about 140 ° C and the top oil temperature reaches approximately 100°C. Given the short duration of the event, these temperatures should be safe, assuming the in-service units are in good working order.

Table 4.8-2 Parameters for Example 2 MVA Base for Loss Data

180

Temperature Base for Loss Data

65

C

146265

W

Winding Eddy Losses

0

W

Stray Losses

0

W

Core Losses

47894

W

Winding I2R Losses

Cooling Mode Type

FA

Nameplate MVA

336

Guaranteed Average Winding Rise

55

C

Rated Average Winding Rise

53.6

C

Rated Hot Spot Rise

68.6

C

Rated Top Oil Rise

38.2

C

Rated Bottom Oil Rise

12.4

C

40

C

Rated Ambient Temperature Winding Conductor

Figure 4.8-5 Calculated transformer temperatures for Example 1 with cyclical load.

Load (PU)

Load (Per Unit)

Load

Original Load

1.4 1.2 1 0.8

MVA

MVA

Copper

Per Unit Eddy Loss at Winding Hot Spot

0

Winding Time Constant

5

Per Unit Winding Height to Hot Spot

1

min

Weight of Core & Coils

190600

lbs

Weight of Tank & Fittings

145750

lbs

Fluid Type

Mineral Oil

Oil Volume

26973

gals

0.6 0.4 0.2 0 0

10

20

30

40

50

60

Time (hrs)

Figure 4.8-6 Predicted load during outage for Example 2.

Ambient Temp (deg C)

Ambient Temperature 50 40 30 20 10 0 0

10

20

30

40

50

Time (hrs)

Figure 4.8-7 Predicted air temperature for outage.

60

Figure 4.8-8 Calculated transformer temperatures during outage

4-41


Insulation Aging Age Acceleration Rate

250

25

200

20

150

15

100

10

50

5

0

0 0

10

20

30

40

50

Time (hrs)

Figure 4.8-9 Insulation aging during outage.

4-42

60

Age Acceleration Rate

Total Aging (hrs)

Cumulative Aging (hrs)

Figure 4.8-9 shows the cumulative aging during the outage, in hours, for the in-service units. The total aging over the 48 hour period is approximately 220 hours. If this event is relatively rare, this increased aging should be acceptable over the expected 180,000 hour life of the unit.



REFERENCES

Aubin, J. and T. Langhame. 1992. “Effect of Oil Viscosity on Transformer Loading Capability at Low Ambient Temperatures.” IEEE Trans. on Power Delivery. Vol. 7. No. 2. pp. 516-524. April. Cengel, Y. A. 1997. Introduction to Thermodynamics and Heat Transfer. McGraw-Hill. Boston, MA. Dakin, T. W. 1948. “Electrical Insulation Deterioration Treated as a Chemical Rate Phenomenon.” AIEE Transactions. Vol. 67. pp. 113-122. November. Emsley, A. M. and G. C. Stevens. 1994. “Review of Chemical Indicators of Degradation of Cellulosic Electrical Paper Insulation in Oil-filled Transformers.” IEE Proc. Sci. Meas. Technol. Vol. 141. No. 5. pp. 324-334. September. IEC. 1991. IEC 60354: 1991. Loading Guide for Oilimmersed Power Transformers. January. IEC. 2004. IEC 60076-7. Power Transformers – Part 7: Loading Guide for Oil-immersed Power Transformers. Committee Draft 2. IEEE. 1995a. Standard Requirements for Load Tap Changers. IEEE Standard C57.131-1995. March. IEEE. 1995b. Guide for Loading Mineral-Oil-Immersed Transformers. IEEE Standard C57.91-1995. June. IEEE. 1995c Guide for Application of Power Apparatus Bushings. IEEE Standard C57.19.100-1995. August.


Lesieutre, B. C. Hagman, W.H. and J. L Kirtley Jr. 1997. “An Improved Transformer Top Oil Temperature Model for Use in An On-Line Monitoring and Diagnostic System.” IEEE Trans. on Power Delivery. Vol. 12 No. 1. pp. 249-256. McNutt, W. J. 1992. “Insulation Thermal Life Considerations for Transformer Loading Guides.” IEEE Transactions on Power Delivery. Vol. 7. No. 1. pp 392401. January. Montsinger, V. M. 1930. “Loading Transformers by Temperature.” Trans. AIEE. Vol. 49. pp 776-790. Montsinger, V. M. 1951. Transformer Engineering. John Wiley & Sons. New York. pp. 275-351. Pierce, L. W. 1992.“An Investigation of the Thermal Performance of an Oil Filled Transformer Winding.” IEEE Trans. on Power Delivery. Vol. 7. No. 3. pp. 13471358. July. Pierce, L. W. 1994. “Predicting Liquid Filled Transformer Loading Capability.” IEEE Trans. on Industry Applications. Vol. 30. No. 1. pp. 170-178. January/February. Schroff, D. H. and A. W. Stannett. 1985. “A Review of Paper Ageing in Power Transformers.” IEE Proc. Vol. 132. Pt. C. No. 6. pp. 312- 319. November. Teetsel, M. 2003. “Winding Temperature Measurement: Techniques, Devices and Operation.” From presentation before IEEE/PES Transformers Committee. October.

Lundgaard, L., W. Hansen, D. Linhjell, and T. Painter. 2004. “Ageing of Oil Impregnated Paper in Power Transformers.” IEEE Trans. on Power Delivery. Vol. 19. No. 1. pp. 230-239. January.

4-43


CHAPTER 5


5.1

INTRODUCTION

In comparison to overhead lines, underground cables, and power transformers, substation terminal equipment is usually much less expensive to replace, and since terminal equipment is within the utility substation boundaries, its replacement does not require public hearings or regulatory approval. Nonetheless, in many cases, the benefits of increasing the rating of lines, cables, and transformers may be limited by one or more breakers, line traps, or current transformers, and replacement of such equipment can be both time consuming and disruptive due to required circuit outages. Finally, just as with lines, cables, and transformers, when relatively modest increases in terminal equipment rating are required, more detailed knowledge of thermal behavior can often be obtained quite easily. Substation terminal equipment consists of many different types and designs of power equipment. Included in this classification are line traps, oil circuit breakers, SF6 circuit breakers, rigid tubular bus, line disconnects, current transformers, bolted connectors, and insulator bushings. In a recent Electra article entitled “Dynamic Loading of Transmission Equipment – An Overview” (CIGRE 2002), representatives of Study Committee 23 concluded, “there is scope for implementing dynamic loading principles for a wide range of transmission assets.” The need for increased power flow in substation terminal equipment is illustrated in Figure 5.1-1 taken from (New York Power Pool 1982). It shows that the thermal rating of over 50% of the transmission circuits in New York State are thermally limited by substation equipment.

Figure 5.1-1 Thermally limiting transmission circuit equipment. 5-1

Chapter 5: Substation Terminal Equipment

The increase in circuit rating, resulting from applying the various methods of increasing power flow in overhead transmission lines, underground cable, and power transformers is often limited by terminal equipment, as shown in Figure 5.1-2. This figure illustrates the unexpected conclusion that relatively modest investments in terminal equipment (replacement of the CT in Circuit A) yields an increase in that circuit rating and a 50-MW increase in the rating of the complex interface. Here a large increase in circuit rating is obtained for a very modest expenditure on terminal equipment rather than a relatively large investment in lines, cables, or transformers. This chapter is limited to studying practical, rather simple methods of increasing the power flow through less capital-intensive equipment such as switches, bus, line traps, breakers, and power transformer auxiliary equipment. Because the substation equipment being uprated is generally less expensive to replace than lines, cables, and transformers, some of the more elaborate methods of monitoring are difficult or even impossible to justify economically. Also, because of the large number of switches, circuit breakers, etc., in any power system, and the variety of designs, both the thermal models that represent the equipment and the requirements for weather monitoring must be kept simple.


This chapter includes four sections:

• Section 5.2, Summary: Equipment Types and IPF Opportunities, is a summary of terminal equipment types, their thermal response to changes in weather and current, and the risks associated with high current loading.

• Section 5.3, Thermal Models for Terminal Equipment, describes specific thermal models for each type of equipment and suggests common limits on temperature.

• Section 5.4, Uprating of Substation Terminal Equipment, reviews dynamic thermal rating of terminal equipment, including a discussion of the need for weather and load data.

• Section 5.5, Thermal Parameters for Terminal Equipment, describes methods of determining specific thermal parameters from field test, laboratory test, and manufacturer heat-run tests. 5.2

SUMMARY—EQUIPMENT TYPES AND IPF OPPORTUNITIES

Substation terminal equipment includes a wide variety of equipment types with varying opportunities for increased power flow. This section provides a broad overview of the types of equipment that might limit power circuit thermal ratings. 5.2.1

Equipment Rating Parameters

For each type of terminal equipment, the following issues are compared:

• Primary reasons for temperature and deterioration limits

• • • • •

Type of thermal model used in rating calculations Consequences of over-temperature Degree of thermal interaction with other equipment Sensitivity to weather parameters Response to short-time emergency loads

The comparisons included here are not intended to be exhaustive, but rather to be an initial guide as to what can be expected to result from the various methods of increasing power flow.

Figure 5.1-2 Diagram showing the limiting element for each of multiple circuits making up a complex power flow interface. The total interface transfer limit is shown at the top labeled “Transfer (MW)”. Note that replacing the CT in Circuit A yields an increase in the transfer limit from 450 to 500 MW! (Diagram courtesy of N. Dag Reppen, Niskayuna Power Consultants, Inc.)

5-2

Temperature and Deterioration Limits Manufacturers of terminal equipment usually follow ANSI or IEEE or IEC standard recommendations with regard to maximum operating temperatures of substation terminal equipment. One clear exception is bus. While there are manufacturing standards for strain bus and tubular bus, temperature limits and thermal models are not typically included in the standards.



One obvious way to increase the rating of substation terminal equipment involves the use of higher than recommended equipment component temperatures, especially when this is done for limited periods of time and when such events occur infrequently. However, when the exceedence of normally recommended maximum equipment temperatures are to be allowed, the consequence of such events on the life and proper function of terminal equipment must be known. Thermal Models Thermal models for substation terminal equipment fall into one of two categories. The first category is similar to the power transformer “top oil” model (see Chapter 4). In this “ambient-adjusted” model, the temperature rise above ambient for critical components of the equipment (e.g., switch contact temperature), determined by reference to the appropriate standard, by a manufacturer test report (if available), or by field or laboratory measurement, is specified for a known current (typically the rated current of the equipment). This “reference” temperature rise is then adjusted for other currents according to an equation of the form:

⎛ I2 ⎞ ⎟ ⎝ IR ⎠

2n

θ2 = θR ⎜

5.2-1

Where: θ2 is the temperature rise to be calculated. θR is the “reference” temperature rise. I2 is current for which the temperature rise is to be calculated. IR is the “reference” current which causes θR. n is an exponent, generally close to 1.0. The second category of thermal model consists of an actual heat balance similar to that used for overhead lines and underground cables. In this model, the temperature rise is calculated with a heat balance equation of the form:

I 2 R + qs = qr + qc

5.2-2

Where: I is current in amps. R is the ac resistance of the component. qs is the solar heat gain. qr is the radiation heat loss. qc is the convective heat loss. With either sort of thermal model, heat storage in the equipment can be included in order to simulate transient thermal response to changes in current flow. Circuit breakers, CTs, and line traps are usually modeled with the “ambient adjusted” thermal model. Strain

and tubular bus, bolted connectors are usually modeled with the heat balance approach. Switches and line traps can be modeled either way, but the heat balance approach usually requires too many dimensional and material parameters to be practical. Determination of Equipment Thermal Parameters As discussed in Section 5.5, the determination of other than default thermal parameters for substation terminal equipment is one of the most challenging parts of determining and increasing power flow through them. Unlike power transformers, for which certified heat run data is typically available, thermal test data from the manufacturer is seldom required by the utility and, if it was originally supplied, it may no longer be available for older equipment. For newer equipment, it should be possible to obtain documentation of a thermal design test. This documentation will contain measurements of the temperature rises above ambient of critical equipment parts at rated current. Thermal time constants and exponents are not typically available and must be determined by measurement or assumed. Estimate and Consequences of Over-temperature Unless one chooses to be extremely conservative, the magnitude and consequences of equipment over-temperature must be evaluated when rating substation equipment. For example, strain bus is seldom rated for still air conditions, because this would yield extremely low thermal ratings. But when strain bus is rated at 100oC on the basis of a 3-foot-per-second crosswind, then the temperature that it might obtain under still air conditions (the “temperature rise”) must be estimated, and the consequences of occasionally attaining such a temperature on bus strength and clearance evaluated. Degree of Thermal Interaction with Other Equipment Spacing of equipment in most substation designs is driven by electrical clearance considerations. At distances sufficient to meet these electrical clearance needs, there is little or no thermal interaction by means of convection or radiation. On the other hand, substation equipment is connected by electrical conductors that may conduct heat as well as current. The source of such heat may be either other electrically connected equipment or the conductor itself. Fortunately, the conduction of heat between equipment by means of typical bus conductors is unlikely to be significant. The impact of heat from conductors that are themselves hot, however, is a source of concern. Sensitivity to Weather The thermal rating of most substation equipment is sensitive to air temperature, solar heating, and wind speed and direction. Nonetheless, within the typical substation, because of the many equipment orientations and

5-3



the degree of sheltering by other equipment and buildings, determination of reasonable values for solar heating, wind speed, and wind direction is very difficult. Air temperature, on the other hand, is easily determined for all equipment at a particular location. Therefore, with the possible exception of strain and rigid bus work, wind and solar effects are typically ignored. Response to Short Time Emergency Overloads In transmission power systems, normal power flows in most circuits are modest (i.e., less than 30% of the circuit thermal capacity). This occurs because the system must be capable of transmitting sudden increases in power flows due to the sudden loss (outage) of key components (e.g., generators and bulk transmission circuits). In order to limit the magnitude of such sudden “emergency” loads, the operator may intervene within a short period of time (e.g., 15 minutes) in order to reduce power flow levels to normal continuous ratings or below. In such situations, short-time emergency ratings of substation terminal equipment may be useful. Two factors determine the short-time emergency (STE) rating of substation terminal equipment (and other power equipment). These factors are the equipment’s thermal time constant and its ability to withstand occasional high temperature events with an acceptable degree of deterioration. The thermal time constant is defined as that time, after a sudden increase in electrical current, after which the equipment temperature rise equals 63% of that which will ultimately occur if the new higher load continues indefinitely. An example of with-

standing occasional high temperature exposure is the aging of free-standing current transformer insulation, which may shorten the life but not cause short-term catastrophic failure. Maximum Multiple of Nameplate Rating For short-time and long-time emergency ratings, the thermal rating calculation formulas may allow for operation at many times the continuous “nameplate” rating, but there may be perfectly good engineering reasons to limit these transient rating to a multiple of the nameplate rating. For example, this is done with power transformers, which are normally limited to 200% of nameplate regardless of the STE or long-time emergency (LTE) rating calculations. 5.2.2

Thermal Rating Parameter Comparison

Tables 5.2-1 and 5.2-2 compare thermal rating parameters of substation terminal equipment. 5.3

THERMAL MODELS FOR TERMINAL EQUIPMENT

As noted in the preceding section of this chapter, there are many types and designs of terminal equipment, and detailed thermal test data, particularly for older equipment, is unlikely to be available. As a result, simplicity is preferred in modeling terminal equipment. 5.3.1

Bus Conductors

Bus conductors in substations come in a wide variety of sizes and types. To keep things reasonably simple, three

Table 5.2-1 Summary of IPF Characteristics for Substation Terminal Equipment (Part I) Substation Terminal Equipment Type

Temperature or Temp Rise Limits (oC)

Thermal Models

Consequence of Over- Thermal Interaction with Temperature Other Equipment

Strain Bus

75 to 125 (cont.)

Heat balance

Loss of strength, sag clearance

Possible

Rigid Bus

75 to 125 (cont.)

Heat balance

Loss of strength

Possible

Switches (Air Disconnects)

70/93 rise normal 105/120 rise LTE

Ambient Adjusted

Contact damage, annealing of parts

None

Line Traps

90 to 115 rise (cont.)

Ambient Adjusted

Damage to Insulation or reduction in tensile strength of aluminum

None

Bushings

150 conductor temp

Adjusted for top oil of PT or OCB.

Reduction in insulation life, overpressure, gasket deterioration

Directly influenced by oil temp in OCB or PT

CTs - Bushing

120 hot spot


Decrease in insulation life

Can be directly influenced by oil temp in OCB or PT

CTs – Free-standing

45 rise oil 55 to 80 winding rise.

PT model, ambient adjusted

Decrease in insulation life

None

Circuit Breakers

90 (metal in oil) 80 (top oil)

Ambient Adjusted

Damage to contacts, annealing of parts

None

Current Limiting Reactors

55 or 80 rise

Ambient Adjusted

Damage to insulation

None

5-4



Table 5.2-2 Summary of IPF Characteristics for Substation Terminal Equipment (Part II) Substation Terminal Equipment Type

Sensitivity of cont. rating to air temp. (% change per oC)

Practical Sensitivity to weather

Thermal Time Constant (min)

Strain Bus

Wind speed and direction, air temp, solar heating

5 to 15

0.6% to 0.8% 10% per fps wind

None

Rigid Bus

Wind speed and direction, air temp, solar heating

10 to 30

1.0% to 0.8% 10% per fps wind

None

Switches (Air Disconnects)

Air temp

30

0.8% for new 53oC rise 1.2% for older 30oC rise

200%

Line Traps

Air temp

15

0.2%

None

Bushings

Indirectly through transformer or breaker oil temperature


Reduction in insulation life

Directly influenced by oil temp in OCB or PT

CTs - Bushing

Air temp

15

Same as PT

Same as PT

Maximum Multiple of Nameplate

CTs – Free-standing

Air temp

15

Similar to PTs with OA cooling.

Circuit Breakers

Air temp

30

1%

200%

15 to 30

0.8% for 55oC rise 0.4% for 80oC rise

200%

Current Limiting Reactors (Dry-type)

Air temp

types of substation bus are recognized: rigid bus, strain bus, and jumpers:

• Rigid bus is normally tubular, functionally similar to copper or aluminum conduit or pipe, but some older rigid bus may be square or “L” shaped in cross-section.

• Strain bus is under tension (thus the name “strain”), and usually identical to stranded conductor used in overhead transmission lines. It usually is stranded aluminum wires with a steel wire core (i.e., ACSR).

• Jumpers are also made from stranded transmission

qs qr qc qcond

is the solar heat gain (W/m). is the radiation heat loss (W/m). is the convective heat loss (W/m). is heat loss/gain due to conduction (W/m).

One difference between substation bus and overhead lines is that reflected solar heating is negligible for lines, but not for substation bus, where the conductor are somewhat closer to the ground. There are other important thermal rating differences, even for the same conductor applied as substation strain

conductor but are not under tension. The three types of bus conductor are shown in Figure 5.3-1. The thermal model for these bus types are similar to that of an overhead line (CIGRE 1997, IEEE 1993), consisting of a heat balance between Ohmic and solar heat input and convective and radiation heat losses. The steady state temperature given a constant load, ambient temperature, and effective wind speed must be solved by iteration so as to satisfy the following heat balance equation:

I 2 R + qs = qr + qc + qcond

5.3-1

Where: I is current in amps. R is the ac resistance at temperature T in ohms/meter.

