14bus Matlab Code

VOLTAGE SECURITY ANALYSIS UTILIZING VOLTAGE COLLAPSE PROXIMITY INDICATOR IN POWER SYSTEM

LING TING YI

This thesis is submitted in fulfillment for the requirement for the award of the degree of Bachelor of Engineering (Electrical)

Faculty of Electrical Engineering Universiti Teknologi Malaysia

MAY 2011

iii

To my parents, Ling Yoke Hook and Chew Chui Har;  younger sister, Ling Zhi Han;  younger brothers, Ling Ting Yan and Ling Ting Rui; all my friends and those great people who appear in my life that makes me who I am today

iv

ACKNOWLEDGMENT

First of all, I would like to express my heartiest gratitude to Assoc. Prof. Dr Azhar Khairudin for his comments, guidance and advice in the preparation of this research from scratch to successfully accomplish. Besides, I would like to thank Assoc. Prof. Dr. Mohd. Wazir Mustafa for his lectures and guidance on Power System Analysis course which enhance my knowledge to complete the research. My deepest appreciation goes to my family, friends and colleagues as well for their patience and cooperation during the entire research process. Finally, I was also greatly indebted to who helped our research very much directly and indirectly.

v

ABSTRACT

Voltage instability leading to voltage collapse phenomenon is mostly due to the inability of power system to meet the demand for reactive power at certain critical load  buses. The primary purpose of identifying weak load buses is to maintain control of voltage at those buses, in particular to prevent voltage collapse. This research was carried out for voltage security analysis utilizing voltage collapse proximity indicator for contingency screening and ranking process, as part of the voltage stability assessment. Two benchmark results were adopted which were relative voltage change index (VC) and continuation power flow (CPF) to be compared to the proposed voltage collapse  proximity indicator (VCPI). MATPOWER and MATLAB were used as the primary software to carry out load flow analysis required to generate the data for the indices. IEEE 14-bus and 30-bus test system were the power system network used to implement the indices. The overall findings indicated that proposed VCPI was satisfactory in terms of accuracy, but has longer computation time compared to VC. While for comparison with CPF, their results deviated much due to the assumption of critical loading condition on VCPI index calculation, and VCPI was superior to CPF from the perspective of computation time. In conclusion, some suggestions have been made to enhance the efficiency of the VCPI and recommendations for future research have also been included in the final part of the report.

vi

ABSTRAK

Fenomena ketidakstabilan voltan yang menyebabkan voltan runtuh sebahagian  besar adalah disebabkan oleh ketidakmampuan sistem tenaga untuk memenuhi keperluan kuasa reaktif pada bus beban kritikal tertentu. Tujuan utama untuk mengenalpasti bas beban lemah adalah untuk mempertahankan kawalan voltan terhadap  bus tersebut, khususnya untuk mencegah runtuh voltan. Penyelidikan ini dilakukan untuk analisis keselamatan voltan dengan menggunakan penunjuk jarak runtuh voltan (VCPI) untuk penapisan kontingensi dan proses peringkat, sebagai sebahagian daripada  penilaian kestabilan voltan. Dua keputusan benchmark, indeks relatif penukaran voltan (VC) dan kelanjutan aliran kuasa (CPF) akan dibandingkan dengan VCPI yang dicadangkan. MATPOWER dan MATLAB digunakan sebagai perisian utama untuk melakukan analisis aliran beban yang diperlukan untuk menghasilkan data untuk indeks. IEEE 14-bus dan 30-bus adalah sistem tenaga rangkaian yang digunakan untuk  pelaksanaan indeks. Penemuan keseluruhan menunjukkan bahawa VCPI dicadangkan adalah memuaskan dari aspek kejituan, namun ia mempunyai masa pengiraan yang lebih lama dibandingkan dengan VC. Sedangkan untuk perbandingan dengan CPF, keputusan CPF menyimpang jauh disebabkan andaian keadaan pembebanan kritikal pada  perhitungan indeks VCPI. Walau bagaimanapun VCPI lebih unggul daripada CPF dari  perspektif masa pengiraan. Sebagai kesimpulan, beberapa cadangan telah dibentang untuk meningkatkan kecekapan VCPI dan cadangan untuk kajian akan datang juga telah disertakan di bahagian akhir laporan.

vii

TABLE OF CONTENTS

CHAPTER

TITLE

PAGE

THESIS STATUS CONFIRMATION FORM SUPERVISOR CONFIRMATION

1

TITLE COVER

i

DECLARATION

ii

DEDICATION

iii

ACKNOWLEDGEMENT

iv

ABSTRACT

v

ABSTRAK

vi

TABLE OF CONTENTS

vii

LIST OF TABLES

x

LIST OF FIGURES

xii

LIST OF SYMBOLS

xiii

LIST OF APPENDICES

xiv

INTRODUCTION

1

1.1

Introduction

1

1.2

Background of the Study

1

1.3

Problem Statement

2

1.4

Objectives of the Study

3

1.5

Scope of the Study

3

1.6

Significance of the Study

4

1.7

Thesis Organization

4

viii

2

3

LITERATURE REVIEW

6

2.1

Introduction

6

2.2

Power System Security

6

2.3

Voltage Security Assessment

8

2.4

Relative Voltage-Change Method (VC)