Figure 5.3-1 Three types of substation bus conductor.

5-5


bus and as a phase conductor in an overhead line. These differences include:

• The decrease in electrical clearance at high temperature is less likely to be a problem for substation bus where strain bus spans are short.

• The issue of loss in strength due to annealing is less likely to be a concern in bus applications since the increase in tension under ice and wind load is less than for lines.

• High electrical losses in bus are not a concern because of the short length involved.

• Inspection of connectors is much simpler in a substation than in a line, which might be 50 or more miles in length. On the other hand, the temperature attained under high load conditions for both strain bus and line conductors is very sensitive to wind cooling (forced convection). Given these observations, it seems reasonable that substation bus could be rated “less conservatively” than overhead lines. Consider Drake ACSR used as both substation bus and as the phase conductor in a line. One end of the line terminates at the substation with the Drake bus conductor. Assume that both conductors are rated at 990 A for a conductor temperature of 100 o C, wind speed 2 ft/sec perpendicular to the conductor, air temperature of 40oC, and full sun. If the wind drops to 0 ft/sec, the conductor temperature with full rated load would increase to 130oC. This is acceptable in both applications. Now consider the impact of increasing the assumed wind speed from 2 ft/sec wind to 3 ft/sec. The risk associated with this change in the assumed rating conditions appears to be greater for the line than for the strain bus in the substation. Any possible deterioration in the physical conductor and associated hardware is easier to spot by a single trip to the substation. A line inspection is far more expensive, requiring more time and travel. Any permanent increase in sag is a genuine safety concern along the line, not within the substation. Any loss in conductor strength is more likely to result in a high tension failure of the line during the next severe ice storm than in the shorter substation span. Oddly enough, however, substation bus is normally rated more conservatively than lines in terms of weather assumptions. Thus, one simple possible approach to

5-6


increasing power flow in substation bus might be the use of less conservative weather assumptions. 5.3.2

Switch (Air Disconnect)

ANSI standards (ANSI 1979) specify certain requirements for high-voltage air disconnect switches. The standards specify the rated current (thermal rating) of the switch and the weather conditions and equipment temperatures under which the rating is calculated. For example, modern switches, produced after 1971, with silver contacts, are rated for continuous operation at a temperature rise of 53oC, whereas those manufactured after 1971 are rated for continuous operation at a rise of 30oC. In both cases, the continuous rating is calculated for an air temperature of 40oC. A typical, rather simple switch design is shown in Figure 5.3-2. The PJM Interconnection has published detailed rating data (PJM 1999) for air disconnects. The conclusions drawn in the PJM documents reflect the operating philosophy of PJM and should be considered by anyone utilizing the analysis. For example (New York Power Pool 1995), the NY Power Pool (presently NY ISO) utilizes limits of 93oC, 120oC, and 140oC in calculating the rating of pre-1971 air disconnects for normal continuous, long-time emergency (LTE) and short-time emerg e n c y ( S T E ) r a t i n g s. T h e m o s t r e c e n t P J M recommendations are 93oC, 115oC, and 125 oC for the same ratings. The PJM standard also considers the temperature of conducting material joints, switch terminals with bolted connections, and flexible connectors. The PJM discussion also considers annealing of copper and aluminum component parts as a factor in high-temperature limits, while the NY ISO discussion does not.

Figure 5.3-2 Typical air disconnect (switch).



Simple Dynamic Rating Switch Model The adjustment of steady-state switch rating, IR, with air temperature, TA, may be approximated as follows: 1

⎛ T − TA ⎞ 2 I2 = IR ⋅ ⎜ R ⎟ ⎝ TR − 40 ⎠

5.3-2

Table 5.3-1 shows the variation of steady-state switch rating with air temperature, using this simple equation. Notice that the variation in the rating of the newer switches, having a higher allowable contact temperature rise over air temperature, is less. In any event, Table 5.3-1 indicates that the switch rating can be 5% to 20% higher on a cool day. The following, more general equations, are given in ANSI C37.30. They allow adjustment of manufacturer nameplate rating for both steady-state and transient loads. The critical contact temperature may also be tracked with these equations as load and air temperature vary over time.

θ2 is the contact temperature rise at the present time step, t2. TA is the ambient temperature. θ1 is the contact temperature rise at the previous time step, t1. Δt is the time step. τ is the switch thermal time constant (default 30.0 min). The switch rating can be determined by one of several “observable temperature” rises with different limiting temperatures. It seems likely that the switch contacts will most often be the limiting temperature. In addition, it must be assumed that the contacts are kept in good condition such that there is not an appreciable increase in contact resistance. Thermodynamic Dynamic Rating Switch Models As part of the development of the EPRI DTCR software, thermodynamic models of certain switches were developed (Coneybeer 1992) and verified through laboratory testing. For example, Figures 5.3-3, 5.3-4, and 5.3-5 show a comparison of contact temperature mea-

1

⎛ T − TA ⎞ 2 n I2 = IR ⋅ ⎜ R ⎟ ⎝ TR − 40 ⎠ ⎛ I2 ⎞ ⎟ ⎝ IR ⎠

5.3-3

2n

θU = θ R ⎜

5.3-4

θ 2 = θ1 + (θU − θ1 ) (1 − e

−Δt τ

)

5.3-5

T2 = TA + θ 2

5.3-6

Where: θU is the ultimate contact temperature rise. θR is the rated contact temperature rise. I2 is switch current at the present time step, t2. IR is the rated switch current. n is an exponent, generally between 0.7 and 1.0 (default 0.8).

Figure 5.3-3 Laboratory current step-sequence for switch tests.

Table 5.3-1 Impact of Air Temperature on the Normal Rating of Air Disconnects

Ambient Temperature (oC)

Thermal Rating (53°C rise in silver contact temp) %Nameplate (after 1971)

Thermal Rating (30°C rise in silver contact temp) %Nameplate (before 1971)

45

95

91

40

100

100

35

105

108

30

109

115

25

113

122

20

117

129

Figure 5.3-4 Comparison of laboratory measurements of contact segment temperature to IEEE/ANSI and EPRI Dynamp thermodynamic model with adjusted parameters.

5-7



In addition, the laboratory testing of an old weathered switch with contacts that were in poor condition showed that the ANSI/IEEE model (or presumably the Dynamp thermal model with default parameters) underestimated the contact temperature, as shown in Figure 5.3-4. The good agreement between the measured temperature and the EPRI Dynamp thermal model was accomplished by noting the poor condition of the switch contacts and adjusting the parameters accordingly—hardly a practical solution to a “bad” switch. In reality, this switch should have been de-rated or replaced if part of a heavily loaded power circuit.

Figure 5.3-5 Comparison of laboratory test results to the ANSI/IEEE model and the EPRI Dynamp thermodynamic model.

sured in a laboratory to temperature calculated with a thermodynamic switch model. The thermodynamic switch model consists of modeling three switch segments separately—the contact segment, the bus bar segment, and the shunt. The model is basically a heat balance much like that used to model a bare overhead line. The detailed model had the advantage that it adjusted ratings for wind cooling, but it had a number of disadvantages, primarily consisting of the requirement for detailed geometrical dimensions and electrical and thermal parameters as illustrated by the following list:

• Outer and inner diameters of the bus segment. • Contact material and surface emissivity/absorptivity. • Switch rated current, contact temperature at rated current, and ratio of contact resistance to that of a new contact.

• Dimensions of contacts. • Shunt material and emissivity/absorptivity. • Shunt width and thickness.

Field Testing of Switches Both as part of the original series of substation terminal tests and as part of more recent field measurements of switch temperature in operating substations, it was concluded that even in heavily loaded circuits, switch temperatures rarely reach levels that allow for meaningful measurements. The older DTCR tests concluded that the temperature rise due to solar heating was generally higher than the temperature rise due to electrical current.

The more recent tests utilized infrared (IR) imaging cameras and prepared (white painted) switch surfaces. It was found that this approach to measurement provides a noncontact measurement of temperature with an accuracy of within 1° to 2° C. The camera used was not unusual, but the experience of the operator was. The primary impediment to field testing involves the relatively low current levels that most switches and other substation equipment experience. At a current equal to 30% of the switch's thermal rating, the temperature rise is only about 10% of the rated rise. 5.3.3

Air-core Reactor

Series-connected air-core reactors are governed by ANSI standards (ANSI 1996, 1965). The rating is limited by the hot-spot temperature rise of the conductor in contact with the insulation or encapsulation material. The limiting temperature varies depending upon the insulation material (as indicated by the temperature index). For specific limits, refer to Table 5.3-2. No therTable 5.3-2 Temperature Limits for Air-Core Reactors

Utility advisors on the project concluded that these requirements were onerous and impractical, given the number of switch designs being used in large utilities. In addition to these problems, the tests indicated that the switch contact temperature calculation was adequately modeled with the simpler ANSI/IEEE equations and with previously developed utility models (Bendo et al. 1979). This is illustrated in Figure 5.3-5.

5-8

Insulation Temperature Index (°C)

Average Winding Rise by Resistance Hottest-spot Winding (°C) Temperature Rise (°C)

105

55

85

130

80

110

155

100

135

180

115

160

220

140

200



mal model is specifically outlined in the applicable standards. The following simple model should reflect a reasonable compromise between accuracy and efficiency. ⎛ I2 ⎞ ⎟ ⎝ IR ⎠

2n

θU = θ R ⎜

5.3-7

θ 2 = θ1 + (θU − θ1 ) (1 − e

−Δt τ

T2 = TA + θ 2

)

5.3-8 5.3-9

Where: θU is the ultimate winding hot spot temperature rise. θR is the rated winding hot spot temperature rise. I2 is winding current at the present time step, t2. IR is the rated current. n is an exponent, generally between 0.7 and 1.0 (default 0.8). θ2 is the winding hot spot temperature rise at the present time step, t2. θ1 is the winding hot spot temperature rise at the previous time step, t1. Δt is the time step. τ is the winding thermal time constant (default 5.0 min). T 2 is the winding hot spot temperature at the present time step, t2. TA is the ambient temperature. 5.3.4

Oil Circuit Breaker

ANSI standard (ANSI 1998) gives an expression for allowable continuous current at different ambients. This expression can be rearranged to give the temperature rise as a function of the current as follows:

The transient formulation is as follows:

θO ,U

⎛I ⎞ = θO ,R ⎜ 2 ⎟ ⎝ IR ⎠

m

(

θO ,2 = θO ,1 + (θO ,U − θO ,1 ) 1 − e ⎛ I2 ⎞ ⎟ ⎝ IR ⎠

−Δt τ O

5.3-11

)

5.3-12

n

θ HS ,U = θ HS ,R ⎜

(

θ HS ,2 = θ HS ,1 + (θ HS ,U − θ HS ,1 ) 1 − e −Δt τ THS ,2 = TA + θO ,2 + θ HS ,2

W

)

5.3-13 5.3-14 5.3-15

Where: θO,U is the ultimate oil temperature rise. θO,R is the rated oil temperature rise. I2 is current at the present time step, t2. IR is the rated current. m is an exponent, generally between 1.5 and 2.0 (default 1.8). θO,2 is the oil temperature rise at the present time step, t2. θO,1 is the oil temperature rise at the previous time step, t1. Δt is the time step. τO is the oil thermal time constant. θHS,U is the ultimate hot spot temperature rise over oil. θHS,R is the rated hot spot rise over oil. n is an exponent, generally between 1.5 and 2.0 (default 1.8). θHS,2 is the hot spot rise over oil at the present time step, t2.

1.8

⎛ I ⎞ ⎟ ⎝ IR ⎠

θC = θC ,R ⎜

5.3-10

Equation 5.3-10 is for steady state. To calculate the temperature during transient loading periods, it is necessary to break the contact temperature rise over ambient into two components with different time constants: contact rise over oil and oil rise over ambient (ANSI 1979). This may cause some difficulty in application, as the rated contact rise over oil may not be available. In addition, an expression or some guidance needs to be developed in estimating the time constant.

Figure 5.3-6 Oil circuit breaker.

5-9



θ2

is the contact temperature rise at the present time step, t2. TA is the ambient temperature. θ1 is the contact temperature rise at the previous time step, t1. Δt is the time step. τ is the breaker contact thermal time constant (default 5.0 min). 5.3.6

Bushings (Oil-immersed Equipment Only)

This model (ANSI 1995a) applies to capacitance graded (condenser) bushings with oil-impregnated paper or resin-impregnated paper. Draw-lead bushing applications are not considered, because the temperature rises will depend upon the size of the draw lead conductor and the amount of insulation on the draw lead. Note that use of this model requires tested values for K1, K2, and n.

Figure 5.3-7 SF6 circuit breaker.

θHS,1 is the hot spot rise over oil at the previous τW THS,2 TA 5.3.5

time step, t1. is the winding thermal time constant (default 5.0 min). is hot spot temperature at the present time step, t2. is the ambient temperature.

SF6 Circuit Breaker

The equations given in (ANSI 1998) and (ANSI 1979) also apply to SF6 breakers. However, whereas it is necessary to divide the contact temperature rise into two components for oil circuit breakers, it should be sufficient to consider only the temperature rise of the contacts over ambient for SF6 breakers. There should be no appreciable thermal capacitance between the contacts and the ambient air.

⎛I ⎞ θU = θ R ⎜ 2 ⎟ ⎝ IR ⎠

2n

θ 2 = TA + θ1 + (θU − θ1 ) (1 − e

5.3-16 −Δt τ

)

5.3-17

Where: θU is the ultimate contact temperature rise. θR is the rated contact temperature rise. I2 is breaker current at the present time step, t2. IR is the continuous current rating of the breaker. n is an exponent, generally between 0.7 and 1.0 (default 0.8).

5-10

Figure 5.3-8 Bushings.



The bushing model is as follows:

θTO ,U

⎛ ( I I )2 R + 1 ⎞ 2 E ,R ⎟ = θTO ,R ⎜ ⎜ ⎟ R +1 ⎝ ⎠

(

5.3.7 m

θTO ,2 = θTO ,1 + (θTO ,U − θTO ,1 ) 1 − e

−Δt τ O

)

5.3-18 5.3-19

Note: Equations 5.3-18 and 5.3-19 are for the calculation of the oil temperature that the bushing is immersed in, and are included for the sake of completeness. Equations 5.3-18 and 5.3-19 can be substituted by simply specifying the oil temperature.

θ HS ,U = K1 ( I 2 I B ,R )

Current Transformers

The rating of CTs can be complex. They are rated according to (ANSI 1993), but unlike other substation terminal equipment, the limits on current are a function of the tap selection and the secondary burden as well as the CT itself. No single set of rating factors can be specified for all applications, even in the same utility substation. To develop continuous ratings, the continuous thermal current rating factor (CTRCF), defined in (ANSI 1993), must be used. The standard does not consider LTE or STE ratings, so these must be determined by nonstandard methods, which should be different for free-standing and for bushing-type CTs.

n

(

θ HS ,2 = θ HS ,1 + (θ HS ,U − θ HS ,1 ) 1 − e −Δt τ THS ,2 = TA + K 2θTO ,2 + θ HS ,2

b

)

5.3-20 5.3-21 5.3-22

Where: θO,U is the ultimate oil temperature rise. θO,R is the rated oil temperature rise. I2 is current at the present time step, t2. IE,R is the rated current of the equipment (transformer, OCB, etc.). m is an exponent, generally between 0.7 and 1.0 (default 0.8). θTO,2 is the oil temperature rise at the present time step, t2. θTO,1 is the oil temperature rise at the previous time step, t1. Δt is the time step. τO is the oil thermal time constant. θHS,U is the ultimate bushing hot spot temperature rise over oil. K1 is constant equal to the rated bushing hot spot rise over oil (15-32). IB,R is the rated bushing current. n is an exponent, generally between 1.6 and 2.0 (default 1.8). θHS,2 is the bushing hot spot rise over oil at the present time step, t2. θHS,1 is the bushing hot spot rise over oil at the previous time step, t1. τb is the bushing thermal time constant (default 5.0 min). THS,2 is bushing hot spot temperature at the present time step, t2. TA is the ambient temperature. K2 is a bushing-specific constant between 0.6 and 0.8.

In general the rating of bushing-type CTs is considered equal to that of the circuit breaker or power transformer in which the CT is installed. If the tap setting on a bushing CT is less than its maximum ratio, then the thermal capacity may be greater than that of the CT when set to its full winding tap position. The adjustment of thermal capacity for tap position can allow operation at currents above the rating for full tap position. For example, at the 50% tap position, the CT rating would be 140% of its full winding position rating. The adjustment of a free-standing CT whose tap position rating is Itap, and whose rated maximum temperature rise is θR, the rating for air temperature (θair), can be obtained in much the standard ambient adjustment method using the tap rating as a basis: 1

⎡ 30 − θ R − θ air ⎤ 2 I = I tap * ⎢ ⎥ θR ⎣ ⎦

5.3-23

Noncontinuous ratings can be calculated based on the power transformer model loading guide with 55oC average winding rise and OA cooling mode parameters. The winding rise exponent of 2 is typically used to be conservative. 5.3.8

Line Traps

Line traps consist of an air-core inductance coil. They are described by reference (ANSI 1981), but the standard does not make rating adjustments terribly clear, and there is some disagreement between sources. Following the method and suggestions outlined in the PJM document on rating of line traps (PJM 1999), suitable temperature limits are a function of the manufacturer as shown in Table 5.3-3.

5-11



Table 5.3-3 PJM Recommended Temperature Limits for Line Traps Line Trap Manufacturer

Limit of Rise for Rated Continuous Current (°C)

Normal Max Temperature (°C)

LTE (>24 hrs) Max Temperature (°C)

STE (<24 hrs) Max Temperature (°C)

GE Type CF (1954-1965)

90

130

145

160

Westinghouse Type M

110

150

165

180

Trench Type L

110

150

170

190

GE Type CF (after 1965)

115

155

170

190

The adjustment of line trap continuous rating for air temperature is obtained using the usual equation form with an exponent of 2.0 in (PJM 1999). Other sources use 1.8. The calculation of an STE rating can be obtained using the temperature limits shown in Table 5.3-3 in an equation of the form similar to transient calculations with other substation terminal equipment. For a 2-hour STE rating with a GE Type CF, pre-1965 line trap, having a 30-minute thermal time constant, the STE rating is:

I STE

30 ⎛ ⎞ ⎜ 1 − 0.0183 + 160 − 130 ⎟ =⎜ ⎟ = 134% 90 ⎜⎜ ⎟⎟ ⎝ ⎠

5.3-24

Other Types of Terminal Equipment

UPRATING OF SUBSTATION TERMINAL EQUIPMENT

Overhead lines and underground cables are not considered in this chapter but are considered elsewhere. The replacement or physical modification of overhead or underground transmission lines is very expensive and can be extremely difficult to schedule given the need for reliable power service. Failure of lines and cables occurs outside of the restricted access of a substation and can result in legal and safety issues. Because of this, realtime monitoring and dynamic rating of lines and cables is relatively easy to justify even though the monitoring and communications can be expensive and complex. Similarly, power transformers (the primary cost component of substations) and their replacement typically involve large capital outlays and extended service out-

5-12

• Conductors that connect current-carrying (and noncurrent-carrying) equipment (strain bus, jumpers, rigid tubular bus, bolted and welded connectors). free-standing current transformers, series reactors, and power line carrier [PLC] line traps).