10

2.4

Continuation Power Flow (CPF)

11

2.4

Voltage Collapse Proximity Indicator (VCPI)

12

2.4

Summary

14

RESEARCH METHODOLOGY

15

3.1

Introduction

15

3.2

Research Procedure

15

3.2.1

Critical Loading Condition

16

3.2.2

Relative Voltage-Change Method

17

3.2.3

Continuation Power Flow

18

3.2.4

Voltage Collapse Proximity Indicator

19

3.3

3.4

3.5

4

Research Instruments

20

3.3.1

21

MATPOWER Software

Data Analysis

27

3.4.1

PV Curve

27

3.4.2

Microsoft® Office Excel 2007 SP2

27

Summary

28

RESULTS AND DISCUSSION

29

4.1

Introduction

29

4.2

Results and Discussion

29

ix 4.2.1

4.2.2

4.3

5

IEEE 14-Bus Test System

30

4.2.1.1 Benchmark Results

31

4.2.1.1.1

VC

31

4.2.1.1.2

CPF

33

4.2.1.2 Critical Bus Ranking by VCPI

34

4.2.1.3 Discussion

36

IEEE 30-Bus Test System

36

4.2.1.1 Benchmark Results

38

4.2.1.1.1

VC

38

4.2.1.1.2

CPF

40

4.2.1.2 Critical Bus Ranking by VCPI

42

4.2.1.3 Discussion

45

Summary

48

CONCLUSIONS AND RECOMMENDATIONS

49

5.1

Introduction

49

5.2

Conclusions

49

5.3

Recommendations

50

5.4

Future Research Work

51

REFERENCES APPENDICES A  –  E

52 55-70

x

LIST OF TABLES

TABLE NO

4.1

TITLE

Determination of critical loading condition for IEEE

PAGE

31

14-bus system 4.2

Calculation of VCi on heavy load state (IEEE 14-bus

32

system) 4.3

Critical load bus ranking of IEEE 14-bus system using

33

VCi 4.4

Critical load bus ranking of IEEE 14-bus system using

33

VCi 4.5

Critical load bus ranking of IEEE 14-bus system using

34

voltage collapse point from PV curve 4.6

Calculation of VCPI on heavy load state (IEEE 14-bus

35

system) 4.7

Critical load bus ranking of IEEE 14-bus system using

35

VCPI 4.8

Comparison of 3 proximity measures for contingency

36

ranking of IEEE 14-bus system 4.9

Determination of critical loading condition for IEEE

38

30-bus system 4.10

Calculation of VCi on heavy load state (IEEE 30-bus

39

system) 4.11

Critical load bus ranking of IEEE 30-bus system using

40

VCi 4.12

Real power and voltage magnitude of P-Q bus at

41

xi voltage collapse point from PV curve (IEEE 30 -bus system) 4.13

Critical load bus ranking of IEEE 30-bus system using

42

voltage collapse point from PV curve 4.14

Calculation of VCPI on heavy load state (IEEE 30-bus

43

system) 4.15

Critical load bus ranking of IEEE 30-bus system using

44

VCPI 4.16

Comparison of 3 proximity measures for contingency

45

ranking of IEEE 30-bus system 4.17

Comparison of 3 proximity measures in terms of

47

computation time per load flow for both test systems 4.18

Comparison of 3 proximity measures in terms of overall computation time for both test systems

47

xii

LIST OF FIGURES

FIGURE

TITLE

PAGE

NO.

2.1

Voltage Stability Assessment Flowchart

9

2.2

PV curve of a load bus

12

3.1

Flowchart for methodology of critical loading condition

17

3.2

Flowchart for methodology of critical bus ranking utilizing

18

VC 3.3

Flowchart for methodology of critical bus ranking utilizing

19

CPF 3.4

Flowchart for methodology of critical bus ranking utilizing

20

VCPI 3.5

System summary of runpf command

22

3.6

Bus data of runpf command

23

3.7

Branch data of runpf command

23

3.8

PV curve of IEEE 14-bus system, bus 4

26

4.1

IEEE 14-bus system

30

4.2

IEEE 30-bus system

37

xiii

LIST OF ABBREVIATIONS

CPF

-

Continuation Power Flow

GUI

-

Graphic User Interface

IEEE

-

Institute of Electrical and Electronics Engineering

PD

-

Real Power Demand

QD

-

Reactive Power Demand

SCADA

-

Supervisory Control and Data Acquisition

SNB

-

Saddle Node Bifurcation

TNB

-

Tenaga Nasional Berhad

VC

-

Relative Voltage-Change Index

VCPI

-

Voltage Collapse Proximity Indicator

VSA

-

Voltage Stability Assessment

xiv

LIST OF APPENDICES

APPENDIX

TITLE

PAGE

A1

IEEE 14-bus system MATLAB M-file

55

A2

IEEE 30-bus system MATLAB M-file

58

B

test_cpf MATLAB M-file

62

C

PV curves for each load bus in IEEE 14-bus system

64

D

PV curves for each load bus in IEEE 30-bus system

66

E

MATLAB command for constant power factor load increment MATLAB M-file for command computation time

69

F

70

1

CHAPTER 1

INTRODUCTION

1.1

Introduction

This project proposes Voltage Security Analysis utilizing Voltage Collapse Proximity Indicator in power system. This analysis is very important in contingency screening and ranking as part of the voltage security assessment.

In this chapter, background of the study, problem statement, objectives of the study, scope of the study, significance of the study, and thesis organization are to be  presented.

1.2

Background of the Study

Up to year 2009, industrial sector is the second largest consumer of energy in Malaysia, followed closely by transport sector [1]. Electrical energy is the major energy supply for the industries, and the result of the energy audit in 2008 shows that the highest energy consuming equipment is electric motor followed by liquid pumps and air compressors which are used most in industry sectors [1].

2 Thus the power system is expected to be more heavily loaded from day to day. However, many environmental and economic constraints preventing the constructions of new or upgrading power system. The power producing utilities such as Tenaga Nasional Berhad (TNB) shows reluctance to expand their generation and transmission capabilities due to social pressure, such as the public concerns about the effect of electric and magnetic field around the housing area near to transmission lines.

All the constraints lead the current power system to operate closely to stability limits, causing loss of control of the voltage levels in a power system. Usually the voltage decay is gradual that makes system operators unaware that it is the symptom of voltage collapse which will lead to complete blackout. Therefore, constant attention is required to ensure the systems are operated above desired level of voltage stability margin.

Voltage Stability Assessment (VSA) is the process to ensure the voltage security in power system. There are two main scope of the assessment, which is static security and dynamic security of system. One of the various steps of carrying out the assessment is contingency screening and ranking of weak load buses. Numerous ways were developed by researchers and industries to indicate the weakest bus in the power system. This step is vital to make preventive maintenance before the voltage collapse happen.

1.3

Problem statement

The problem statements of this project are:

i.

Most of authors realized voltage collapse in power system as a static  phenomenon;

3 ii.

Static study is appropriate for bulk power system study, which involves enormous number of buses and generators;

iii.

1.4

Static voltage instability is most affected by reactive power imbalance.

Objectives of the Study

The objectives of this project are:

i.

To develop an indicator to perform contingency screening and ranking as part of the voltage security assessment on standard IEEE test system using MATLAB language;

ii.

To compare the results obtained from the proposed VCPI to two benchmark results.

1.5

Scope of the study

The scope of this project is:

i.

Contingency screening and ranking of Voltage Security Assessment;

ii.

Static power system analysis;

iii.

Analysis applied to offline system;

iv.

Weak load buses and critical lines identification in power system.

The assumptions made in the project are:

4 i.

The PQ-buses with zero loads are assumed to be of zero loads throughout the analysis;

ii.

The parameters of the PV-buses, i.e. bus voltage magnitude and injected power, P are assumed to be constant throughout the analysis;

iii.

The slack bus is capable to absorb the losses in the system.

There is limitation in the project. Only load with sufficient reactive power will be considered as the proposed VCPI is considering reactive power solely.

1.6

Significance of the study

Although there are various ways of contingency screening and ranking in the research field, the findings of this study are important as part of Voltage Security Assessment. Critical load bus identification is vital to ensure the priority of preventive and correction action is given to the most critical load bus in the power system.

Through this research, a simplified implementation of VCPI that was proposed  by Chen is presented [2], thus ease the researchers from similar field as well as the  power utility industries who implement it.

1.7

Thesis Organization

This thesis consists of 5 chapters.

Chapter 2 presents literature review on the project, namely the background of Power System Security, Voltage Security Assessment, and the available voltage collapse  proximity indicators and indexes to perform the analysis.

5

Chapter 3 discusses the methodology used in the project, including methodology to perform continuation power flow analysis, critical loading condition, voltage change index analysis and VCPI analysis.

Chapter 4 presents the findings and results obtained from the project. The data are analyzed and the three critical bus rankings are compared and discussed.

Chapter 5 discusses the conclusion of the project, and suggestions for further extension on the current work.

6

CHAPTER 2

LITERATURE REVIEW

2.1

Introduction

In this chapter, literature review starts with screening the concept of power system security, which is the big picture of the research. The research is part of the effort to ensure power system to operate without interruption of supply to the consumers in the same time it can withstand credible contingencies. Next the voltage stability analysis  procedure is examined and the scope steep down to static security assessment. Finally two benchmark methods and the proposed method are reviewed from the original authors, and the reviews of some other methods are presented as well.

2.2

Power System Security

Voltage stability problems normally occur in heavily stressed systems. A system enters a state of voltage instability when a disturbance, increase in load demand, or change in system condition causes a progressive and uncontrollable drop in voltage. The main factor causing instability is the inability of the power system to meet the reactive  power demand. The heart of the problem is usually the voltage drop that occurs when active power and reactive power flow through inductive reactance associated with the transmission network. Moreover, a criterion for voltage stability is at a given operation

7 condition for every bus in the system, the bus voltage magnitude increases as the reactive power injection at the same bus is increased. A system is voltage unstable if, for at least one bus in the system, the bus voltage magnitude (V) decreases as the reactive  power injection (Q) at the same bus is increased. [3]

The phenomenon of voltage collapse on a transmission system, due to operation near the maximum transmissible power, is characterized by a fall in voltage, which is at first gradual and then rapid. The theoretical relationship between power transferred across a system and the receiving-end voltage follows an approximately parabolic shape. The gradient of the curve becomes steeper as the apogee of the parabola is approached, and a small increase in power demand at the receiving end can cause its voltage to collapse to an unacceptably low level, rather than to continue declining in a controlled and predictable manner. [4] The curve is also known as PV curve.