Other types of substation terminal equipment, while not specifically described here, are derived similarly. Two excellent articles on increased power flow for substation terminal equipment are noted as references (Cronin 1972, Conway et al. 1979). 5.4

Substation terminal equipment considered here fall into one of four categories:

• Air-insulated terminal equipment (line disconnects,

Because of the lack of a clear rating adjustment method in the ANSI standard, the engineer should review the various assumptions before doing such adjustments. 5.3.9

ages. Failure of transformers can occur in a number of ways, and cooling equipment can be complex. As with lines and cables, real-time monitoring of transformers and the development of dynamic thermal rating methods are often easily justified.

• Oil-insulated equipment associated with a power transformer (load tap changers, transformer bushings).

• Oil circuit breakers and associated bushings. None of the terminal equipment considered have associated forced cooling equipment (fans, circulating pumps for oil, etc.). All have much simpler failure modes than cables, lines, and power transformers. All are considerably less expensive to replace. As a result, as the comedian Rodney Dangerfield might have said, they don’t get the same “respect.” There are several ways in which the rating of substation terminal equipment is unique. A large substation may have only a few power transformers and three or four lines connected to it, yet it may have tens or hundreds of line disconnects, bus segments, connectors, etc. Even a moderately short overhead line has miles of conductor that the public can stand under or ride under, whereas all of the substation equipment at a location is enclosed by a fence and warning signs. Imminent failures in power transformer windings, underground cables, and overhead conductor splices are not directly visible or measurable, but in many cases overheated terminal equipment can be detected with a simple infrared scan. As shown previously, ANSI, IEEE, and IEC standards for substation terminal equipment usually allow the nameplate rating of the equipment to be adjusted for air temperatures other than 40 o C. Numerous technical


publications suggest that the equipment thermal rating can be further adjusted for heat storage capacity, and that the attainment of equipment temperatures higher than the continuous limits is acceptable for short periods of time. In reference (Coneybeer 1992), basic thermodynamic methods are applied to switches, bus, and wave traps. The experiments (sponsored by EPRI) and resulting thermal algorithms account for solar heating and forced convection (wind) cooling. In these models, the terminal substation equipment is modeled by multiple, thermodynamically coupled components. While shown to be accurate, the dynamic rating algorithms based on this work required a great deal of detailed weather data, and equipment parameters and dimensions not readily available to the utility engineer. Choosing practical thermal models for the various types, sizes, and designs of substation terminal equipment is a matter of maximizing accuracy while minimizing complexity. As discussed in the following, the complexity of thermal models and monitoring methods must be balanced against the cost and complexity of implementation, the practicality of maintenance procedures, and the consequences of equipment failure. Increasing the thermal rating of terminal equipment can be accomplished by one or more of the following methods: 1. Accepting increased deterioration rates by using higher equipment temperature limits. 2. Using actual equipment temperature rise data from manufacturer or field tests rather than conservative estimates. 3. Adjusting the rating for actual weather conditions (e.g., air temperature) and precontingency circuit loading. Unless detailed experimental data is available, the first of these methods can result in unexpected equipment failures. The use of manufacturer or field test data is discussed in Section 5.5.1. Adjusting ratings by monitoring weather conditions and circuit load is discussed in Section 5.4.1. 5.4.1

Monitoring and Communications

Communications is an essential part of dynamic thermal monitoring and rating of any power circuit components. Dynamic rating of overhead lines may require communication of measured data from multiple remote locations along the line route to a nearby substation, where the data is collated and communicated to an


operations center by means of RTU channels. This process can be complex and require frequent maintenance visits to unprotected sites. Dynamic rating of power transformers and terminal substation equipment is much simpler, since any equipment or weather monitoring equipment is kept within the secure boundaries of the substation, and the communications link to the utility operations center is near at hand. Given the number of switches and other terminal substation equipment, the use of equipment monitors (e.g., a switch contact temperature monitor) is impractical and almost certainly uneconomical. On the other hand, a single weather station located in or near the substation is probably sufficient to dynamically rate all equipment in the station. 5.4.2

Maintenance and Inspection Procedures

An initial inspection and periodic inspection visits are crucial to reliable operation of dynamically rated terminal substation equipment, since it is not economic to monitor the equipment in real-time. In contrast to overhead lines, the inspection of most terminal equipment can be performed quickly and easily with infrared imaging equipment and a trip to the single substation location. Clearly, algorithms for the dynamic rating assume that the equipment is operating in excellent condition. It may be very difficult to detect imminent failures of overhead lines (particularly full tension splices) or underground cables, but thermal problems in substation terminal equipment can usually be spotted before an unexpected outage can occur. 5.4.3

Reliability and Consequences of Failure

Substations are designed to be reliable with alternate configurations available if certain equipment should fail. Thus the consequences of failure of a single substation component may be less than for a critical line or cable. Failures may occur as the result of metallic deterioration (e.g., switch contact plating), annealing (e.g., strain bus), or insulation aging (e.g., wave traps or free-standing CTs). The mechanism of failure depends on the type of terminal equipment. In any event, the consequence of failure may be less for substation terminal equipment. Overhead lines and underground cables are placed in corridors that are not secured against public access. If either fails, the public or property may be harmed. Substation equipment is

5-13


enclosed by fencing designed to limit access, and neither the public nor nonutility property is likely to be damaged in the event of a failure. On the basis of this observation, certain dynamic rating calculation methods that yield higher thermal ratings in exchange for an increased (but low) probability of temperature limit exceedence may be justified. Such approaches can seldom be justified for overhead lines where the public safety may be directly involved. 5.5

THERMAL PARAMETERS FOR TERMINAL EQUIPMENT

Given the various thermal models for terminal equipment, the calculation of thermal ratings depends on having certain thermal parameters. There are three basic methods by which these thermal parameters can be found. In order of preference the methods are: 1. The manufacturer provides laboratory test data for the device, including transient behavior. 2. Laboratory tests or field measurements are performed to obtain thermal parameters. 3. Typical thermal parameters are selected from the technical literature or from the appropriate standards. 5.5.1

Manufacturer Test Report Data

Two examples of manufacturer test reports are included here. The first involves temperature measurements at rated load for an SF6 circuit breaker. The second is for an air disconnect switch. With the SF6 circuit breaker, the design margins for the various components vary somewhat, but are surpris-


ingly large for most parts. For example, the 44oC temperature rise of the main contact is the highest measured for the various CB components, yet it is considerably less than the default rise of 65oC. The current in the circuit breaker would need to exceed the rated current by more than 20% before the main contact temperature rise reaches 65oC, but at this current level the bushing terminal would exceed its rise limit of 50oC. Considering all the measured temperature rises for all the circuit breaker components, the equipment could be operated at about 15% over nameplate without exceeding the normal ANSI limits. For the air disconnect, the maximum temperature rise occurs for TC #1. Assuming an allowable temperature rise of 53oC, the measured rise of 42.5oC would allow for a switch load above nameplate of approximately 15%. 5.6

CONCLUSIONS AND SUMMARY

In the preceding discussion of increasing power flow for substation terminal equipment, certain methods of calculation are presented that allow safe, reliable operation of terminal equipment above its “nameplate” rating. Thus a 1200 A switch may be operated at more than 1200 A by considering actual air temperature (rather than 40oC), the manufacturer’s test data for temperature rise at rated load (rather than default ANSI values), and possible operation at higher than usual temperature limits. In addition, for emergency ratings, the limited duration emergency rating may be higher if the heat storage capacity of the switch is considered. Table 5.5-1 Steady-State Temperature Measurements for SF6 Breaker

Location of TC Measurement

Figure 5.5-1 SF6 circuit breaker with measuring locations for laboratory tests.

5-14

Measured Temperature Rise (oC)

Specified Maximum Temperature Rise (oC)

1 – Conductor for test

41

-

2 – Bushing terminal

38

50

3 – Bushing conductor

42

-

4 – Conductor junction

41

65

5 – Conductor junction

40

65

6 – Finger contact

42

65

7 – SF6 gas

29

-

8 – Enclosure

22

70

9 – Main contact

44

65

10 - Conductor junction

40

65

11 - Conductor junction

41

65

12 - Bushing conductor

41

-

13 - Bushing terminal

38

50

14 - Conductor for test

40

-

Ambient temp

32

Loading duration

12 hours



Table 5.6-1 Laboratory test data for switch at rated loading.

If air temperature at the substation and the electrical loading of the equipment are reported to SCADA/EMS in real-time, substation terminal equipment can be dynamically rated. This is particularly useful in increasing the circuit rating when overhead lines, power transformers, or underground cables, in series with the terminal equipment, are also dynamically rated. Field verification of substation equipment thermal behavior is particularly important since the basic rating of the equipment and all methods of increasing the rating depend upon the equipment being in excellent condition. Field measurements made with infrared imaging cameras are an excellent way to affirm the thermal condition of substation equipment. Not only is it possible to use infrared imaging cameras to spot high temperatures and detect damaged equipment, but if small areas of the surface of bus, switches, etc. are prepared by painting, a high-quality camera in the hands of an experienced operator can be used to measure temperatures within a few degrees centigrade. Under high current load conditions, equipment temperature measurement can serve to verify the thermal models and parameter assumptions. In summary, it is possible to operate substation terminal equipment at current levels exceeding “nameplate” by 5% to 15% in most cases without reducing reliability,

but the condition of the equipment must be verified by periodic inspections. REFERENCES

ANSI. 1965. Appendix to C57.99-1965. Application Guide for Loading Dry-type and Oil-Immersed Current-Limiting Reactors. ANSI. 1979. C37.37-1979. Loading Guide for AC HighVoltage Air Switches (in excess of 1000 volts). ANSI. 1981.C93.3-1981. Requirements for Power-Line Carrier Line Traps. ANSI. 1988. C37.010-1979. Application Guide for AC High Voltage Circuit Breakers Rated on a Symmetrical Current Basis. Reaffirmed 1988. ANSI. 1993. C57.13-1993. Requirements for Instrument Transformers. ANSI. 1995a. C57.19.100-1995. Guide for the Application of Power Apparatus Bushings. ANSI. 1995b. C57.91-1995. Annex B. Effect of Load Transformers Above Nameplate Rating on Bushings, Tap Changers, and Auxiliary Components.

5-15



ANSI. 1995c. C57.131-1995. IEEE Standard Requirements for Load Tap Changers. March.

Cronin, J. 1972. “Rate Substation Equipment for Shorttime Overloads.” Electrical World Magazine. April 15.

ANSI. 1996. C57.16-1996. Requirement, Technology, and Test Code for Current-Limiting Reactors.

Douglass, D. A. and Edris, A. 1999. “Field Studies of Dynamic Thermal Rating Methods for Overhead Lines.” IEEE T&D Conference Report. New Orleans. April 7. New Orleans, LA.

Bendo, I. S. et al. 1979. “Loading of Substation Electrical Equipment with Emphasis on Thermal Capability, Part II – Application.” IEEE Transactions. PAS-98. No.4. July/August. pp. 1403-1419. CIGRE. 1997. Working Group 12-22. Thermal State of Overhead Line Conductors. Electra. No. 121. pp.51-67. CIGRE. 2000. Working Group 22.12. Description of State of the Art Methods to Determine Thermal Rating of Lines in Real-Time and Their Application in Optimising Power Flow. CIGRE 2000. Paper 22-304. CIGRE. 2002. Study Committee 23. “Dynamic Loading of Transmission Equipment–An Overview.” Electra. No. 202. June. Coneybeer, R. T. 1992. “Transient Thermal Models for Substation Transmission Components.” Master's Thesis, School of Mechanical Engineering, Georgia Institute of Technology. Conway, B. J. et al. 1979. “Loading of Substation Electrical Equipment with Emphasis on Thermal Capability.” IEEE Transactions on Power Apparatus and Systems. Vol. PAS-98. No. 4. July/August. pp. 1394– 1419.

5-16

Douglass, D. A., Edris, A. et al. 2002. “Dynamic Loading–Lessons Learned.” CIGRE Report. September 2002, Paris, France. IEEE. 1993. Standard 738-93. “IEEE Standard for Calculation of Bare Overhead Conductor Temperatures.” New York Power Pool. 1982. “New York Power Pool Task Force on Tie Line Ratings.” Final Report. Final Issue. June. New York Power Pool. 1995. Tie-Line Ratings Task Force. “Final Report on Tie-Line Ratings.” November. PJM. 1999. PJM Interconnection Planning & Engineering Committee. “Air Disconnect Switch Ratings.” February. PJM. 1999. PJM Interconnection Planning & Engineering Committee. “Guide for Determination of Line Trap Normal and Emergency Ratings.” August. Seppa, T. O. et al. 1998. “Use of On-Line Tension Monitoring Systems for Real Time Ratings, Ice Loads and Other Environmental Effects.” CIGRE Report 102-22. September. Paris, France.


CHAPTER 6

Dynamic Thermal Ratings Monitors and Calculation Methods

6.1

INTRODUCTION

The opening of the transmission system to independent power generators and the reduction in traditional regulation has led many utilities, both in the United States and around the world, to employ methods where transmission lines and equipment can be operated reliably at higher loadings. Since the mid-1980s, considerable attention has been paid to increasing the power flow of overhead lines, power transformers, underground cables, and substation terminal equipment by means of monitoring weather and the equipment thermal state and by developing more accurate thermal models. The resulting dynamic thermal rating techniques have typically yielded increases of 5 to 15% in capacity. Chapter 6 provides an overview of dynamic thermal rating methods. Each of the other chapters in this book includes a section dealing with the dynamic rating of each type of equipment (lines, cables, power transformers, and substation terminal equipment). The goal of this chapter is to present a balanced overall view of when dynamic rating methods are appropriate, how they are best implemented in a practical operational application, and how such methods can be applied to complex interconnections consisting of multiple circuits and many circuit elements. Though the EPRI DTCR software is used to illustrate practical methods of implementation, the observations and technical insights are generally applicable. Chapter 6 includes seven sections:

• Section 6.2, Issues Related to Dynamic Thermal Rating Methods, discusses concerns related to dynamic ratings, including where calculations should be performed, the impact of ratings on engineering, planning and operations functions, and the connection between ratings and increased utilization.

• Section 6.3 Power Equipment Condition Assessment and Real-Time Monitors, outlines the need for inspections and/or real-time monitors and the problems that may arise without them.

• Section 6.4, Dynamic Thermal Rating Models for Power Equipment, provides an overview on models for overhead lines, transformers, underground cables, and substation terminal equipment.

• Section 6.5, EPRI’s DTCR Technology, describes the use of DTCR software. • Section 6.6, Operating with Dynamic Thermal Ratings, identifies operating issues related to dynamic thermal ratings.

• Section 6.7, Field Studies of Dynamic Ratings, describes field studies of dynamic ratings used for overhead lines, transformers, underground cables, substation terminal equipment, and power circuits.

• Section 6.8, Conclusions, summarizes a number of observations concerning dynamic ratings.

6-1

Chapter 6: Dynamic Thermal Ratings Monitors and Calculation Methods

6.2

ISSUES RELATED TO DYNAMIC THERMAL RATING METHODS

Utilities around the world are undergoing a major transformation, seeking to increase the utilization of existing power equipment within the electric transmission network while attempting to increase, or at least not decrease, service reliability. Traditionally, power utilities operated in a tightly regulated and predictable business environment where capital investments in generation and transmission were carefully planned many years in advance and return on investment was guaranteed. In this environment, there was little reason to load power equipment to levels close to thermal limits, and there was little need for exact thermal models. More recently, in many countries, power utilities are moving to an “open access” business environment in which transmission rights are not assured to the owner/investor in generation. Those who own and operate the transmission system must respond to the transmission capacity needs of new generators with little or no ability to make long-term plans, yet anticipating only moderate and regulated return on investment. At the same time, environmental hurdles and legal battles limit the construction of new transmission media (overhead lines and underground cables) and inhibit the placement and construction of new substations. Thus significant transmission network additions and reinforcements have been at a virtual standstill for over 25 years while load growth has continued. As a result of the difficulties in financing, planning, and gaining approval for new facilities, the normal and postcontingency loading of existing equipment has increased. This has occurred both system-wide and (with the addition of new generation in “unplanned” but commercially or environmentally attractive locations) on specific circuits. In response, dynamic loading and real-time monitoring of power equipment has become an important tool in attempting to maintain system reliability while allowing increased power flows. The improved thermal models of power equipment, developed in pursuit of higher utilization levels, can improve our understanding of high-temperature operation. In the mid-1980s, EPRI initiated research projects involving the dynamic rating of both overhead lines and underground cables. The overhead line project was referred to as Dynamp. It produced a thermal rating model for bare overhead conductor that gives results similar to both the IEEE and CIGRE thermal models. In 1993, EPRI initiated research into the “real-time thermal monitoring of transmission circuits.” As described

6-2


in (Douglass and Edris 1996), certain existing thermal models for underground cable, overhead lines, power transformers, and substation equipment such as line traps, circuit breakers, bus, switches, and current transformers were included in an integrated software model capable of calculating the dynamic thermal rating of transmission circuits consisting of one or more such elements. The resulting software was tested and improved as a result of an extensive series of field tests. The result of the initial series of field tests, primarily on overhead lines, was summarized in (Douglass and Edris 1999). During the same period, a number of real-time temperature and condition monitoring devices have been developed and refined. These include the EPRI Sagometer, the Valley Group’s CAT-1 line tension monitor, many types of oil monitoring devices for power transformers, and optical time-domain reflectometry instruments to measure temperature along underground cables. In addition, low power communication methods have matured, simplifying the process of real-time monitoring for lines and cables that may extend over many miles. Computerized database and storage techniques used by utilities have also evolved until it has become relatively easy to obtain real-time data and to store equipment thermal parameters in utility SCADA and maintenance systems. This section explores a number of key issues related to the use of dynamic ratings. 6.2.1

Where Should Dynamic Thermal Circuit Rating Calculations Be Performed?