Since it is impossible to eliminate completely random faults and failures, measures must be taken to reduce the likelihood that disturbances degenerate into major incidents involving the disconnection of consumers. We will therefore define power system security as the ability of the system to withstand unexpected failures and continue operating without interruption of supply to the consumers. [5]

A power system can never be totally secure. It is always possible to devise a sequence of events that will lead to a total or partial collapse of the system. The  probability of such a sequence of events may be very small but it will never be zero. At the other extreme, a power system operating on its stability limit has zero security  because any deterioration in its condition (such as the outage of a component or a small increase in load) will result in the disconnection of at least some consumers. [5]

There are some other important terms to understand for this research, which is defined in [6]:

8

i.

Voltage stability - the ability of a system to maintain voltage magnitude at all the  buses in the system after disturbance;

ii.

Voltage collapse - a process by which voltage instability leads to a very low voltage;

iii.

Voltage security - the ability of a system not only to operate stably but also to remain stable following credible contingencies or adverse system changes.

2.3

Voltage Stability Assessment

Voltage stability security assessment should indicate with:

a.

Where the voltage collapse occurs for any equipment outage or operating change,

 b.

All contingencies and operating changes that cause voltage collapse in that location (a specific sub region in the transmission, sub transmission, or distribution network),

c.

The cause of the voltage collapse in terms of

i.

lack of reactive supply on specific reactive sources or

ii.

an inability to deliver reactive to the specific region experiencing voltage collapse,

d.

What operating changes could be made in anticipation to prevent the voltage instability from occurring when a specific contingency and operating change combination predicted to cause voltage instability occurs. [ 7]

9 Figure 2.1 is the modified flowchart from [8] which represents the voltage stability assessment. The VSA environment receives its input from a real time database. Voltage stability assessment of the current operating point is necessary to enable the system engineer know the voltage stability status of the system. The outcome of this assessment determines the next line of action. If the result of the assessment is positive, i.e. the system is secured at the present operating point, the next step would be to initiate some credible contingencies, such as line outages and critical loading conditions, which would be analyzed further. The large list of contingencies is screened and ranked with respect to their margins to voltage collapse, using any fast and accurate ranking algorithm available. Finally, the contingencies flagged as potentially harmful to the system‟s stability are investigated further using tools like continuation power flow (CPF)

and consequently develop some control schemes to be executed in either a precontingency or post-contingency mode. [9] mode. [9]

Figure 2.1: Voltage Stability Assessment Flowchart

10 In this research, the focus is on the dotted box in the flowchart, which is contingency selection, screening and ranking of potential harmful load bus in power system.

System dynamics influencing voltage stability are usually slow. Therefore many aspects of the problem can be effectively analyzed by static methods, which examine the viability of the equilibrium point represented by a specified operating condition of the  power system. The static analysis techniques allow examination of a wide range of system conditions and, if appropriately used, can provide much insight into the nature of the problem and identify the key contributing factors. Dynamic analysis, on the other hand, is useful for detailed study of specific voltage collapse situations, coordination of  protection and controls, and testing of remedial measures. Dynamic simulations also examine whether and how the steady state equilibrium point will be reached. [3]

2.4

Relative Voltage-Change Method (VC)

Introduced by [10] and adopted by [2], the first benchmark method is based on the relative change in the bus voltages going from the initial operating point to the voltage stability limit.

Let

  and   be the voltage magnitudes at bus i at the initial operating

state and the voltage stability limit, respectively. A voltage change index is defined for each load bus as,

     

(2.1)

As mentioned previously, the „weak‟ or critical bus in the network is the most

(electrically) remote bus from the point of constant or controllable voltage. It is expected that the critical bus would be the worst affected (voltage wise) because of a shortage of

11 local VARs or VARs transferred from a remote source. [10] It is anticipated that for a specified operating regime, going from an initial operating point to the voltage stability limit, the weakest bus would experience the largest voltage change (or drop), i.e., the largest index VC, defined by eqn. 14. Therefore if bus k is the weakest bus,

max{VC i } VC k   max i J  L

 

(2.2)

Based on the index VCi, the system buses may be arranged in order of weakness, the weakest bus corresponding to that with the largest index.

2.5

Continuation Power Flow (CPF)

First introduced by [11], CPF employs predictor-corrector scheme to find solution path that have been reformulated to include load parameter. It belongs to a general class of methods for solving nonlinear algebraic equations known as pathfollowing methods. [3]

In the research, a MATLAB M-file which was programmed in MATPOWER by [12] to plot PV curve was adopted. The PV curves are the most used method of  predicting voltage security. They are used to determine the loading margin of a power system. The power system load is gradually increased and, at each increment, is necessary recomputed power flows until the nose of the PV curve is reached. The margin between the voltage collapse point and the current operating point is used as voltage stability criterion. [13]

Fig. 2.1 presents the PV curves of the power flow solution when generator limits are neglected. Any attempt to increase PR  (QR ) beyond point A in the figure would result in a system voltage collapse. The maximum loading points are depicted in the figure

12 with A and C. Different PV and QV curves can be computed based on the system  parameters chosen to do so. Each curve shows the maximum power that can be transferred at a particular power factor. [9]

Figure 2.1: PV curve of a load bus

2.6

Voltage Collapse Proximity Indicator (VCPI)

A variety of analysis like the PV curve, QV curve, minimum eigenvaule/singular value, right eigenvector, family of test functions, tangent vector, reduced Jacobian, sensitivity analysis and energy based methods have been proposed [11, 14, 15, 16]. These methods usually use simple generator and load models (e.g. constant power loads at high voltage buses).

Greene [17] proposed sensitivity analysis of the pre-contingency conditions to avoid voltage collapse on the system. Also, Yorino et al [18] used a fast computation method to evaluate the load power margin with respect to saddle node bifurcation. Also, the use of the reactive power reserves was proposed as an index for evaluation of the voltage stability of post-contingency system [19]. In [20], the improved voltage stability

13 index L1 was adopted as a fast and accurate tool to trace the SNB point, regardless of the type of load model. This takes care of the limitations of the index-L proposed by Kessel [21] that is only suitable for constant power type of load. Fast curve fitting method was proposed by Ejebe et al [8] to calculate the limit of the nose curve.

This project adopted voltage collapse proximity indicator (VCPI) method  proposed by Chen et al [2], to carry out the screening and ranking of the test system  buses. The critical lines are determined by linearly increasing the loads. VCPI proposed  by Chen [2] is used to identify weak load buses and areas in the power network. The rationale behind this definition in is that voltage is the most affected by reactive power. For a voltage stability system, all VCPIQ will have a value greater than but close to unity, whereas a system close to voltage collapse would have at least one VCPIQ which is large, approaching infinity at the point of collapse. In other words, the weakest bus in the network would have the maximum value of VCPI.

VCPI for i load bus is defined as:

          

(2.3)

                             Therefore if bus k is the weakest bus,

VCPI Qk   max   {VCPI i } i L

 

(2.4)

14

Based on the index VCi, the system buses may be arranged in order of weakness, the weakest bus corresponding to that with the largest index.

2.8

Summary

This chapter has presented the related knowledge of the research and numerous of past works which were developed by other researchers. It starts from power system security concept, and go deep to voltage stability assessment overview, until the  benchmark methods and proposed method as well as other methods of developing VCPI.

15

CHAPTER 3

RESEARCH METHODOLOGY

3.1

Introduction

This section discusses the methodology used to archive the objective of the research. Three procedures of implementing the indices were explained, namely VC, CPF and VCPI. Before that another additional procedure is the pre-requisite of acquiring VC and VCPI ranking, which is obtaining the critical loading condition. The main research software, MATPOWER and Microsoft® Office Excel 2007 SP2 were discussed. Finally data analysis was done utilizing PV curve.

3.2

Research Procedure

Two benchmark results produced from different method is adopted to be compared to a proposed VCPI, which is simplified from the original version. All  procedures of the indices are presented, plus an additional procedure which is a prerequisite for two of the three critical load bus ranking methods.

16 3.2.1

Critical Loading Condition

Before the indices VC and VCPI could be calculated, critical loading condition must be obtained to ensure the weakest load bus was exposed for identification. When the power system is stressed to heavy load state, the voltage magnitude will drop and reactive power shortage will appear. In this research, ±10% margin is adopted as one of the test systems exceeds 5% tolerance at basecase. Undervoltage will cause voltage instability and malfunction of electrical equipments, inducing economic losses especially for heavy industries.

To obtain the critical loading condition for a power system, firstly a load flow analysis is ran at basecase, and the voltage magnitude on each load bus is recorded. Next, the load of the power system is increased linearly at constant power factor, on a step of 10%. Constant power factor load increment is done by increasing both real and reactive  power at the same time with same step size. To obtain more precise of critical loading condition, a smaller step size such as 5% or 1% can be adopted. The increment is continued with the record of load bus voltage magnitudes until the magnitudes exceeded the specified range of voltage margin, which is 0.9 p.u. to 1.1 p.u. in this research. Therefore the last increment of the load before the voltage magnitude exceeded the limit will be the critical loading condition of the power system. Figure 3.1 shows the  procedure of obtaining critical loading condition for this research in flowchart.

17

START

Run a load flow at basecase, record the load bus voltage magnitude

Increase load of IEEE 14bus test system linearly at constant power factor on a step of 10%

Repeat the procedure for IEEE 30-bus test system

Record the maximum increment as critical loading condition

Stop the iteration when load bus voltage magnitude is dropped out of specified range (0.9
END Figure 3.1: Flowchart for methodology of critical loading condition

3.2.2

Relative Voltage-Change Index (VC)

VC is calculated based on the relative voltage change during initial and critical loading condition of the power system. The weakest bus will be experiencing largest voltage drop; hence will produce the largest index. Firstly the critical loading condition is obtained for the power system. Next, from the load flow results of basecase and critical loading condition, the voltage magnitude for each load bus is tabulated. After that, VC index is calculated according to the formula in Chapter 2. When all the indices are obtained for each load bus, they are ranked from highest to lowest value, indicating the weakest to strongest bus in the system. Figure 3.2 shows the procedure of obtaining critical bus ranking utilizing VC for this research in flowchart.