In early field tests, the dynamic thermal rating software, developed by EPRI and others, was installed on computers placed in the substation environment, close to the power equipment being monitored. This generally yielded unsatisfactory and unreliable results. Problems included hardware thefts, travel to remote locations to investigate problems, and unreliable communications. In consequence, the software was modified in its most recent version to obtain real-time input from, and send calculated output to, volatile ASCII files on the PC. These files are read and written by simple SCADAbased software programs. In this newer arrangement, real-time monitors are interfaced with the SCADA system, not with the dynamic loading computer. Calculated dynamic thermal ratings, based on real-time data obtained through SCADA, are read back into the SCADA database from which they can be displayed according to the needs of each utility or utility function. The advantage of this arrangement is primarily one of simplicity and reliability. Other benefits


include centralizing the DTCR application onto one computer, and having this computer near computer maintenance personnel. Communication between remote monitors and the utility SCADA database is handled by separate commercial software and hardware that has nothing to do with the dynamic rating calculation software. Utilities may have existing interface methods, in use for other applications, and may choose the most appropriate interface based on maintenance and ease of use criteria. This arrangement also allows the utility operations people to display or utilize the calculation results in the fashion they prefer, rather than being forced to use an embedded display. The information may be dynamically linked to transmission/generation scheduling or generation shedding systems. The calculated and measured information is available for data storage by a component of an Energy Management System (EMS) making historical information available to dispatchers. The advantage of this arrangement is primarily one of simplicity and reliability. The communication between remote monitors and the utility SCADA database is handled by separate commercial software and hardware that has nothing to do with the dynamic rating calculation software. This arrangement also allows the utility operations people to display the calculation results in the fashion they prefer rather than being forced to use the output screen provided. 6.2.2

Costs—Capital and Otherwise

Traditionally, in regulated power utilities, the engineering, planning, and operations functions are somewhat segregated. Where dynamic loading (rating) methods are implemented, it is likely to have an impact on all three of these areas. This can make the implementation and use of dynamic rating methods challenging.


line current increases over time, the operator will need to take action more frequently.

• Unless dynamic ratings are implemented, the system planner would need to upgrade the capacity of this circuit before the line current begins to exceed the static line rating. If the line is dynamically rated, the necessary upgrade may be postponed since the dynamic rating is typically higher than the static.

• Unless line monitors are used, the equipment engineer’s thermal model for the line cannot be tested experimentally. With line monitors installed, the detailed temperature and sag clearance response of the line can be improved by comparison with the field data. The implementation of line monitors and the calculation of dynamic ratings for the line have an impact on the interaction of the three groups. The planner may be able to postpone capital investment in uprating the line, and the design engineer may be able to improve the accuracy of existing thermal models, but the operator may need to act more frequently to reduce line current. The improved accuracy of the design engineer’s thermal line model may improve reliability by avoiding flashovers to trees and other electrical circuits, but the system planner may find that a reduction in line rating leads to difficulties in operating the system and the need for increased capital investment in line upgrades. In summary, dynamic rating technology may allow the postponement of capital investment and lead to better thermal modeling and physical reliability, but its application may also require increased operator actions and, if the static rating is too high, it may lead to the need for physical line upgrades.

Figure 6.2-1 shows a typical statistical distribution of line current and dynamic ratings for a circuit consisting of an overhead line. The figure applies equally well to normal loadings and normal dynamic ratings or to postcontingency loadings and long-time emergency ratings. With reference to this figure, consider how such data may be utilized differently within the utility:

• Unless dynamic rating methods are employed, the system operator does not have to take action for any of the load levels shown since all are below the static rating. If the line is dynamically rated, the operator may have to take action very occasionally when the line current exceeds the dynamic rating. If the average

Figure 6.2-1 Current load versus dynamic rating probability distributions.

6-3


6.2.3

Why Dynamic Ratings Go With Increased Utilization

The original EPRI dynamic thermal circuit rating project (3022-7) was proposed as part of the EPRI Flexible AC Transmission System (FACTS) technology research program (Edris 2000). FACTS is a power electronic-based technology for enhancing controllability and increasing power transfer capability of transmission circuits. FACTS controllers provide the system operator with the means of rapidly controlling loads on particular circuits in order to maximize power transfer capability of transmission corridors. The ultimate goal of FACTS controllers is to bring the power transfer stability limit as close as possible to the thermal rating of transmission circuits. Dynamic thermal ratings of power equipment vary over time, of course. As such, while dynamic equipment ratings may often be higher than manufacturers’ ratings, there may be times when thermal capacity is inadequate, and the load needs to be reduced quickly in order to prevent damage. One of the most attractive applications for dynamic equipment ratings involves automatic actions after (“post”) contingency occurrences. Here, after loss of a major system component, the thermal capacity in realtime is tested against actual loads. Utilizing the thermal time delay, certain pre-programmed actions can be undertaken if the temperature limits might otherwise be exceeded and no action is taken when capacity is adequate. Given the ability to control circuit load, the knowledge of both predicted load and dynamic ratings may be utilized to warn the operator well in advance of potential overloads. The EPRI dynamic rating software does this by providing a parameter called Time-To-Overload (TTO). TTO indicates to the system operator how much time is left until equipment temperatures exceed safe limits. In the case of most distribution station transformers and other transmission circuits, the load profile is repeated daily with only a variation in magnitude. With this predicted load and predicted weather for overhead lines, the TTO can be calculated and updated in real-time. This allows the dispatcher to shed load or redispatch generation in a precise manner.


6.3

POWER EQUIPMENT CONDITION ASSESSMENT AND REAL-TIME MONITORS

As part of increasing power flow, is it necessary to track the condition of power equipment? This section discusses the need for periodic inspections and monitoring. Two of the results of utility deregulation and growing public opposition to new lines and substations are the aging of the transmission system and the increased utilization of existing equipment. When building new facilities was easier and when the regulated economic environment allowed a fixed return on investment, power equipment was typically operated at lower utilization levels and was easily replaced as it aged. While the goal of increased utilization of aging equipment is understandable in the present utility environment, it can lead to a reduction in system reliability unless the equipment is carefully maintained and monitored, either by frequent inspections or by real-time instrumentation or both. Real-time instrumentation has an additional advantage in that field data from heavily loaded equipment can be analyzed in order to improve our thermal models. Dynamic ratings of lines, transformers, cables, and substation terminal equipment can be calculated on the basis of weather data alone. For example, the operating conductor temperature and dynamic rating of an overhead line can be calculated based on air temperature and wind data from a nearby weather station. This is attractive because no instruments need to be installed on the structures or energized high voltage conductors. The resulting instrumentation cost is low and the instruments can be installed without taking an outage. The drawback to this approach is that there is no direct means of confirming that the dynamic ratings are correct or that the estimated conductor temperature and sag are correct. Some simple examples of the kind of problems that can result are: 1. Electrical clearances may be inadequate, even though the conductor temperature does not exceed the maximum allowable design temperature, because the line sags are not in accordance with design plan-profile drawings. 2. Conductor temperature may exceed the calculated conductor temperature because of broken or corroded strands at certain points along the line. This may, in turn, lead to local annealing and/or tensile failure.

6-4


3. The conductor sag at high temperature may be greater than that calculated in the original design because of incorrect ruling span assumptions or errors in the estimate of thermal elongation rates. The first problems can be prevented by continuing physical inspections both before the dynamic rating calculation method is initiated and as long as it continues. The second problem is difficult to detect without climbing inspections since IR scans and video recordings may not show such damage. The last problem, cannot be detected by physical inspection of the line at normal electrical load levels since the unfortunate result (i.e., inadequate electrical clearance) only occurs during extremely high line loadings. Continuous sag or tension monitoring can be used to detect such problems. 6.4

DYNAMIC THERMAL RATING MODELS FOR POWER EQUIPMENT

A number of distinctions can be made between real-time monitoring and the determination of dynamic thermal equipment ratings. Equipment monitors provide the system operator with an indication of the thermal state (e.g., critical temperatures) of remote power equipment but offer no guide to safe load levels. Weather monitors provide air temperature, wind speed, wind direction, and solar heating data. Dynamic ratings provide the system operator, and system security assessment programs, with an upper bound on circuit electrical loading that, if adhered to, keeps equipment temperatures below userspecified maximums. Monitor parameters may be in any one of a variety of units (degrees C or pounds of line tension). Dynamic ratings are expressed in amps or MVA, the same units as electrical load, so the comparison is obvious. Real-time equipment monitors may report equipment temperatures (or for overhead lines, possibly sag or tension), electrical current, and/or weather data such as air temperature, solar heating, and wind speed and direction. When communicated to the dispatcher, this data may be useful in establishing the present thermal state of the monitored equipment (e.g., the top oil temperature of a power transformer) or in developing a rough idea of dynamic load capability. For example, many utilities may allow substation equipment to be loaded above normal operating limits if the air temperature is relatively low or if the critical equipment temperatures are well below safe limits during an emergency. Analysis of monitor data is often dependent on the operator’s knowing specific equipment temperature limits, however, and is seldom useful to system planners making capital investment decisions.


Dynamic thermal ratings are calculated with mathematical thermal models, which require equipment parameters (e.g., maximum conductor temperature, resistance per unit length), real-time equipment monitor data (e.g., underground cable shield temperature or sag-tension for lines), real-time weather data (air temperature, wind speed, solar heating, etc.), and real-time load current. The calculation determining a safe dynamic load limit typically consists of repeated calculation of equipment temperature(s) for some period of time into the future to determine the load current that just meets the safe limits on equipment temperature. These calculations include the present equipment temperature(s) and use predicted weather data. The resulting maximum allowable load current, expressed in amperes or MVA, is the dynamic load limit (thermal rating) and may be compared directly to the actual equipment load. Certain types of real-time monitors (line sag or tension monitors, transformer oil or winding monitors, and underground cable thermocouples) are essential to the verification of any dynamic safe loading method. They provide verification that the dynamic rating method works. Without such verification, incorrect or inaccurate dynamic rating methods could damage power equipment. In some cases this process of verification may only be required during startup, after which the real-time equipment monitors may be removed. Therefore, real-time equipment monitors are important to the verification of dynamic load limits but are not of themselves a reliable guide to the safe loading of equipment. Both real-time monitors and dynamic load limit calculation methods are important to the reliable operation of transmission power equipment at high load levels. 6.4.1

Accounting for Heat Storage (Pre-load Monitoring)

Thermal time constants of power transmission equipment vary significantly. For example, Figure 6.4-1 shows the relative time constants of typical lines and cables. The time constant of the overhead line is about 10 minutes, while the buried cable time constants are greater than 1000 minutes. These time constants are important when considering emergency ratings (temporary application of load beyond the normal continuous rating). The long thermal time constant of buried cables yields very high, short-duration, emergency ratings as compared to overhead lines. Transformers are somewhere in between.

6-5



Qrad = Heat loss by radiation [watts/m], a function of temperature rise, diameter, and emissivity. Qconv= Heat loss by convection [watts/m], a function of temperature rise, diameter, and heat transfer coefficient (wind speed). MCp*dT/dt= Heat storage term [watts/m]. This is zero in the steady state.

I rating = Figure 6.4-1 Temperature response to step changes in current load.

6.4.2

Overhead Lines

For overhead lines, dynamic ratings can be calculated based on weather monitors alone or in combination with conductor temperature, tension or sag monitors. Each type of monitoring has its own advantages and disadvantages but dynamic ratings based on data from sag or tension monitors appear to have significant advantages over the use of weather monitoring alone. Weather-Based Dynamic Line Ratings Weather-based dynamic line ratings can be based on:

• • • •

Air temperature alone Air temperature and solar heating Air temperature, solar heating, and wind speed Air temperature, solar heating, wind speed, and wind direction.

In all cases, the dynamic line rating is calculated with a heat balance method and if the real-time current is measured, then the line conductor temperature can also be calculated. Equation 6.4-1 is the heat balance equation, consisting of heat input, output, and storage terms. It is based on the fact that at steady state, the heat input must equal the heat output. In the steady state, where dT/dt is zero, this can be solved for current, as shown in Equation 6.4-2.

Qgen + Qsun = Qrad + Qconv + mC p *

dT dt

6.4-1

Where: Qgen = Heat input by ohmic losses, I2R [watts/m], a function of current and resistance. Qsun = Heat input by solar [watts/m]. This can be directly measured or calculated.

6-6

Qconv + Qrad − Qsun R AC_conductor

6.4-2

The weather-based model is very accurate if the weather stations are positioned appropriately to measure the weather actually seen by the line conductors. Multiple weather stations may be required if the weather is expected to vary along the line route. The weather-based model, which uses standard weather instruments, is usually the simplest method of dynamic line rating to implement. No instruments need to be mounted on the line itself, and therefore they do not need to survive in a high electromagnetic stress environment. The measurement of wind speed and direction by an anemometer is not dependent on the line’s electrical loading, so the method works equally well under preand post-contingency loading. Conductor Temperature-Based Dynamic Line Ratings This system is capable of calculating dynamic line ratings based on direct conductor temperature measurements in combination with the line current, air temperature and solar heating. To calculate line ratings, the real-time conductor temperature is converted to an equivalent wind speed perpendicular to the line. Then the wind speed is used in combination with the other weather data to calculate the dynamic line rating. The advantage of temperature-based ratings is that the user has a direct measurement of conductor temperature. If the line rating is intended to limit the loss of conductor strength at high temperature, then this direct measurement of the primary parameter makes sense. The disadvantage of using conductor temperature monitors is that these instruments must function in the very high electrical stress immediately around the energized conductor on which they are mounted. The measured conductor temperature must be communicated to a ground station some distance away, and the conductor temperature may or may not be a good estimate of the average conductor temperature along the line, which is related to the line sag and tension. Additionally, it is possible for the process of temperature measurement to


actually interfere with the temperature being measured. That is, if the measurement device introduces significant mass and/or shielding in the measurement area, the temperature being recorded might not be representative of conductor temperatures a few meters away. Sag/Tension-Based Dynamic Line Ratings The fundamental parameter of interest on most overhead lines is the sag or clearance at maximum allowable conductor temperature. Thus real-time measurement of sag or tension provides a direct measurement of the limiting parameter. Also, sag-tension monitors respond to the weather conditions along an entire line section being monitored rather than to weather conditions at a single point along the line. Therefore, ratings based on a single sag-tension monitor are equivalent to several weather stations along a line section. Of course, most lines consist of multiple line sections, so that one sag-tension monitor does not indicate the rating of the whole line.

DTCR is capable of calculating dynamic line ratings for commercial conductor tension monitors such as the widely used “CAT-1” line tension monitor. The CAT-1 uses load cells placed in series with the insulators at a strain structure. Air temperature and solar heating are measured at the same structure. The monitors are linked by radio or cellular telephone to a PC running DTCR or to the utility SCADA/EMS system. Tension monitors can be installed with the line in service but are normally installed with the line de-energized. As with the use of temperature monitors, the real-time tension is converted to an equivalent wind speed. This is done in two steps. First the tension is converted to an average conductor temperature along the line section based on field calibration data. Second, the average conductor temperature (in combination with the line current, air temperature, and solar heating) is converted to an effective average wind speed along the line section. The line rating is then calculated using the weatherbased heat balance algorithm. DTCR allows for a similar process based on a real-time sag monitor, but no such commercial device presently exists. 6.4.3

Power Transformers

The dynamic rating algorithms used to rate power transformers are usually based on the IEEE Top Oil model (IEEE 1996), the IEEE Bottom Oil model (IEEE 1996) or the “IEC” model (IEC 1991). Each of the models requires slightly different transformer test data (the IEEE Bottom Oil model requiring considerably more detailed test data than the other two), and the more complex Bottom Oil model does a better job modeling short time loads.


Transformer ratings are primarily a function of air temperature and electrical load. Solar heating of equipment in unshaded areas and wind effects on transformers that do not have forced air cooling are secondary but occasionally important parameters. Since wind is less important to power transformers, the calculation of dynamic ratings and the prediction of ratings are simpler than for overhead lines. However, in comparison to overhead lines and underground cable, real-time monitoring and dynamic loading of power transfor mers present some special difficulties:

• The critical transformer temperature is the winding hot spot. Normally, it is impossible to directly measure the hottest spot winding temperature in older transformers without a fiber optic hot spot monitor, so there is a level of uncertainty as to the difference between the hot spot and the average winding temperature.

• All of the transformer dynamic loading calculation models require laboratory test data for hot spot rise over top oil and oil rise over air temperature at rated electrical load. This data may be difficult or impossible to find for a 40 year-old unit.

• In addition to maximum winding current limits, the dynamic thermal rating of power transformers may depend on loss of insulation life, maximum oil temperature, maximum hot spot temperature, or the formation of bubbles in winding insulation. The present state of insulation may be difficult to determine.

• Auxiliary equipment such as bushings, conductor leads, tap-changers, and associated protection limits may limit transformer dynamic loading. This can be dealt with either by replacing such limiting elements with ones of higher capacity or by dynamically rating the auxiliary equipment as well as the transformer itself.

• Protection settings must also be considered. Unwanted tripping could occur in overload situations.

• Older units may be in poor condition, requiring that limits on winding temperature and insulation loss-oflife be reduced below those of newer units. Rating Constraints for Power Transformers Dynamic (and static) thermal ratings for overhead lines and underground cables are typically calculated for a single rating constraint (conductor temperature). However, the dynamic rating of power transformers is typically determined by simultaneous constraints on maximum winding hot spot temperature, maximum bulk top oil temperature, maximum % loss of insulation

6-7


life per loading event, and avoidance of gas bubble formation in the winding insulation (Figure 6.4-2). Thus while the thermal model itself may not be more complicated than that of overhead lines or underground cables, the multiple constraints often complicate the rating calculation. Also, while dynamic and static thermal ratings for overhead lines may utilize higher temperatures for shorter rating durations (e.g., 75°C for continuous operation and 100°C for emergencies), power transformers are typically rated using multiple rating limits as shown in Table 6.4-1. These limitations are used to calculate thermal ratings with either the “Top Oil” or “Bottom Oil” thermal models and apply to both static and dynamic rating calculations. The possibility of gas bubble formation in transformer windings is also considered but only for short time emergency loadings where the sudden change in electrical loading may lead to the formation of gas bubbles in regions of high electrical stress near the transformer windings. Transformer “Top Oil” Thermal Model In this thermal rating model, the transformer is represented with only two temperatures, the bulk oil temperature at the “top” of the tank and the winding hot spot temperature. The “Top Oil” model is described in IEEE Standard C57.91-1995, section 7-2 (IEEE 1996).

Given a constant measured load, the “ultimate top oil temperature rise over air” is:

ΔΘTO ,U = ΔΘTO , R

⎡ K 2 R + 1⎤ ⋅⎢ U ⎥ ⎢⎣ R + 1 ⎥⎦


Ku R N

= Ratio of measured load to rated load, Imeas/IR. = Ratio of load loss at rated load to noload loss. = Empirical constant, typically between 0.8 and 1.

The hot spot temperature rise over the top oil temperature for a constant load is:

ΔΘ H ,U = ΔΘ H , R * K U

2m

After the winding and oil thermal time constants have been entered, the calculation of dynamic thermal ratings for the transformer involves tracking the hot spot winding temperature and bulk top oil temperatures in realtime, as the electrical load and air temperature change, and based on the present thermal state of the transformer, calculating its thermal response to predicted air temperature and electrical loadings. For any type of dynamic rating (continuous, long-time emergency, or short-time emergency), the maximum allowable electrical load is calculated such that one or more of the rating constraints (hot spot or top oil temperatures, loss of life, bubbles) is reached but none are exceeded.

n

6.4-3

Where: ΔΘTO,U = Ultimate top oil temperature reached with measured load. ΔΘTO,R = Top oil temperature at rated load.

Daily 24-Hour Dynamic Rating Example In the power transformer dynamic rating example shown in Figure 6.4-3, the tracking of the top oil temperature over the preceding 24 hours is shown to the left. The predicted hourly average air temperatures over

Table 6.4-1 Temperature Limits for Ratings From IEEE C57.91-1995 Rating Constraint [°C]

Continuous

Long-Time Emergency

Short-Time Emergency

Insulated Winding Temperature [°C]

120

140

180

Top Bulk Oil Temperature [°C]

105

110

110

Loss-of-Insulation Life [%]

0.0133% [per day]

0.1% [per event]

1% [per event]

6-8

6.4-4

Where: ΔΘH,U = Ultimate hot spot temperature reached with measured load. ΔΘH,R = Hot spot temperature at rated load. Ku = Ratio of measured load to rated load, Imeas/IR. m = Empirical constant, typically between 0.8 and 1.

Figure 6.4-2 Dynamically rated 93 MVA power transformer at Con Ed.


the next 24 hours are shown. The predicted electrical load is also shown. As part of the dynamic rating calculation process, the top oil temperature that results from the predicted air temperatures and loads is calculated for the shown pre-load. In this example, the transformer has a nameplate rating of 1000 A (HV winding), and the oil temperature only reaches a peak value of a bit more than 70°C about 18 hours from “NOW”.


Given the thermal model, the historical values of air temperature and electrical loading for the last 24 hours, and the predicted air temperature and load shape (not absolute magnitude), the maximum electrical load for the next 24 hours can be calculated. Since we are assumed to be using real-time air temperature and electrical loading, this is a dynamic rating calculation. With reference to Figure 6.4-4, it may be seen that, although the “nameplate rating” of this transformer is

Figure 6.4-3 Example of 24-hour daily dynamic rating calculation considering only top oil temperature limits.

Figure 6.4-4 Dynamic rating calculation for the next 24 hours.

6-9


1000 A (HV winding), the peak loading predicted to occur 18 hours from NOW can reach 1200 A without exceeding the 100°C limit on top oil temperature. This rather busy figure also shows that the allowable electrical load is a function of the predicted load shape being only 1120 A with a “flat” load. Transformer “Bottom Oil” Thermal Model The “Bottom Oil” model is a newer and more complex thermal model. It is more of a physical model than the empirical “Top Oil” model. Bottom oil and duct oil temperatures, as well as the top oil temperature, represent the thermal state of the transformer fluid. Variations of viscosity and winding resistance with temperature are included. The “Bottom Oil” model is described in Annex G of IEEE Standard 57.91-1995 (IEEE 1996).

When applied to dynamic rating calculations, however, the results of using the bottom oil model in place of the Top Oil model, are small except during certain shorttime emergency loading events. 6.4.4

Underground Cables

The dynamic thermal rating module for cables is based upon the 1957 paper prepared by J.H. Neher and M.H. McGrath (Neher and McGrath 1957), and includes numerical methods from IEC-287 and IEC-853 (IEC


1982, 1989). The cable rating algorithms in DTCR are based on EPRI's ACE (Alternative Cable Evaluation) program from UTWorkstation. The approach essentially solves an analogous equivalent thermal circuit (Temperature = Heat x Thermal Resistance, see Figure 6.4-5) to Ohm’s Law (Voltage = Current x Resistance) for electrical circuits. Heat is transferred away from the conductor by thermal conduction through the thermal resistances in the insulation, jacket, duct (if present), and earth out to ambient soil (for a solid dielectric cable). The thermal resistances can all be calculated based on knowledge of the cable construction, details of the installation configuration, and assumptions about the earth thermal parameters (thermal resistivity and ambient temperature). The equivalent thermal circuit from Figure 6.4-5 is described in Equation 6.4-5 (thermal quantities are shown with an overline). Since the system voltage is generally held to be a constant, the dielectric heating is constant, and the temperature rise caused by dielectric heating is fixed. Then, if a maximum conductor temperature (limited by insulation material) is selected, the conductor current can be found by solving Equation 6.4-5 for current as shown in Equation 6.4-6.

Figure 6.4-5 Cable equivalent thermal circuit (extruded dielectric cable).

(

TConductor = W Conductor RInsulation + RJacket + RJacket to Duct + RDuct + REarth

(

+ W Shield/Sheath RJacket + RJacket to Duct + RDuct + REarth + WDielectric

I=

6-10

(

1 2

)

) )

RInsulation + RJacket + RJacket to Duct + RDuct + REarth + TAmbient

6.4-5

TConductor − ΔTDielectric − T Ambient ΣR AC RCable and Earth

6.4-6


The thermal capacitance of each cable component and the earth determine the temperature response of the cable to changing load conditions, both during emergency rating calculations and normal load cycling. The time constant for buried cables is typically 24 hours or more. As a result, the change in conductor temperature as a function of time, in response to a sudden change in current, is quite slow as shown in Figure 6.4-6. As a consequence of the long thermal time constants associated with underground cable, and the stable environment (soil temperature and thermal resistivity) in which it is immersed, the dynamic thermal rating of underground cable is primarily a function of the load shape over considerable time periods. Thus the reduced loading of an underground cable circuit over the weekend may yield a significantly higher load capability on Monday, whereas the same phenomenon has no impact on the rating of an associated overhead line. 6.4.5


Early in the research into dynamic thermal ratings, substation terminal equipment (bus, switches, CTs, line traps, bushings, LTCs, circuit breakers, etc. ) were either not considered or represented by only the simplest of thermal models. Almost all of the researcher’s attention was focused on overhead lines, underground cables, and power transformers. This “benign neglect” of substation terminal equipment seemed justified because the thermal model data requirements were considerable, the condition of old equipment was uncertain, and the economic benefit of dynamically rating relatively inexpensive substation terminal equipment was questionable. The replacement or physical modification of overhead or underground transmission lines is very expensive and can be extremely difficult to schedule, given the need for


reliable power service. Failure of lines and cables occurs outside of the restricted access of a substation and can result in legal and safety issues. Because of this, realtime monitoring and dynamic rating of lines and cables are relatively easy to justify, as is the use of sometimes expensive and complex monitoring systems. Similarly, power transformers are usually the primary cost component of substations. Their replacement typically involves large capital outlays and extended service outages. Failure of transformers can occur in a number of ways, and cooling equipment can be complex. Because of this, as with lines and cables, real-time monitoring of transformers and the development of dynamic thermal rating methods is also easily justified. On the other hand, after dynamically rating lines, cables, and transformers, the useful increase in circuit rating is often found to be limited by substation terminal equipment, and the replacement of switches, line traps, etc. can be both difficult operationally and expensive in terms of required outages. Also the dynamic thermal rating of substation terminal equipment can often be accomplished with the same real-time weather and electrical load data used for other more capital-intensive power equipment, and the dynamic rating of lines and power transformers is usually highly coordinated with the dynamic rating of terminal equipment in circuit rating for little additional complexity and investment. Thermal Models for Substation Terminal Equipment Substation terminal equipment falls into one of four categories: 1. Conductors, which connect current-carrying (and non-current-carrying) equipment (strain bus, jumpers, rigid tubular bus, bolted and welded connectors) 2. Air-insulated terminal equipment (line disconnects, free-standing current transformers, series reactors, and PLC line traps) 3. Oil-insulated equipment associated with a power transformer (load tap changers, transformer bushings) 4. Oil circuit breakers and associated bushings. None of these types of terminal equipment has associated forced cooling equipment (fans, circulating pumps for oil, etc.). All have much simpler failure modes than cables, lines, and power transformers. All are considerably less expensive to replace. As a result, as Rodney Dangerfield might have said, they don’t get the same “respect.”

Figure 6.4-6 Tracking underground cable temperature.

There are several ways in which the dynamic rating of substation terminal equipment is quite different than for lines, cables, and transformers. Even a large substation

6-11


may have only a few power transformers and three or four lines connected to it, yet it may have tens or hundreds of line disconnects, bus segments, connectors, etc. Even a moderately short overhead line has miles of conductor, which the public can stand under or ride under, whereas all of the substation equipment at a location is enclosed by a fence and warning signs. Imminent failures in power transformer windings, underground cables, and overhead conductor splices are not directly visible or measurable in most cases, whereas an overheated line disconnect is readily apparent with a simple infrared scan. ANSI, IEEE, and IEC standards (ANSI 1978, 1979a, 1979b, 1981) for substation equipment usually allow the nameplate rating of the equipment to be adjusted for air temperatures below 40°C. Numerous technical publications suggest that the equipment thermal rating can be further adjusted for heat storage capacity and that the attainment of equipment temperatures higher than the continuous limits is acceptable for short periods of time (Cronin 1972, Conway et al. 1979, Massey 1971). In (Coneybeer 1992), basic thermodynamic methods are applied to switches, bus, and wave traps. The experiments and resulting thermal algorithms account for solar heating and forced convection (wind) cooling. In these models, the terminal substation equipment is modeled by multiple, thermodynamically coupled components. While shown to be accurate, the dynamic rating algorithms based on this work required a great deal of detailed weather data, and equip-ment parameters and dimensions not readily available to the utility engineer. The choice of a practical dynamic thermal model for the various types, sizes, and designs of substation terminal equipment is a matter of maximizing accuracy without requiring excessive complexity in monitoring or characterizing the equipment. The complexity of dynamic thermal models and monitoring methods must be balanced against the cost and complexity of implementation, the practicality of maintenance procedures, the consequences of equipment failure. Monitoring and Communications for Substation Terminal Equipment Communications is an essential part of dynamic thermal monitoring and rating of any power circuit components. Dynamic rating of overhead lines, may require communication of measured data from multiple remote locations along the line route to a nearby substation where the data is collated and communicated to an operations center by means of RTU channels. This process can be complex and require frequent maintenance visits to unprotected sites.

6-12


Dynamic rating of power transformers and terminal substation equipment is much simpler since any equipment or weather monitoring equipment is kept within the secure boundaries of the substation, and the communications link to the utility operations center is near at hand. Given the number of switches and other terminal substation equipment, the use of equipment monitors (e.g., a switch contact temperature monitor) is impractical and almost certainly uneconomical. On the other hand, a single weather station located in or near the substation is probably sufficient to dynamically rate all equipment in the station. Maintenance and Inspection Procedures – Substation Terminal Equipment An initial inspection and periodic inspection visits are crucial to reliable operation of dynamically rated terminal substation equipment since it is not economic to monitor the equipment in real-time. In contrast to overhead lines, the inspection of most terminal equipment can be performed quickly and easily with infrared imaging equipment and a trip to the single substation location. Clearly, algorithms for the dynamic rating assume that the equipment is operating in excellent condition.

It may be very difficult to detect imminent failures of overhead lines (particularly full tension splices) or underground cables, but thermal problems in substation terminal equipment can usually be spotted before an unexpected outage can occur. Reliability and Consequences of Failure Substations are designed to be reliable with alternate configurations available if certain terminal equipment should fail. Thus the consequences of failure of a single substation component may be less than for a critical line or cable.

Failures may occur as the result of metallic deterioration (e.g., switch contact plating), annealing (e.g., strain bus), or insulation aging (e.g., wave traps or free-standing CTs). The mechanism of failure depends on the type of terminal equipment. Overhead lines and underground cables are built in corridors that are not secured against public access. If either fails, the public or property may be harmed. Substation equipment is enclosed by fencing designed to limit access, so neither the public nor nonutility property is likely to be directly involved in the event of a failure. On the basis of these observations, dynamic rating calculation methods that yield higher thermal ratings in



exchange for an increased (but low) probability of exceeding temperature limits may be justified when applied to substation ter minal equipment. Such approaches can seldom be justified for overhead lines where the public safety may be directly involved.

6.5.2

6.5

• • • •

EPRI'S DTCR TECHNOLOGY

In the 1990s, EPRI developed a software product called Dynamic Thermal Circuit Rating (DTCR) for the purpose of rating transmission circuits in real time. DTCR calculates dynamic thermal ratings of power equipment based on actual load and weather conditions that are generally accessed through the utility’s SCADA/EMS system. Given series or parallel combinations of equipment, the software determines dynamic circuit ratings by evaluating all equipment ratings on a circuit and finding the most limiting ampacity for each rating scenario. This section describes how the software is used. 6.5.1

Power Circuit Modeling

Circuits may be modeled using series-only or parallel circuit branches. Series-only circuits are analyzed by evaluating ratings of all circuit elements (assumed to be connected in series) and then picking the lowest rating of any of the elements (circuit rating). Parallel circuit branches are modeled assuming each branch is comprised of one or more series elements, but the software accounts for the effects of one of the parallel branches being out of service and impacting the loading on the other branches. Three types of data are entered into the system:

DTCR Output

The software tracks critical equipment temperatures and calculates up to four dynamic thermal ratings for each power circuit element. These are saved to the output file and displayed on the screen (see Figure 6.5-2). Typical dynamic ratings might include the following: 24 hour “continuous” rating 1 to 24 hour “long-time emergency” rating 1 to 60 minute “short-time emergency” rating 1 to 24 hour “maintenance” starting at some time in the next 24 hours

Emergency ratings up to 300 hours can be specified for underground cables to calculate ampacities based on the typical repair times of these systems at some utilities. The system also determines the limiting circuit element for each circuit and displays that element’s dynamic rating as that of the circuit. Finally, if the electrical load current exceeds one of the calculated ratings (selected by the user), the software estimates the time until the equipment temperature will begin to exceed a critical

• Data Channels – This input specifies the source of monitored parameters – whether from “real-time” sources or from “override” files. The data may include load, air and soil temperatures, wind speed and direction, solar radiation, and line tension/sag.

Figure 6.5-1 Setting up two circuits in DTCR.

• Circuit Data – This data specifies overall circuit parameters such as emergency rating periods and the rating that is evaluated for time-to-overload. The data channel to use for incoming load data is selected from one of the data channels.

• Circuit Element Data – This data is specific to the equipment being modeled – conductor sizes, maximum allowable temperatures, and installation conditions. The data channels associated with weather parameters or other monitored physical data are also specified. The main input screen for the program is shown in Figure 6.5-1. Double-clicking on a cell brings up data screens specific to that item.

Figure 6.5-2 DTCR output screen.

6-13


temperature for the equipment – this is called “Time to Temperature Overload.” 6.5.3

DTCR is a Calculation Engine for SCADA

While the software provides a simple spreadsheet-like output on a PC monitor, it is intended that each utility user will integrate the output within the standard SCADA operational displays. In most setups, the dynamic rating programs will run on a PC that is networked to SCADA. Figure 6.5-3 illustrates the methods of obtaining realtime data and supplying output to SCADA. Data can either be supplied to the system by SCADA itself or by non-SCADA monitors. A file-based method of input and output is used, so that any monitor that can write a file to the PC hard drive or network can be used for realtime data. SCADA can also retrieve the output calculations from the DTCR output files. 6.5.4

Modeling Complex Interfaces—California “Path 15”

In a recent EPRI research project, a dynamic thermal software model was developed and tested for the California “Path 15” power transmission interface. This complex dynamic thermal model incorporated real-time


rating calculations for four 230-kV lines and three single-phase 500/230-kV autotransformers, which supply the 230-kV lines at the Gates substation. Either the autotransformer or one of the 230-kV lines can determine the Path rating depending upon system operating conditions. As shown in Figure 6.5-4, Path 15 is a complex interface whose total pre-contingency power flow rating can determine maximum power flow from southern to northern California under certain system operating conditions. One of the most important power flow limitations through this interface concerns the postcontingency power flow on the four 230-kV lines if both of the 500-kV lines are suddenly taken out of service. Independent of any dynamic thermal rating procedures, if the two 500-kV lines are suddenly taken out of service, the power flow on the 230-kV lines is reduced through a process of automatic load shedding of interruptible loads and a manual generation reduction at the Diablo Canyon nuclear plant. The 230-kV lines that are most heavily loaded after the loss of the two 500-kV lines are those between Gates and Panoche substations. These lines were dynamically rated in order to reduce the need for post-contingency load reduction and/or to increase the pre-contingency power flows on the 500-kV lines.

Figure 6.5-3 Real-time data transfer flowchart for DTCR.

6-14



use of “effectiveness factors” relating the pre-contingency loads on the 500-kV lines and the other monitored components to the post-contingency loads. “Effectiveness factors” are decimal fractions (derived by studying numerous load flow solutions) that equal the fraction of load shed at a particular location that reduces the load on Path 15.

The Path 15 rating (maximum pre-contingency loading) is calculated as follows (refer to Figure 6.5-4): 1. Tension monitors and weather stations were installed on the two 230-kV lines between Gates and Panoche substations. Real-time air temperature from the weather station near Gates is used for the transformer rating calculations. Electrical loads are available for all components, as is the list of loads that may be shed if the 500-kV double-line outage occurs (“remedial actions or RAS”).

3. The calculated post-contingency loads are reduced according to the list of nearly instantaneous remedial actions (load reductions and generation reductions) and the ramp load reduction undertaken manually at Diablo Canyon. The post-contingency loads for the GP 230-kV lines and the Gates Power Transformers are calculated as shown in Figure 6.5-5.

2. The post-contingency electrical loads on the GatesPanoche (GP) line (singular again) and on the Gates Power Transformer (GPT) are calculated through the

Figure 6.5-4 Circuit diagram for California’s “Path15”. Conductor Temp (C)

Conductor Loading (Amps) Diablo Canyon Ramp Down

Loading Curve

Peak Loading

Max Temp. 100C

Temperature Curve

PostLoading

Pre-outage temp

Preloading Los Banos South DLO

0

2

4

6

8

10

12

14

16

Time (min)

Figure 6.5-5 Post-contingency load shape for Gates-Panoche 230-kV line and Gates 500/230-kV autotransformers with the temperature response of the 230-kV line.

6-15


4. The temperature of the GP lines and the oil/winding temperatures of the GPT are limited in the dynamic rating calculation.


6.6

OPERATING WITH DYNAMIC THERMAL RATINGS

6. The pre-contingency Path 15 power flow is adjusted until the post-contingency power flow through both the GPT and the GP 230-kV lines is less than their dynamic ratings. This pre-contingency Path 15 rating does not incorporate other system limiting conditions such as voltage and stability limits.

The implementation of dynamic thermal ratings usually requires certain changes in operating rules and procedures. The biggest change is simply incorporating the variability of dynamic ratings into operating rules and calculations. Historically, ratings for power equipment have been defined for “worst-case” conditions and do not vary with time and weather or system conditions. The increased capacity attainable with dynamic rating methods requires a major shift in thinking for operations personnel.

6.5.5

6.6.1

5. The loss-of-life and the possibility of gas bubble formation due to the post-contingency power flow in the GPT windings are limited.

Conclusions about the Dynamic Rating of Complex Interfaces

The Path 15 dynamic thermal rating is calculated such that, in the event of a “double-line outage” (DLO), where both 500-kV lines are suddenly taken out of service, the post-contingency power flow in the two GatesPanoche 230-kV lines and in the Gates 500/230-kV transformers does not exceed the dynamic rating of the equipment. Path 15 is probably the most complex transmission interface in the California power system. The successful development and field-testing of this dynamic model of Path 15 strongly suggests that similar dynamic models can be developed for other less complex transmission interfaces. It appears that any such dynamic model development requires:

• System analysis to define the power flow relationships (distribution factors) and the impact of load and generation reduction events.