18

START

Obtain critical loading condition for IEEE 14-bus test system

Tabulate data of the voltage magnitude at initial state and critical state

Repeat the procedure for IEEE 30-bus test system

Rank the load buses from the highest to lowest value of VC index

Calculate the VC index for each load bus

END Figure 3.2: Flowchart for methodology of critical bus ranking utilizing VC

3.2.3

Continuation Power Flow (CPF)

CPF method is a graphical method, plotting the PV curve and acquires the data from the voltage collapse point. Firstly, PV curve is plotted for each load bus using MATPOWER, the primary research software which will be discussed in the latter section. Next, values for the voltage and real power magnitude at the voltage collapse  point are tabulated. The ranking is done by examine the real power value from lowest to highest, indicating the lowest power handling bus as the weakest bus. Higher the value of real power at voltage collapse point, stronger the load bus. Figure 3.3 shows the  procedure of obtaining critical bus ranking utilizing CPF for this research in flowchart.

19

START

Plot PV curve for each load bus of IEEE 14-bus test system

Tabulate data of the voltage magnitude and real power magnitude at voltage collapse point

END

Repeat the procedure for IEEE 30-bus test system

Rank the load buses from the lowest to highest value of real power

Figure 3.3: Flowchart for methodology of critical bus ranking utilizing CPF

3.2.4

Voltage Collapse Proximity Indicator (VCPI)

VCPI is based on the reactive power compensation of the power system. When a load bus is having small increment of reactive power, other generation buses will compensate the load increment by generating more reactive power. The load bus that needs more reactive power compensation from the generation will be indicated as the weakest bus as it will cause reactive power shortage in the system more likely than other  buses with the same increment of reactive power loading. Therefore the weakest bus will  be taking largest reactive power compensation; hence will produce the largest index. Critical loading condition is implemented to ensure the system was critically stressed and this will amplify the effect of reactive power shortage, giving larger value of VCPI index.

Firstly the critical loading condition is obtained for the power system, same as the methodology for VC. Next, the reactive power for specific load bus is increased by a

20 small increment, in this research it is simplified by value one (1). The load flow is rerun after the increment to monitor the additional reactive power generated by the generation  buses. The increment of reactive power of each generation bus is summed up as one of the parameter for the calculation of VCPI. Then VCPI index is calculated according to the formula mentioned in Chapter 2. When all the indices are obtained for each load bus, they are ranked from highest to lowest value, indicating the weakest to strongest bus in the system. Figure 3.4 shows the procedure of obtaining critical bus ranking utilizing VCPI for this research in flowchart.

START

Obtain critical loading condition for IEEE 14-bus test system

Increase reactive power of specific load bus by ΔQi and rerun the load flow

Repeat the procedure for remaining load buses

Calculate VCPI for the specific load bus

Obtain the sum of increment of reactive power of each generation bus, ΔQGj

Rank the load buses from the highest to lowest value of VCPI

Repeat the procedure for IEEE 30-bus test system

END

Figure 3.4: Flowchart for methodology of critical bus ranking utilizing VCPI

3.3

Research Instruments

The main research software used in the research was MATPOWER. It is a third  party freeware MATLAB power system simulation package, including several M-files for solving power flow and optimal power flow problems. The latest version for MATPOWER is Version 4.0b4, 21-May-2010. Data analysis was done using

21 conventional spreadsheet software, Microsoft® Office Excel 2007 spreadsheet. The research was implemented on IEEE 14-bus test system and IEEE 30-bus test system. After the data was extracted from MATPOWER load flow solution, it was analyzed using Microsoft® Office Excel 2007 SP2.

3.3.1

MATPOWER

MATPOWER is a package of MATLAB® M-files for solving power flow and optimal power flow problems. It is intended as a simulation tool for researchers and educators that are easy to use and modify. MATPOWER is designed to give the best  performance possible while keeping the code simple to understand and modify. [12]

The primary functionality of MATPOWER is to solve power flow and optimal  power flow (OPF) problems. This involves (1) preparing the input data defining the all of the relevant power system parameters, (2) invoking the function to run the simulation and (3) viewing and accessing the results that are printed to the screen and/or saved in output data structures or files. [12]

The input data for the case to be simulated are specified in a set of data matrices  packaged as the fields of a MATLAB struct, referred to as a “MATPOWER case” struct

and conventionally denoted by the variable mpc. This struct is typically defined in a case file, either a function M-file whose return value is the mpc  struct or a MAT-file that defines a variable named mpc when loaded. The main simulation routines, whose names  begin with run (e.g. runpf , runopf ), accept either a file name or a MATPOWER case struct as an input. Use loadcase  to load the data from a case file into a struct if modifications need to be made to the data before passing it to the simulation. [12]

22 loadcase is used to load the data from a case file into a struct if modifications

need to be made to the data before passing it to the simulation. To load the IEEE 14-bus test system, defined in case14.m M-file into the mpc variable, the following function can  be entered:

>> mpc=loadcase (‘case14’);

The solver is invoked by calling one of the main simulation functions, such as runpf , passing in a case file name or a case struct as the first argument [12]. To run a

 Newton power flow with default options on the 14-bus system, the following function can be entered at the MATLAB prompt:

>> runpf (‘case14’);

Figure 3.5 to 3.7 shows the results of AC power flow results when command runpf(‘case14’) was entered in MATPOWER:

Figure 3.5: System summary of runpf  command

23

Figure 3.6: Bus data of runpf  command

Figure 3.7: Branch data of runpf  command

24 System summary, bus data, and branch data are displayed. The bus data includes the voltage, angle and total generation and load at each bus. The branch data shows the flows and losses in each branch. From the minimum and maximum voltage magnitude  printed in Figure 3.1, it is used in the research for determination of critical loading condition while bus voltage magnitude in Figure 3.2 is used for VC computation.

On the other hand, real and reactive power demand can be modified to suit the research need. To load the IEEE 30-bus test system data denoted from case30.m, increase its real power demand at bus 2 to 30 MW, then run a Newton power flow with default options, this could be accomplished as follows:

>> define_constants; >> mpc = loadcase('case30'); >> mpc.bus(2, PD) = 30; >> runpf(mpc);

The define constants in the first line is simply a convenience script that defines a number of variables to serve as named column indices for the data matrices. In this example, it allows us to access the “real power demand” column of the bus matrix using

the name PD without having to remember that it is the 3rd column [12]. Another variable used in the research is reactive power demand, which is denoted as QD.

For realization of CPF, continuation power flow code contributed by Rui Bo and implemented in MATPOWER is used. Implementation of continuous power flow solver allows the plot of PV curve as well as the prediction-correction trajectory [12]. A MATLAB M-file test_cpf  as the test program for CPF is a PV curve plotter for IEEE 30 bus test system with respect to load at bus 7. The program can be simply run by typing test_cpf in the command window. The full code can be obtained in Appendix B.

25 To suit the research need, the program is modified in order to change the case file to be analyzed. To analyze 14-bus system, line 34 is modified:

>>casename=(‘case14’);

30-bus test system can be implemented by changing case14 into case30 that represented 30-Bus data. Currently, continuous power flow with respect to demand  being provided to one bus only. So, only one graph for one bus can be drawn at a time. The number of bus to be analyzed can be simply done by changing the next line:

>>loadvarloc=4

In order to change to other bus, it can be done by changing number 4 to number 10 in order to analyze Bus 10.

Figure 3.8 shows the PV curve for 14-bus system, with respect to bus 4. It is significant to ensure which buses are critical in this project. PV curves were used to determine system load handling capability. System performance can be shown for various types of contingencies. In addition, the curves reflects how much load can be served at minimum operating voltage level and the contingencies combination that lead to system voltage collapse. The voltage and power limit for the specific bus can be determined. For this research, CPF serves as a graphical method to obtain critical bus ranking for the test power system.

26

Figure 3.8: PV curve of IEEE 14-bus system, bus 4

To record the pure CPU calculation time of a MATLAB programme for computation time performance analysis, tic  and toc  function is used. They are the internal stopwatch timer in MATLAB, where tic starts the timer while toc prints the elapsed time since tic was used. For example, to measure the computation time of a  power flow of IEEE 14-bus test system, the following MATLAB code can be entered:

>>tic >>runpf('case14'); >>toc

After the code is entered, the following result will be shown:

 Elapsed time is 0.038411seconds.

27 3.4

Data Analysis

To analyze the data, various ways are adopted including graphical method and tables.

The data from the power flow results are transcribed and analyzed and tabulated in tables using spreadsheet software. The results present through tables. Table is the best way to show the ranking of a series of data. In this research, the main purpose is to  produce weak bus ranking in power system network, thus table is the most effective way. Ranking is done by arranging the indices ascending. Comparison table is tabulated for clearer judgement in terms of accuracy and deviation of results.

3.4.1

PV Curve

PV curve is adopted as a graphical method to obtain the critical bus ranking in  power system. From the PV curve shown in Figure 3.4, data cursor is placed at the voltage collapse point (also known as nose point or knee point) to acquire the real power and voltage magnitude at critical point. After that all the data is tabulated and ranking is made from the data as mentioned in section 3.2.3.

3.4.2

Microsoft® Office Excel 2007 SP2

Good spreadsheet computer software is crucial to analyze numerous data, and it is vital especially for power system analysis research. Microsoft® Office Excel 2007 SP2 is used in the research to simplify the load increment for the power test system used, computation of VC, critical loading condition computation and computation time and many more. The ability of Excel to key in formulae in tables and solve numerous data in

28 short time is very helpful in the research. The implementation can be referred from the attached CD to the thesis.

3.5

Summary

This research proposes two benchmarks, which are VC and CPF, and one simplified VCPI to examine the ranking of critical bus in power system. As mention earlier in the introduction, the purpose of this study is to develop an indicator to perform contingency screening and ranking as part of the voltage security assessment on standard IEEE test system using MATLAB language, as well as compare the results obtained from the proposed VCPI to two benchmark results. The research instruments that the researchers are going to use are MATPOWER and Microsoft® Office Excel 2007 SP2. Then, researcher performs a data analysis base on the results in the form of table and PV curve.