• Installations of line and power transformer monitors and communication links from remote locations to a server through SCADA.

• Development of a real-time software “shell,” which allows the calculation of pre-contingency and postcontingency loads on critical interface components and includes iterative calculation of interface rating.

• Inclusion of previously developed and tested thermal model algorithm objects such as the EPRI DTCR library.

• Inclusion of off-line power flow limits reflecting concerns about voltage and stability limits.

• Economic trade-off analysis. The Path 15 dynamic modeling project serves as a prototype for managing complex transmission interface power flow with state-of-the-art technology.

6-16

Traditional Rating Definitions

Traditionally, transmission circuits have one or more assigned limits on power flow that the operator must heed. These limits may be set in order to avoid excessive voltage drop or electrical phase shift, to maintain system reliability under certain contingencies, or to avoid overheating equipment in the circuit. This discussion concerns only thermal limits (i.e., ratings) specified in order to avoid damaging power equipment by causing excessively high temperatures in power equipment. A good example of a fairly complex definition of traditional thermal circuit ratings is as follows:

• Continuous (Normal) rating – Power flows at this level may continue indefinitely without infringing minimum electrical clearances of bare energized conductors in lines and substations, without exceeding agreed-upon maximum (Normal) temperatures for conductors in all types of power equipment, and, for up to 7665 hours over the life of such equipment, without reducing the 40-year assumed life of such power equipment or reducing the strength of line conductors by more than 10%.

• Long-time Emergency (LTE) rating – Power flows may continue at this level for infrequent nonconsecutive four-hour periods without infringing minimum electrical clearances of bare energized conductors in lines and substations, without exceeding agreed-upon maximum (LTE) temperatures for conductors in all types of power equipment, and, for up to 300 hours over the life of such equipment, without reducing the 40-year assumed life of such power equipment or reducing the strength of line conductors by more than 10%.

• Short-time Emergency (STE) rating – Power flow may continue at this level for very infrequent postcontingency periods of up to 15 minutes without infringing minimum electrical clearances of bare energized conductors in lines and substations, without exceeding agreed-upon maximum (STE) temper-



atures for conductors in all types of power equipment, and, for up to 12.5 hours over the life of such equipment, without reducing the 40-year assumed life of such power equipment or reducing the strength of line conductors by more than 10%.

implemented depend on the severity of the equipment overloads.

• The “agreed-upon” maximum temperatures, and loss

1. As long as the circuit load is below the Normal rating, no action is required.

of life per event, are usually allowed to increase in going from Normal to LTE to STE ratings. For example, with an overhead line having ACSR conductors, if the Normal maximum temperature is 95ºC, the LTE maximum might be 115ºC, and the STE maximum temperature, 125ºC. Similarly, for power transformers, if the loss of insulation life per event for Normal ratings is 0.0133% (per 24 hours), then the loss of life during an LTE rating could be increased to 0.25%.

• The shorter duration emergency ratings, heat storage should be considered. This may be a factor is the STE rating of lines and the STE and LTE rating of transformers. For example, an overhead transmission line with 1590 kcmil 45/7 ACSR (Lapwing) might have a Normal Summer rating of 1794 amps (100%), an LTE rating of 1924 amps (107%), and an STE rating of 2247 amps (125%), all calculated for the same weather conditions. In many transmission systems, the available thermal rating categories are often simpler. For example, the system operator may be given a single rating for lines (and transformers) with the understanding that normal loads will be no more than 60% of the rating and that emergency loads not exceed it. In this case, the duration of the emergency rating is typically indefinite and equipment damage is avoided by defining modest temperature limits on equipment. 6.6.2

Traditional Operating Rules

Given a rating hierarchy, the transmission system operator is also normally given rules that govern his/her actions in keeping circuit loads below these limits. The goal of these operating rules is that the power system should remain “secure.” That is, all equipment is operating below “normal” ratings and, contingency analysis programs determine that, even with a major generating station or bulk transmission circuit out of service, no equipment exceeds its long-time emergency rating. Should the system be found not to be “secure,” then the operator must take action to restore system security. The type of action and the speed with which it is to be

For example, given the Normal LTE and STE ratings for a circuit, the system operator is instructed to apply them in this fashion:

2. If the circuit load exceeds the Normal rating but is less than the LTE rating, the circuit load must be reduced until it is below the Normal rating within four hours. 3. If the circuit load exceeds the LTE rating but is less than the STE rating, the circuit load must be reduced until it is below the Normal rating within 15 minutes. 4. If the circuit load exceeds the STE rating, the circuit load must be reduced until it is less than the Normal rating immediately. Thermal ratings for other durations can also be defined if useful with the operating rules functioning in a similar fashion. In addition to this desire to keep the power system operating in a secure mode, there is considerable economic motivation to maximize the utilization of low cost generation to meet load demands. To accomplish this, short-term and longer-term economic dispatch calculations are performed. 6.6.3

Operating with Dynamic Ratings

When circuit flows are limited by thermal concerns (rather than stability limits), dynamic thermal ratings offer advantages (and challenges) compared to traditional static thermal ratings. Since dynamic thermal ratings are normally higher than static ratings, the advantages to their use are:

• When dynamic normal ratings are available, the operator may determine that normal load levels that exceed the static rating do not require action since the load does not exceed the dynamic rating.

• When dynamic emergency ratings are available, lowprobability, post-contingency loads that exceed static emergency ratings may be less than dynamic emergency ratings, thus avoiding the need for operator intervention to reduce load.

• Dynamic ratings may allow for considerable cost savings during generation dispatch calculations because they are higher than static ratings, though this may require accurate prediction of dynamic rating values up to a day ahead.

6-17


• SCADA/EMS flexibility and capability • Instrumentation reliability • Availability and reliability of communication links to SCADA

• Rating variability • Engineering acceptance The purpose of this discussion is not be exhaustive but rather to identify obvious barriers to implementation and suggest solutions that might overcome them. SCADA/EMS Flexibility and Capability SCADA/EMS systems are constantly being upgraded, and some older systems may not possess the capability to incorporate dynamic ratings. This limitation is much less common today than it was 5 to 10 years ago. It is likely that any new operational software will be capable of updating circuit ratings if provided by dynamic rating calculation programs. Instrumentation Reliability Instruments may be used to monitor power transformer oil and winding hot spot temperatures, soil temperatures, weather conditions, and tension or sag of overhead lines. Instruments within the substation perimeter are generally safe from vandalism and protected to some extent from lightning and extreme weather conditions. Instruments mounted on overhead line structures and in underground cable manholes are more vulnerable.

Verification of proper instrument function needs to be considered as part of any dynamic rating calculation software. Ideally, indications of malfunction would be reported to system operations in conjunction with dynamic rating values to help in assessing the accuracy of dynamic ratings. Availability and Reliability of Communication Links to SCADA In many power systems, the number and capability of communication links connecting remote substations to SCADA may be a limitation in implementing dynamic ratings.

line rating need be communicated to SCADA/EMS. No similar advantage exists for substation equipment. Communication of monitor data from remote locations to a substation has been successfully accomplished by means of spread spectrum radio and by Cellular Digital Packet Data (CDPD). Solar power sources are usually adequate for such low power transmitters and avoid all the reliability issues inherent in supplying distribution power in remote locations. Rating Variability To many system operators, one of the most annoying aspects of dynamic ratings involves their variability. It is difficult to establish system security if ratings are changing rapidly.

There are several ways to minimize the variability of dynamic ratings. The simplest method is to be sure that the rating variability is not based on monitor inaccuracy or communication problems. Another method of limiting variability is through a combination of averaging and limiting the range of dynamic rating values. Expressing dynamic ratings as the moving average of values calculated over the last several time intervals can reduce variability with little or no loss of accuracy. Limiting dynamic rating values to no more than 30% above static can be a simple method of limiting variability. Figure 6.6-1 illustrates how the use of a moving average calculation can reduce the variability of dynamic ratings for an overhead line. Engineering Acceptance Engineering personnel, both in asset management and operations, typically question the accuracy of important

2700

2500

Rating & Load - amperes

A number of challenges may arise with the use of dynamic ratings, which results in their not being more widely integrated into power system operations. These challenges include:


2300

2100

1900

1700

For overhead lines, where multiple monitors may be required to ensure that worst-case locations are included, the number of real-time data values coming into SCADA may be 10 or more. In this case, placement of computation in a substation location might be preferable to placement at a central location, since only the

6-18

1500 0:00

2:24

4:48

7:12

9:36

12:00

14:24

Time-of-Day LTE-4Hr

6 per. Mov. Avg. (LTE-4Hr)

Figure 6.6-1 Dynamic ratings with moving average to reduce variability.

16:48


calculated equipment parameters such as ratings. Certainly, fundamentally, dynamic ratings need to be based on the same equipment limitations as are used for static ratings. For example, with an overhead line, conventional static ratings are calculated for a maximum conductor temperature. That same maximum conductor temperature would also be used in performing dynamic rating calculations. One way to improve engineering acceptance of dynamic ratings is by using the same calculation method for dynamic ratings as is used for static ratings. For example, the EPRI DTCR software models power transformers with the same “Top Oil” and “Bottom Oil” models that are used in the IEEE Loading Guide C57.92-1995 and in the engineering program PTLOAD. The provision of the PTLOAD software for static rating calculations has been very helpful in gaining acceptance for the DTCR dynamic rating calculation method and eases the set-up and results checking necessary to verify the dynamic rating results. 6.7

FIELD STUDIES OF DYNAMIC RATINGS

Dynamic ratings have been employed to allow increased loading of lines, power transformers, and underground cables. More recently, substation equipment has been included in the list of equipment for which dynamic ratings may be applicable. Real-time thermal algorithms have been developed for overhead lines, underground cables, power transformers, and substation switches, bus, and line traps. Most of the research has centered on verifying these algorithms with field test data. 6.7.1


when compared to differences produced by measurement methods. That is, given a certain series of chronological weather and load values, each real-time algorithm will yield very similar calculated temperatures (and consequently, dynamic ratings). Conclusions based on these field measurements include the following: 1. For a line section (multiple suspension spans having nearly the same tension), limited by electrical clearance, dynamic ratings based on a single sag or tension monitor are more accurate than those based on a single weather station or temperature monitor. 2. For lines consisting of many line sections, multiple measurement locations coupled by radio communication links are necessary for accurate dynamic rating calculations of the whole line. 3. At low wind speeds, when the dynamic rating is lowest and most sensitive to weather, the prediction of wind direction and persistence is nearly impossible due to limitations on equipment and the turbulent nature of low speed winds. In particular, Figure 6.7-1 illustrates the need to monitor multiple line sections for long lines. It shows the dynamic rating of each of four different line sections (from the same line) over a 24- hour period. Note that the limiting line section (the section with the lowest rating) varies during the day. Thus all would need to be monitored to ensure a safe dynamic rating for the whole line. 4. At current levels less than 0.5 A per kcmil, dynamic thermal ratings determined by sag or tension monitors are not accurate.

Overhead Lines

The potential increase in thermal rating of overhead lines through the use of dynamic rating methods is larger than for other power equipment. As a result, there have been many field studies of lines. A variety of overhead line thermal model algorithms have been field tested. (Examples are the EPRI “DYNAMP” algorithm [Black and Byrd 1983], the IEEE P738 thermal model, and a slightly different model proposed by CIGRE Study Committee 22 [CIGRE 1997].) Each algorithm is capable of tracking the present conductor temperature based on real-time weather station data and on line current or on sag or tension monitor data. A study by Schmidt (Schmidt 1997) indicates that any difference between these algorithms and the IEEE Standard 738-1993 (IEEE 1993) is quite small, particularly

Figure 6.7-1 Variation in limiting line section for a monitored 230-kV line.

6-19


6.7.2

Power Transformers

Three distinct dynamic loading algorithms are available in the DTCR software to model power transformers. These are based on the IEEE Top Oil model (IEEE 1996), the IEEE Bottom Oil model (IEEE 1996) and the “IEC” model (IEC 1991). As is the case for overhead lines, except for very short time loads, the calculated dynamic loadings using the three models for power transformers are relatively similar. Each requires slightly different transformer test data (the IEEE Bottom Oil model requiring considerably more detailed test data than the other two). The more complex Bottom Oil model does a better job modeling short-time loads. In comparison to overhead lines and underground cable, real-time monitoring and dynamic loading of power transformers offer some special difficulties:

• The critical transformer temperature is the winding hot spot. Normally, it is impossible to directly measure the hottest spot winding temperature in older transformers without a fiber optic hot spot monitor.

• All the transformer dynamic loading calculation models require laboratory test data for hot spot rise over top oil, which may be difficult or impossible to find for a 40 year-old unit.

• In addition to maximum winding current limits, the dynamic thermal rating of power transformers may depend on loss of insulation life, maximum oil temperature, maximum hot spot temperature, or the formation of bubbles in winding insulation.

• Auxiliary equipment such as bushings, conductor leads, tap changers, and associated protection limits may limit transformer dynamic loading.

• Protection settings must also be considered. Unwanted tripping could occur in overload situations.

• Older units may be in poor condition requiring that limits on winding temperature and insulation loss-oflife be reduced below those of newer units. 6.7.3

ments, even power transformers. As a result, short-time emergency ratings for underground cable are normally much higher than for other types of power equipment. Chapter 3 in this IPF Guidebook discusses the thermal rating of underground cable in considerable detail. 6.7.4


Substation terminal equipment consists of many different types and designs of power equipment. Included in this classification are line traps, oil circuit breakers, SF6 circuit breakers, rigid tubular bus, line disconnects, current transformers, bolted connectors, and insulated bushings. The dynamic thermal rating of substation terminal equipment centers on practical, rather simple methods that avoid the use of monitoring instruments and dedicated communication links. In dynamically rating equipment such as switches, bus, line traps, breakers, and power transformer auxiliary equipment, it must be kept in mind that replacement is generally less expensive than for lines, cables, and transformers, and therefore the more elaborate methods of monitoring are difficult or even impossible to justify economically. Also, because of the large number of switches, circuit breakers, etc., in any power system, and the variety of designs, thermal models and weather monitoring must be kept simple. 6.7.5

Power Circuits

Power systems are operated with the goal of maintaining a secure system wherein normal circuit loads are less than circuit normal ratings and post-contingency loads (mostly for the loss of a single major system component) are less than circuit emergency ratings. Most circuits consist of multiple series circuit elements. Figure 6.7-2 shows a simple circuit consisting of a switch and an overhead line segment. The static rating of the switch is 1200 A, and the line, consisting of Bunting ACSR conductor, is rated at 1310 A at 90°C. The static circuit rating is therefore 1200 A, limited by the switch.

Underground Cables

Many field tests of dynamic rating for underground cable circuits have been undertaken. By and large this application of dynamic rating methods is the most successful. The dynamic rating of underground cable is determined by the loading of the cable (which varies) and the thermal resistivity of the surrounding soil, which varies between locations but not very much with time. The thermal time constants associated with underground cables are much larger than those of other ele-

6-20


Line Current Switch Line Segment

Figure 6.7-2 Circuit diagram for a simple transmission circuit.


Using DTCR3 to model this circuit, we find that the line segment limits the circuit for short-time emergency ratings, and either element can determine the LTE rating, depending on the wind speed (see Figure 6.7-3). 6.7.6

Communications and Monitoring

In early field tests, the DTCR software was installed on computers placed in the substation environment. This generally yielded unsatisfactory results, which included hardware thefts, travel to remote locations to investigate problems, and unreliable communications. In consequence, the software was modified in its most recent version to obtain real-time input from and send calculated output to, volatile ASCII files on the PC. These files are read and written by simple SCADA-based software programs. Real-time monitors are interfaced with the SCADA system not with the dynamic loading computer, and calculated dynamic thermal ratings are read into the SCADA database from which they can be displayed according to the wishes of each utility. The advantage of this arrangement is primarily one of simplicity and reliability. Other benefits include centralizing the DTCR application onto one computer, and having this computer near computer maintenance personnel. The communication between remote monitors and the utility SCADA database is handled by separate commercial software and hardware, which has nothing to do with the dynamic rating calculation software. Utilities likely have existing interface methods in use for other applications. They may choose the most appropriate interface based on maintenance and ease of use criteria.


This arrangement also allows the utility operations people to display the calculation results in the fashion they prefer rather than being forced to use the output screen provided. The information may be dynamically linked to transmission/generation scheduling or generation shedding systems. The calculated and measured information is available for data storage by a component of an Energy Management System (EMS), making historical information available to dispatchers. The advantage of this arrangement is primarily one of simplicity and reliability. The communication between remote monitors and the utility SCADA database is handled by separate commercial software and hardware, which has nothing to do with the dynamic rating calculation software. This arrangement also allows the utility operations people to display the calculation results in the fashion they prefer rather than being forced to use the output screen provided. 6.8

CONCLUSIONS

Dynamic thermal rating methods apply to all power equipment, indeed to all power circuits. By monitoring the thermal environment and perhaps the equipment itself in real-time, the utilization of thermal capability may be safely increased. Dynamic methods are capable of yielding an increase of 5 to 15% in the effective thermal rating of most power equipment, which can result in both more economic operation and in postponement of equipment capital investment in low growth areas. Certain specific observations about dynamic ratings can be made: 1. Real-time monitoring of power equipment may be used in evaluating dynamic loading methods, but monitoring alone does not predict the future consequences of present loading. Dynamic loading methods allow time for remedial action. 2. Dynamic rating methods require the cooperation of transmission planners, operators, and engineers in order to gain maximum benefit. 3. Wind is the most crucial factor in rating overhead lines correctly. Because of the variability of wind along the line, multiple monitoring locations are required, especially for long lines.

Figure 6.7-3 Short-time and long-time emergency dynamic thermal ratings of 1200 A switch and Bunting line segment.

4. Power transformers are the most complex equipment to rate dynamically since such methods involve limits on insulation life, oil and winding temperature, gas bubbles, and auxiliary equipment. 5. The most attractive candidates for dynamic thermal rating are those requiring the most capital to replace.

6-21


6. Dynamic thermal rating methods and the accurate prediction of post-contingency loadings are most useful in combination with fast-reaction load controls. 7. Real-time data should be obtained from direct SCADA links rather than by direct telephone or radio communication with remote monitors. 8. Probabilistic ratings offer an attractive alternative to dynamic rating methods for certain types of transmission equipment, provided the thermal models and field data are accurate. REFERENCES

ANSI. 1978. ANSI C57.13-1978. Requirements for Instrument Transformers.


Douglass, D. A. and A. Edris. 1999. “Field Studies of Dynamic Thermal Rating Methods for Overhead Lines.” IEEE T&D Conference Report. New Orleans. April 7. New Orleans, LA. Edris, A. 2000. “FACTS Technology Development: An Update.” IEEE Power Engineering Review. Vol. 20. No. 3. March. IEEE. 1993. IEEE Standard 738-1993. “Standard for Calculating the Current-Temperature Relationship of Bare Overhead Conductors.” IEEE. 1996. IEEE Standard C57.91-1995. “IEEE Guide for Loading Mineral-Oil-Immersed Transformers.” April 25.

ANSI. 1979a. ANSI C37.37-1979. Loading Guide for AC High-Voltage Air Switches (in excess of 1000 volts).

International Electrotechnical Commission. 1982. IEC287. “Calculation of the Continuous Current Rating of Cables (100% Load Factor).”

ANSI. 1979b. ANSI C37.010-1979. Application Guide for AC High Voltage Circuit Breakers rated on a Symmetrical Current Basis.

International Electrotechnical Commission. 1989. IEC853-2. “Calculation of the Cyclic and Emergency Current Rating of Cables.” 1st Edition.

ANSI. 1981. ANSI C93.3, 1981. Requirements for Power-Line Carrier Line Traps.

International Electrotechnical Commission. 1991. IEC International Standard 354. 2nd Edition, “Loading Guide for Oil-immersed Power Transformers.”

Black, W. Z. and W. R. Byrd. 1983. “Real Time Ampacity Model for Overhead Lines.” IEEE Transactions. Vol. PAS-102. No. 7. July. pp. 2289–2293. CIGRE. 1997. CIGRE WG12-22. “Thermal State of Overhead Line Conductors.” Electra. No. 121. pp. 51-67. Coneybeer, Robert T. 1992. “Transient Thermal Models for Substation Transmission Components.” Master's Thesis. School of Mechanical Engineering, Georgia Institute of Technology. Conway, B. J. et al. 1979. “Loading of Substation Electrical Equipment with Emphasis on Thermal Capability.” IEEE Transactions on Power Apparatus and Systems. Vol. PAS-98. No. 4. July/August. pp. 1394– 1419. Cronin, John. 1972. “Rate Substation Equipment for Short-time Overloads.” Electrical World Magazine. April 15. Douglass, D. A. and A. Edris. 1996. “Real-time Monitoring and Dynamic Thermal Rating of Power Transmission Circuits.” IEEE Transactions on Power Delivery. Vol. 11. No. 3. July.

6-22

Massey, D. E. et al. 1971 “Determination of Disconnecting Switch Ratings for the Pennsylania-New Jersey– Maryland Interconnection.” IEEE Symposium on High Power Testing. Portland, OR. July. Neher, J. H. and M. H. McGrath. 1957. “The Calculation of the Temperature Rise and Load Capability of Cable Systems.” Paper 57-660. AIEE Insulated Conductors Committee. June. Schmidt, N. 1997. “Comparison between IEEE and CIGRE Ampacity Standards.” IEEE PE-749-PWRD-006-1997. Berlin, Germany. July. Seppa, T. O. et al. 1998. “Use of On-Line Tension Monitoring Systems for Real Time Ratings, Ice Loads and Other Environmental Effects.” CIGRE Report 102-22. September. Paris, France.


Glossary

AAAC. AAC.

All Aluminum Alloy Conductor. (Chapter 2)

All Aluminum Conductor. (Chapter 2)

Annealing. Process wherein the tensile strength of copper or aluminium wires is reduced at sustained high temperatures. (Chapter 2)

ACAR.

Aluminum Conductor Alloy Reinforced. (Chapter 2)

ASTM .

ACCR.

Bottom Oil Model. One of several methods of modeling

ACSR. Aluminum Conductor Steel Reinforced. (Chapter 2)

the winding temperature of power transformers. Temperature calculation methods presented in the 1995 revision of IEEE C57.91 as Annex G. See also Top Oil Model and IEC Model 354-1991. (Chapter 4)

ACSS.

Aluminum Conductor Steel Supported. (Chapter 2)

CGIT .

AEIC.

Compressed Gas Insulated Transmission (CGIT) Cables.

Aluminum Conductor Composite Reinforced. (Chapter 2)

Association of Edison Illuminating Companies. (Chapter 3)

Aeolian Vibration. Most common type of wind-induced motion of conductors. The vibration is caused by the alternate shedding of wind-induced vortices from the top and bottom sides of the conductor. This action creates an alternating pressure unbalance, inducing the conductor to move up and down at right angles to the direction of the air flow. This vibration occurs at relatively low wind speeds, and conductor fatigue damage is cumulative in nature. (Chapter 2) Aluminum Conductor Steel Supported (ACSS). Conductor design consisting of fully annealed strands of aluminum (1350-H0) stranded around stranded steel core. The steel core wires may be aluminized, galvanized, or aluminum clad, and are normally “high strength,” having a tensile strength about 10% greater than standard steel core wire. (Chapter 2)

American Society for Testing and Materials. (Chapter 2)

See Compressed Gas Insulated Transmission. (Chapter 3)

A system of SF6 gas and epoxy insulators used to insulate a hollow, rigid aluminum conductor from a tubular aluminum enclosure. The most common applications for CGIT lines are situations where very high ampacities are required (i.e., > 2000 A), usually to connect with overhead lines entering a station or as a high-capacity bus within a station. (Chapter 3) Conductor Hardware. Noncurrent carrying devices

attached directly to the conductor. Conductor hardware includes components such as suspension clamps (with or without armor rods), dampers, repair sleeves and splices, spacers and spacer dampers, shackles, pins, etc. (Chapter 2) Continuous (Normal) Rating. Current at this level (MVA or amperes) may continue indefinitely without without exceeding agreed-upon maximum (Normal) temperatures for conductors or critical components in all types of power equipment. (Chapter 6)

Ampacity. The ampacity of a conductor is that maxi-

mum constant current that will meet the design, security, and safety criteria of a particular line on which the conductor is used. In this Guidebook, ampacity has the same meaning as “steady-state thermal rating.” (Chapter 2)

Core-Form Construction. Power transformer design constructed with windings that are in the general form of concentric cylinders. (Chapter 4)

G-1

Glossary


Creep Elongation . Creep constitutes an irreversible,

Exceedance Level. Amount of time a conductor exceeds

plastic elongation occurring in the aluminum strands of bare overhead conductor, which occurs as a result of tension over extended periods of time. Higher rates of creep occur when a conductor is operated for extended periods of time at operating temperatures in excess of approximately 50°C. (Chapter 2)

the design temperature expressed as a percentage of total time. (Chapter 2)

Cross-Linked Polyethylene (XLPE) Cables. Most common on modern XD cable systems with applications up to 500 kV. The insulation is cross-linked (vulcanized), forming long polymer chains that are joined to one another at intermediate carbon atoms. (Chapter 3) Deterministic Methods. Method of uprating overhead

transmission lines (without reconductoring) using tradit i o n a l c a l c u l at i o n m e t h o d s, s u c h a s t h e E P R I DYNAMP program, with fixed, worst-case weather condition assumptions. (Chapter 2) Direct Flow Design . Design of power transformer

employing forced oil cooling. The transformer internal assembly is designed with oil manifolds that direct the incoming cool oil to the lower part of the core and windings. A directed flow design is normally used with larger sizes of transformers equipped with heat exchangers rather than radiators. (Chapter 4)

Extruded Dielectric (XD) Cables. Cables are so named

because the insulation is extruded onto the conductor core, as compared to paper-insulated cables (HPFF or SCFF), where the insulation is a laminar application of paper tapes. Three types of XD cables include: crosslinked polyethylene (XLPE) cables, ethylene-propylenerubber (EPR) cables, and linear low- or medium-density polyethylene (LLPE, MDPE) cables. (Chapter 3) Factory Heat Run. A direct measurement of the thermal performance of a transformer at a particular benchmark, the nameplate rating. Two methods are used to perform factory heat runs: the “short-circuit” method and the “loading-back” method. (Chapter 4) Flexible AC Transmission System ( FACTS ). A power electronic-based technology for enhancing controllability and increasing power transfer capability of transmission circuits. FACTS controllers provide the system operator with the means of rapidly controlling loads on particular circuits in order to maximize power transfer capability of transmission corridors. (Chapter 6) Fluidized Thermal Backfill (FTB). Fill used in trenches for

DTCR.

See Dynamic Thermal Circuit Rating. (Chapter 3)

underground cable that helps ensure good heat transfer away from the cable pipes. (Chapter 3)

Dynamic Rating . Limits on the level and duration of

power carried by power equipment based on actual weather conditions. (Chapter 2) Dynamic Thermal Circuit Rating (DTCR). EPRI software developed to take real-time data from “off the shelf ” monitoring hardware, and determine optimal ratings (not worst-case) for the conditions at the time the ratings were performed. (Chapter 3) Emergency Rating. Conductor rating that specifies how much current can flow through power equipment under emergency conditions for a specified amount of time— e.g., 30 minutes. (Chapter 2) EPR.

See Ethylene-Propylene-Rubber. (Chapter 3)

Ethylene-Propylene-Rubber ( EPR ) Cables. Insulation type often considered for distribution cables and transmission cables up to 138 kV. The insulation is very “lossy” as compared to XLPE insulation, resulting in high dielectric losses and charging current. (Chapter 3)

G-2

Gapped ACSR (GTACSR). Type of high-temperature conductor invented in Japan, which consists of a conventional steel core surrounded by layers of trapezoidal zirconium aluminum wires, and the gap filled with grease. The zirconium aluminum does not anneal until reaching temperatures in excess of 200oC. Through the use of special terminations and suspension clamps and by preloading the steel core, the ther mal elongation of the conductor is less than that of conventional ACSR, while maintaining the full strength of a conventional ACSR conductor under heavy ice conditions. (Chapter 2) High-Pressure, Fluid-Filled ( HPFF ) Pipe-Type Cables . One of two kinds of pipe-type cables (the other being HPGF). HPFF cables are installed in cable pipes where the pipe is filled with very clean, very low moisture dielectric fluid. Older HPFF cable systems (before 1970) typically used mineral oil for the pipe filling dielectric fluid. HPFF cable systems installed after 1970 have used alkyl benzene or polybutene dielectric fluid. (Chapter 3)


High-Pressure, Gas-Filled (HPGF) Pipe-Type Cables. One

of two kinds of pipe-type cables (the other being HPFF). HPGF cables use pressurized dry nitrogen gas inside the cable pipe. (Chapter 3) High-Temperature, Low-Sag (HTLS) Conductors. Conductors capable of continuous operation at temperatures above 100oC with stable tensile strength and creep elongation properties. Such conductors are commercially available or under development. (Chapter 2) HPFF.

See High-Pressure, Fluid-Filled. (Chapter 3)

HPGF.

See High-Pressure, Gas-Filled. (Chapter 3)

See High-Temperature, Low-Sag Conductors. (Chapter 2)

HTLS .

Glossary

higher temperatures without forming cross-linking agents present. (Chapter 3) LLPE.

See Linear Low-Density Polyethylene. (Chapter 3)

Load Losses. Losses generated by transformers that vary with load current but not with excitation. (Chapter 4) Long-Term Emergency (LTE) Rating. A rating where the

thermal heat storage capacity of the equipment does not greatly impact the rating. For power transformers, the bulk oil time constant makes this definition a bit unclear given the cyclic variation in load and air temperature. Sometimes defined as a rating greater than 2 to 4 hours in duration. (Chapter 4) Mass Impregnated (MI) Cables. Cables sometimes used

Insulated Cable Engineers Association. (Chapter 3) ICEA.

Ice Galloping. Wind-induced conductor motion occurring with both single and bundled conductors, and requiring high winds and ice on the conductors. (Chapter 2)

International Electrotechnical Commission (Chapter 3) or International Engineering Consortium (Chapter 2)

up to 69 kV for ac systems, although they are not that common at this voltage. These cables have paper tapes that are impregnated with a high-viscosity dielectric fluid. MI cables are used for ac applications, but are more common for HVDC submarine applications where there may be a significant change in elevation along the cable route that would otherwise be complicated by hydrostatic head pressures. (Chapter 3)

IEC.

MDPE. MI.

One of several methods of modeling the winding temperature of power transformers. See also Top Oil Model and Bottom Oil Model. (Chapter 4)

Medium-Density Polyethylene. (Chapter 3)

See Mass Impregnated. (Chapter 3)

IEC Model 354-1991.

The Institute of Electrical and Electronics Engineers. (Chapter 3)

IEEE.

Invar Steel. A type of steel core wire used in transmission conductors, which has a high nickel content. It has a 15-20% lower tensile strength than conventional galvanized steel wire and a much lower coefficient of thermal expansion than regular high-strength steel wire. (Chapter 2)

NESC.

National Electric Safety Code. (Chapter 2)

No-Load Losses. Losses generated by transformers that do not vary with load current but rather vary with excitation or voltage. (Chapter 4) Normal Rating. Power equipment thermal rating that specifies how much current may flow in the circuit on a continuous basis. (Chapter 4)

Linear Low- or Medium-Density Polyethylene ( LLPE , MDPE ) Cables . Insulation type less common for new

ODAF (Directed FOA). One of four cooling configurations used by oil-immersed power transformers. Pumps are used to circulate the oil. Fans are used to force air over the radiators or heat exchangers. The forced circulation of the oil increases the convective heat transfer from the windings to the oil. The forced air increases the convective heat transfer from the oil to the air. With ODAF, ducts are added to direct the oil over the winding. This forces a significant portion of the forced oil to flow upward through the vertical winding ducts. (Chapter 4)

installations, although there are several installations, predominantly in France. As compared to XLPE insulation, LLPE and MDPE were first used at the higher voltage levels because the extrudate could be raised to

OFAF (Non-directed FOA). One of four cooling configurations used by oil-immersed power transformers. Pumps are used to circulate the oil. Fans are used to

Knee-point Temperature. The conductor temperature

above which the aluminium strands of an ACSR conductor have no tension or go into compression. (Chapter 2)

G-3

Glossary

force air over the radiators. The forced circulation of the oil increases the convective heat transfer from the windings to the oil. The forced air increases the convective heat transfer from the oil to the air. With OFAF, there are no ducts to direct the oil over the winding. In general, the bulk of the forced oil flow passes upward between the winding and the tank, bypassing the windings. (Chapter 4) One of four cooling configurations used by oil-immersed power transformers. No pumps are used to circulate the oil. Fans are used to force air over the radiators to increase heat transfer from the bulk oil to the surrounding air. As with ONAN, oil circulates upward through the windings and down through the radiators by natural thermosiphon flow. (Chapter 4)


Ruling (Effective) Span. Hypothetical level span length

wherein the variation of tension with conductor temperature is the same as in a series of suspension spans. (Chapter 2) Sagging Line Mitigator (SLiM). A new class of line hard-

ware that uses a shape-memory alloy actuator, activated by increased temperature, to reduce excessive sag in conductors. (Chapter 2)

ONAF (FA).

Sag-Tension Calculations . Calculations performed using numerical programs in order to determine the sag and the tension of a conductor catenary as a function of ice and wind loads, conductor temperature, and time. (Chapter 2) Self-Contained Liquid-Filled (SCLF) Cables. Cables uti-

One of four cooling configurations used by oil-immersed power transformers. Also referred to as self-cooled, no pumps are used to circulate oil, and no fans are used to increase airflow over the radiators. Oil circulates upward through the windings and down through the radiators by natural thermosiphon flow. (Chapter 4) ONAN (OA).

Paper Insulated Lead Covered ( PILC ) Cables . Cables sometimes used up to 69 kV for ac systems, although they are not that common at this voltage. Uprating approaches would be somewhat similar to those of extruded or self-contained cables. These cables have paper tapes that are impregnated with a high-viscosity dielectric fluid. (Chapter 3) PILC.

See Paper Insulated Lead Covered. (Chapter 3)

Probabilistic Line Rating Methods. Methods that use the

actual weather data and conditions prevailing on a conductor to determine the likelihood or probability of a certain condition occurring. Probabilistic methods include the Absolute Method, the Exceedance Method, the Modified Exceedance Method, and the Safety Method. (Chapter 2) Quasi-Dynamic (Real-Time) Ratings . Quasi-dynamic ratings are applied by monitoring load and temperatures for a period of time and then calculating what the conductor temperature might be as a result of that load. From this, the temperature of the cable conductor at rated temperature can be extrapolated for rating purposes. (Chapter 3) Rated Breaking Strength (RBS). Breaking strength of a

bare overhead conductor as calculated by the methods described in appropriate ASTM or IEC manufacturing standards. (Chapter 2)

G-4

lizing the dielectric liquid impregnated laminated paper insulation similar to pipe-type cables, but with three separate cables installed for the three phases. The cable is called “fluid-filled” because there is a hollow fluid channel in the center of the conductor that allows dielectric liquid to move through the cable with thermal expansion and contraction. Also known as self-contained oilfilled (SCOF) or low-pressure oil-filled (LPOF). (Chapter 3) Self-Contained Oil-Filled (SCOF) Cables. Cables utilizing the dielectric liquid impregnated laminated paper insulation similar to pipe-type cables, but with three separate cables installed for the three phases. Also known as self-contained liquid filled (SCLF). (Chapter 3) Shell-Form Construction. Power transformer design in

which windings are initially assembled flat with insulation and cooling ducts between sections. Complete phase assemblies are then clamped and oriented in a vertical direction so that the plane of the individual sections are upright. (Chapter 4) Short-Term Emergency ( STE ) Rating . Short-term ratings are usually defined as extremely short duration ratings that take advantage of the thermal capacity of the equipment. These ratings range from 5 to 30 minutes in duration. (Chapter 4) SIL.

See Surge Impedance Loading. (Chapter 3)

Simulated Winding Temperature Indicator ( WTI ). The most common device for measuring winding temperatures in power transformers. These devices simply measure the temperature of a specially calibrated heating element that is immersed in the top bulk oil near the tank wall. (Chapter 4)


SLiM. See Sagging Line Mitigator. (Chapter 2) Static Ratings . Limits on the level and duration of power transferred over a line based on specified worstcase weather conditions. (Chapter 2) Stray Flux Heating . Heating of non-current carrying

metal components by the leakage flux of the windings and leads. The leakage flux induces eddy current in any conducting material that it passes through. This includes the steel clamping structure, tie rods or tie plates, metal core bands, and the tank wall itself. Since leakage flux varies proportionally with load current, the stray flux heating increases roughly with the square of winding current. For larger power transformers and GSUs in particular, the problem of stray flux heating can be substantial. (Chapter 4)

Glossary

Time-To-Overload ( TTO ). Parameter indicating to the system operator how much time is left until equipment temperatures exceed safe limits. (Chapter 6) Top Oil Model. One of several methods of modeling the winding temperature of power transformers. Temperature calculation methods presented in Clause 7 of IEEE C57.91-1995. See also Bottom Oil Model and IEC Model 354-1991. (Chapter 4) Trapezoidal Wire (TW). Aluminum trapezoidal wire used

in conductors in place of round wires, which thereby potentially increases the cross-sectional area of a round wire conductor of the same diameter by approximately 20%. (Chapter 2) Upgrading. Using available infrastructure to economi-

cally put in new cables. (Chapter 3) Subconductor Oscillation . Wind-induced conductor

motion occurring with bundled phase conductors when wind speeds exceed a certain critical velocity. (Chapter 2)

Uprating. Improving the capacity of existing equipment. (Chapter 3)

Surge Impedance Loading (SIL) Limits. Limits involving a greater than allowable phase shift in power frequency from one end of a transmission system to the other. As a result, the two ends of the system cannot remain synchronous, resulting in instability and outages. This system stability consideration is generally an issue on overhead transmission lines that are 80-320 km (50-200 miles) in length. (Chapter 3)

Video Sagometer. EPRI device, based on digital video

TACSR.

See Thermal-resistant Aluminum Conductor Steel Reinforced. (Chapter 2)

Thermal Elongation. Metallurgical phenomenon in conductors where the material increases in length in proportion to an increase in temperature. (Chapter 2)

technology, for monitoring conductor sag in real time. (Chapter 2) Voltage Drop. Limit placed on power flow correspond-

ing to the maximum allowable decrease in voltage magnitude. (Chapter 2) “Worst-case” Weather Conditions for Line Rating Calculation. Weather conditions that yield the maximum or

near-maximum value of conductor temperature for a given line current. (Chapters 2 and 5) XD.

See Extruded Dielectric. (Chapter 3)

XLPE.

See Cross-Linked Polyethylene. (Chapter 3)

Thermal Property Analyzer (TPA). Device used for field

and laboratory measurement of thermal resistivity. (Chapter 3)

ZTACIR.

Thermal-resistant Aluminum Conductor Steel Reinforced (TACSR). Conductor widely used in Japan, with a

ZTAL

special type of aluminum strand capable of operating at temperatures up to 150 o C without losing tensile strength. (Chapter 2)

ZTAL aluminium alloy conductor reinforced by an Invar steel core. (Chapter 2) (“Super Thermal-resistant Aluminium”). An aluminium zirconium alloy that has stable mechanical and electrical properties after continuous operation at temperatures of up to 210oC. (Chapter 2)

G-5


Index All references are to section or subsection numbers.

A AAC Sag-tension calculations, 2.2.3 ACCR, 2.6.7 ACSR High-temperature sag, 2.2.3 Sag-tension models, 2.4.3 ACSS, 2.6.3 Air-core reactor, 5.3.3 Ampacity, 3.4.2 Ampacity audit, 3.6.5 Calculating ampacity, 3.4.5 Effect of various parameters, 3.4.6 Increasing ampacity (of underground cables), 3.6 Annealing, 2.4.2 B Bus conductors, 5.3.1 Bushings, 5.3.6 C Case studies Overhead, 2.8 Underground, 3.9 CGIT (Compressed Gas-Insulated Transmission) cables, 3.2.4 Compressed gas-insulated transmission cables, 3.2.4 Conductor blowout, 2.2.4 Conductor hardware, 2.4.14 Constraints on uprating overhead transmission lines, 2.2 Constraints on uprating underground cables, 3.5 Continuous (normal) rating, 6.6.1 Creep elongation, 2.4.12 Cross-linked polyethylene, 3.2.2 Current transformers, 5.3.7 D DTCR (Dynamic Thermal Circuit Rating), 2.7.5, 3.8.2, 3.8.3, 6.5 Dynamic monitoring, 2.7 Real-time monitors, 2.7.5 Video sagometer, 2.7.5

Dynamic ratings (overhead transmission), 2.3.1, 2.7.2 Advantages, 2.7.3, 3.8.3 Calculations, 2.7.6 Disadvantages, 2.7.4 Underground cables, 3.8 Dynamic ratings (underground cables), 3.8, 6.4.4 Benefits, 3.8.3 Dynamic Thermal Circuit Ratings, 3.8.2 Monitoring, 3.8.4 Quasi-dynamic ratings, 3.8.5 Dynamic Thermal Circuit Rating (DTCR), 2.7.5, 3.8.2, 3.8.3, 6.5 DTCR output, 6.5.2 Power circuit modeling, 6.5.1 Dynamic Thermal Ratings Condition assessment and real-time monitors, 6.3 Costs, 6.2.2 Field studies, 6.7 Models, 6.4 Accounting for heat storage, 6.4.1 Overhead lines, 6.4.2 Power Transformers, 6.4.3 Substation terminal equipment, 6.4.5 Underground cables, 6.4.4 Operating with dynamic thermal ratings, 6.6 E Electric field, 1.3.5 Electrical clearance, 2.2.5 Elongation Creep elongation, 2.4.12 Thermal elongation, 2.4.11 Emergency ratings, 2.4.1, 3.4.7 Environmental limits (for overhead transmission lines), 1.3.5, 2.1.4 EPR (Ethylene-Propylene-Rubber) cables, 3.2.2 Ethylene-Propylene-Rubber cables, 3.2.2 Extruded dielectric, 3.2.2 F FACTS (Flexible AC Transmission Systems), 1.3.3, 6.2.3 Flexible AC Transmission Systems, 1.3.3, 6.2.3

I-1

Index

G Gapped Construction, 2.6.6 H Heat balance methods, 2.3.5 Convection, 2.3.5 Ohmic losses, 2.3.5 Radiation, 2.3.5 Solar heating, 2.3.5 Steady-state thermal rating, 2.3.5 High-temperature operations (of overhead transmission lines), 2.4 Connectors at high temperature, 2.4.13 High-pressure fluid-filled cables, 3.2.1 High-pressure gas-filled cables, 3.2.1 High-pressure pipe-type cables, 3.2.1 Hot spots Identification (underground cables), 3.5.6 Remediation (underground cables), 3.6.6 HPFF (High-Pressure Fluid-Filled) cables, 3.2.1 HPGF (High-Pressure Gas-Filled) cables, 3.2.1 Hybrid (underground and overhead) circuits, 3.3.3 Hydraulic circuit, 3.5.8 I Ice loading, 2.2.7 Invar steel core conductor, 2.6.5 L Limiting conditions, 1.3 Circuit power flow limits, 1.3.1 Environmental limits, 1.3.5 Surge impedance loading of line, 1.3.2, 3.3.1 Thermal limits, 1.3.4, 3.3.1 Voltage drop limitations, 1.3.3 Linear low-density polyethylene cables, 3.2.2 Line traps, 5.3.8 LLPE (Linear Low-density Polyethylene) cables, 3.2.2 Long-time emergency rating, 6.6.1 Losses (underground cables), 3.4.3 M Magnetic field, 1.3.5 Mass impregnated cables, 3.2.4 MDPE (Medium-Density Polyethylene) cables, 3.2.2 Medium-density polyethylene cables, 3.2.2 MI (Mass Impregnated) cables, 3.2.4 Modeling Complex interfaces, 6.5.5 Power circuits, 6.5.1 Monitoring (underground cables), 3.8.4 N National Electric Safety Code, 2.2.5 NESC (National Electric Safety Code), 2.2.5 Normal rating, 2.4.1 I-2


O Ohmic losses, 2.3.5 Oil circuit breakers, 5.3.4 Operating with dynamic thermal ratings, 6.6 Overhead transmission lines Case studies, 2.8 Dynamic monitoring and line rating, 2.7 Disadvantages, 2.7.4 Dynamic rating calculations, 2.7.6 Dynamic ratings versus static ratings, 2.7.2 Real-time monitors, 2.7.5 Dynamic thermal rating models, 6.4.2 Effects of high-temperature operations, 2.4 Annealing of aluminum and copper, 2.4.2 Axial compressive stresses, 2.4.4 Built-in stresses, 2.4.5 Calculation of conductor high-temperature sag and tension, 2.4.8 Conductor hardware, 2.4.14 Connectors at high temperature, 2.4.13 Creep elongation, 2.4.12 Sag and tension of inclined spans, 2.4.7 Sag-tension calculations, 2.4.6 Sag-tension models for ACSR conductors, 2.4.3 Thermal elongation, 2.4.11 Wind speed effects on thermal ratings, 2.4.10 Line thermal ratings, 2.3 Heat balance methods, 2.3.5 Line design effects on line ratings, 2.3.4 Maximum conductor temperature, 2.3.2 Transient thermal ratings, 2.3.7 Weather conditions for rating calculations, 2.3.3, 2.3.6 Reconductoring without structural modifications, 2.6 ACCR conductor, 2.6.7 ACSS and ACSS/TW, 2.6.3 Gapped construction, 2.6.6 High temperature aluminum alloy conductors, 2.6.4 Invar steel core, 2.6.5 TW aluminum wires, 2.6.2 Uprating constraints, 2.2 Constraints on structural loads, 2.2.7 Electrical clearance, 2.2.5 Environmental effects, 2.2.8 High-temperature sag, 2.2.3 Loss of conductor strength, 2.2.6 Sag-tension calculations, 2.2.2 Wind-induced conductor motion, 2.2.4 Uprating without reconductoring, 2.5 Deterministic methods, 2.5.2 “Measure of Safety” as a basis for line rating, 2.5.4 Probabilistic methods, 2.5.3 Sagging Line Mitigator, 2.5.6


P Pipe-type cables, 3.2.1 Power flow example, 1.2 Power flow limits, 3.3 Load flow considerations, 3.3.2 Stability limits, 3.3.1 Surge impedance loading limits, 3.3.1 Thermal limits, 3.3.1 Uprating hybrid circuits, 3.3.3 Power system issues, 1.2 Power transformers Design, 4.2 Cooling types, 4.2.2 Core-form construction, 4.2.1 Directed flow designs, 4.2.1 Factory testing, 4.2.4 Losses, 4.2.3 Shell-form construction, 4.2.1 Dynamic thermal rating models, 6.4.3 Examples, 4.8 Modest increases in capacity, 4.7 Risks of increased loading, 4.3 Long-term risks, 4.3.2 Short-term risks, 4.3.1 Thermal modeling, 4.4 Bottom oil model, 4.4.3, 6.4.3 IEC model, 4.4.4, 6.4.3 Mechanisms of heat transfer, 4.4.1 Proposed IEC model, 4.4.5 Top oil model, 4.4.2, 6.4.3 Thermal ratings, 4.5 Ambient air temperature, 4.5.1 Condition-based loading, 4.5.5 Load, 4.5.2 Maintenance considerations, 4.5.6 Rating procedure, 4.5.4 Rating type and duration, 4.5.3 Winding temperature measurement, 4.6 Q Quasi-dynamic ratings (underground cables), 3.8.5 R Ratings Continuous (normal) rating, 6.6.1 Emergency ratings, 2.4.1, 3.4.7 Long-time emergency rating, 6.6.1 Short-time emergency rating, 6.6.1 Traditional rating definitions, 6.6.1 Underground cable ratings, 3.4 Reconductoring Overhead transmission lines, 2.6 Underground cables, 3.7 Resistances (underground cables), 3.4.4 Route thermal survey, 3.6.1

Index

S Sag High-temperature sag with aluminum conductors, 2.2.3 High-temperature sag with ACSR, 2.2.3 High-temperature sag-tension calculations, 2.4.9 SAG10, 2.2.2, 2.4.8, 2.4.9 Sag and tension of inclined spans, 2.4.7 Sag-tension calculations, 2.2.2, 2.4.6, 2.4.8, 2.5 Tension-elongation diagram, 2.2.2 Sag-tension models, 2.4.3 Sagging Line Mitigator, 2.5.5 SCLF (Self-Contained Liquid-Filled) cables, 3.2.3 Self-contained liquid-filled cables, 3.2.3 SF6 circuit breakers, 5.3.5 Shield/sheath bonding scheme, 3.6.8 Short-time emergency rating, 6.6.1 SIL (Surge Impedance Loading), 1.3.2, 2.1.1, 3.3.1 SLiM (Sagging Line Mitigator), 2.5.5 Stability limits, 3.3.1 Static ratings, 2.3.1 STESS software, 2.2.3 Substation terminal equipment Dynamic thermal rating models, 6.4.5 Equipment types and IPF opportunities, 5.2 Rating parameters, 5.2.1 Thermal models, 5.3 Air-core reactor, 5.3.3 Bus conductors, 5.3.1 Bushings, 5.3.6 Current transformers, 5.3.7 Line traps, 5.3.8 Oil circuit breaker, 5.3.4 SF6 circuit breaker, 5.3.5 Switch (air disconnect), 5.3.2 Thermal parameters, 5.5 Uprating, 5.4 Maintenance and inspection procedures, 5.4.2 Monitoring and communications, 5.4.1 Reliability and consequences of failure, 5.4.3 Superconducting cables, 3.7.5 Surge impedance loading, 1.3.2, 2.1.1, 3.3.1 Switches (air disconnect), 5.3.2 T T-Aluminum Conductor Steel Reinforced (TACSR), 2.6.4 Temperature monitoring (underground cables), 3.6.4 Tension-elongation diagram, 2.2.2 Thermal elongation, 2.4.11 Thermal limits, 1.3.4, 2.1.3, 3.3.1 Thermal models Substation terminal equipment, 5.2.1, 5.3 Underground cables, 4.4 I-3

Index

Thermal ratings Overhead transmission lines, 2.3 Dependence on weather conditions, 2.3.6 Dynamic ratings, 2.3.1 Heat balance methods, 2.3.5 Maximum conductor temperature, 2.3.2 Static ratings, 2.3.1 Transient thermal ratings, 2.3.7 Weather conditions for rating calculation, 2.3.3 Wind speed, 2.4.10 Power transformers, 4.5 Ambient air temperature, 4.5.1 Condition-based loading, 4.5.5 Load, 4.5.2 Maintenance considerations, 4.5.6 Rating procedure, 4.5.4 Rating type and duration, 4.5.3 Transformers. See Power transformers. TW aluminum wires, 2.6.2 U Underground cables Cable system types, 3.2 Compressed gas insulated transmission, 3.2.4 Extruded dielectric, 3.2.2 High-pressure pipe-type, 3.2.1 Mass impregnated, 3.2.4 Paper insulated lead covered, 3.2.4 Self-contained liquid-filled, 3.2.3 Case studies, 3.9 Dynamic ratings, 3.8, 6.4.4 Benefits, 3.8.3 Dynamic Thermal Circuit Ratings, 3.8.2 Monitoring, 3.8.4 Quasi-dynamic ratings, 3.8.5 Increasing ampacity, 3.6 Active uprating, 3.6.7 Ampacity audits, 3.6.5 Evaluation of load patterns, 3.6.3 Remediation of “hot spots,” 3.6.6 Review circuit plan and profile, 3.6.2 Route thermal survey, 3.6.1 Shield/sheath bonding scheme, 3.6.8 Temperature monitoring, 3.6.4 Power flow limits and system considerations, 3.3 Load flow considerations, 3.3.2 Stability limits, 3.3.1 Surge impedance loading limits, 3.3.1 Thermal limits, 3.3.1 Uprating hybrid circuits, 3.3.3 Ratings, 3.4 Ampacity, 3.4.2, 3.4.5, 3.4.6 Emergency ratings, 3.4.7 Equivalent thermal circuit and thermal resistances, 3.4.3

I-4


Inferring conductor temperatures from measured temperatures, 3.4.8 Losses, 3.4.3 Reconductoring, 3.7 Cupric oxide strand coating, 3.7.3 Larger conductor sizes, 3.7.2 Superconducting cables, 3.7.5 Voltage upgrading, 3.7.4 Uprating and upgrading constraints, 3.5 Accessories, 3.5.7 Direct buried cable systems, 3.5.1 Duct bank installations, 3.5.3 Fluid-filled cable systems, 3.5.2 Hot spot identification, 3.5.6 Hydraulic circuit, 3.5.8 Trenchless installations, 3.5.4 Uprating, active (underground cables), 3.6.7 Uprating case studies Overhead transmission lines, 2.8 Underground cables, 3.9 Uprating constraints (overhead transmission lines), 2.2 Constraints on structural loads, 2.2.7 Electrical clearance, 2.2.5 Environmental effects, 2.2.8 Limiting high-temperature sag, 2.2.3 Loss of conductor strength, 2.2.6 Sag-tension calculations, 2.2.2 Uprating constraints related to wind-induced conductor motion, 2.2.4 Uprating constraints (underground cables), 3.5 Direct buried cable systems, 3.5.1 Duct bank installations, 3.5.3 Fluid-filled cable systems, 3.5.2 Trenchless installations, 3.5.4 Uprating hybrid (underground and overhead) circuits, 3.3.3 Uprating substation terminal equipment, 5.4 Uprating without reconductoring (overhead transmission lines), 2.5 Deterministic methods, 2.5.2 Probabilistic methods, 2.5.3 Absolute method, 2.5.3 Exceedance method, 2.5.3 Modified exceedance method, 2.5.3 V Video sagometer, 2.7.5 Voltage drop, 1.3.3, 2.1.2 Voltage limits, 3.3.1 Voltage upgrading, 3.7.4 W Wind-induced conductor motion, 2.2.4 Wind loading, 2.2.7 Wind speed, effect on thermal ratings, 2.4.10


Index

X XD (Extruded Dielectric), 3.2.2 XLPE (Cross-Linked Polyethylene), 3.2.2

I-5

Export Control Restrictions

The Electric Power Research Institute (EPRI), with major

Access to and use of EPRI Intellectual Property is granted with the

locations in Palo Alto, California; Charlotte, North Carolina; and

specific understanding and requirement that responsibility for ensur-

Knoxville, Tennessee, was established in 1973 as an independent,

ing full compliance with all applicable U.S. and foreign export laws

nonprofit center for public interest energy and environmental

and regulations is being undertaken by you and your company. This

research. EPRI brings together members, participants, the Institute’s

includes an obligation to ensure that any individual receiving access

scientists and engineers, and other leading experts to work

hereunder who is not a U.S. citizen or permanent U.S. resident is

collaboratively on solutions to the challenges of electric power. These

permitted access under applicable U.S. and foreign export laws and

solutions span nearly every area of electricity generation, delivery,

regulations. In the event you are uncertain whether you or your com-

and use, including health, safety, and environment. EPRI’s members

pany may lawfully obtain access to this EPRI Intellectual Property, you

represent over 90% of the electricity generated in the United States.

acknowledge that it is your obligation to consult with your company’s

International participation represents nearly 15% of EPRI’s total

legal counsel to determine whether this access is lawful. Although

research, development, and demonstration program.

EPRI may make available on a case-by-case basis an informal assessment of the applicable U.S. export classification for specific EPRI

Together...Shaping the Future of Electricity

Intellectual Property, you and your company acknowledge that this assessment is solely for informational purposes and not for reliance purposes. You and your company acknowledge that it is still the obligation of you and your company to make your own assessment of the applicable U.S. export classification and ensure compliance accordingly. You and your company understand and acknowledge your obligations to make a prompt report to EPRI and the appropriate authorities regarding any access to or use of EPRI Intellectual Property hereunder that may be in violation of applicable U.S. or foreign export laws or regulations.

Program: Increased Transmission Capacity

© 2005 Electric Power Research Institute (EPRI), Inc. All rights reserved. Electric Power Research Institute, EPRI, and TOGETHER...SHAPING THE FUTURE OF ELECTRICITY are registered service marks of the Electric Power Research Institute, Inc.

Printed on recycled paper in the United States of America

1010627

Electric Power Research Institute 3420 Hillview Avenue, Palo Alto, California 94304-1338 • PO Box 10412, Palo Alto, California 94303-0813 USA 800.313.3774 • 650.855.2121 • [email protected] • www.epri.com

EPRI - Increased Power Flow Guidebook.pdf

Recommend Documents