29

CHAPTER 4

RESULTS AND DISCUSSION

4.1

Introduction

This section presents the results of critical bus ranking tested on IEEE 14-bus test system and IEEE 30-bus test system. Two benchmark results has been adopted, which are relative voltage-change method (VC) and continuation power flow (CPF). For CPF, the results are tabulated using data obtained from PV curves plotted on each load bus in test systems while for VC, the relative change of bus voltage magnitude between initial state and critical state are recorded. The actual results are computed by proposed VCPI utilizing the reactive power compensation for small increase on each load bus. Both results are compared in terms of accuracy and computation time.

4.2

Results and Discussion

Results for the benchmark results, VC and CPF as well as the proposed method, VCPI are presented, and analysis is done in terms of accuracy and computation time.

30 4.2.1

IEEE 14-bus test system

This project adopts IEEE 14-bus system which is part of American Electric Power System at February 1962 as shown in Figure 4.1. This power system network consists of 14 buses with five machines and 11 loads. There is no line limit for 14-bus system, but it has low base voltages and an overabundance of voltage control capability. Full data of the test system can be referred at Appendix A section.

Figure 4.1: IEEE 14-bus system

Before the computation of VC and VCPI, critical loading condition is obtained for the test system. As shown in Table 4.1, heavy load state happens when the load is increased 180% from basecase, at the same time maintaining 0.9 p.u. to 1.1 p.u. of voltage magnitude on the load bus, which is 10% tolerance of the normal value. It appears when the minimum voltage magnitude is stressed to 0.909 p.u. for bus 14 and maximum voltage magnitude is 1.090 p.u. for bus 8.

31

Table 4.1: Determination of critical loading condition for IEEE 14-bus system % of increment Minimum voltage magnitude Maximum voltage magnitude

0% 1.010  p.u. @  bus 3 1.090  p.u. @  bus 8

10% 1.010  p.u. @  bus 3 1.090  p.u. @  bus 8

20% 1.010  p.u. @  bus 3 1.090  p.u. @  bus 8

…

…

…

170% 0.918  p.u. @  bus 14 1.090  p.u. @  bus 8

180% 0.909 p.u. @ bus 14 1.090 p.u. @ bus 8

190% 0.899  p.u. @  bus 14 1.090  p.u. @  bus 8

4.2.1.1 Benchmark results

Benchmark results consist of VC and CPF. The calculation of the indices and the critical bus ranking are shown.

4.2.1.1.1

Relative Voltage-Change Method

Table 4.2 shows the calculation of VC on IEEE 14-bus system during critical loading condition. For load bus 1, 2, 3, 6, 8, the VC index appears as nil due to their generation bus or P-V bus characteristics, which will maintain their voltage magnitude in spite of load change. Bus 7 is not considered for the ranking as it is not a load bus, containing no load data for active and reactive power.

32 Table 4.2: Calculation of VCi on heavy load state (IEEE 14-bus system) Load bus





1 2 3 4 5 6 7* 8 9 10 11 12 13 14

1.060 1.045 1.010 1.018 1.020 1.070 1.062 1.090 1.056 1.051 1.057 1.055 1.050 1.036

1.060 1.045 1.010 0.933 0.934 1.070 0.984 1.090 0.944 0.943 0.995 1.019 0.998 0.909

           0 0 0 0.091104 0.092077 0 0.079268 0 0.118644 0.114528 0.062312 0.035329 0.052104 0.139714

* Bus 7 was neglected from ranking as it is not a P-Q bus

Table 4.3 shows the critical bus ranking using VC index. Eight rankings are  produced as there are 8 load buses out of 14 buses available for the use this research. Load buses are ranked ascending from weak to strong from the calculated VC index above. Bus 14 appears as the weakest bus according to the index; follow by bus 9, 10, 5, 4, 11, 13 and finally bus 12 as the strongest bus.

33 Table 4.3: Critical load bus ranking of IEEE 14-bus system using VCi Critical bus ranking (weak to strong) 1 2 3 4 5 6 7 8

4.2.1.1.2

Load bus

14 9 10 5 4 11 13 12

Continuation Power Flow (CPF) Based Method

Table 4.4 shows the tabulated real power and voltage magnitude from CPF on IEEE 14-bus system. Only pure load bus is considered for the plotting of CPF, therefore there is no data for bus 1, 2, 3, 6, 7, and 8.

Table 4.4: Real power and voltage magnitude of P-Q bus at voltage collapse point from

PV curve (IEEE 14-bus system) Load bus 4 5 9 10 11 12 13 14

P (p.u.) 7.266 6.055 2.536 1.695 1.871 1.826 2.690 1.354

V (p.u.) 0.6824 0.6249 0.5905 0.5870 0.5781 0.5705 0.5878 0.6008

Table 4.5 shows the critical bus ranking using CPF. Eight rankings are produced from the tabulated data above and load buses are ranked ascending from weak to strong. Bus 14 appears as the weakest bus according to the index; follow by bus 10, 12, 11, 9, 13, 5 and finally bus 4 as the strongest bus.

34

Table 4.5: Critical load bus ranking of IEEE 14-bus system using voltage collapse point from PV curve Critical bus ranking (weak to strong) 1 2 3 4 5 6 7 8

Load bus

14 10 12 11 9 13 5 4

4.2.1.2 Critical bus ranking by VCPI

Table 4.6 shows the calculation of VCPI on IEEE 14-bus system during critical loading condition. For load bus 1, 2, 3, 6, 7, and 8, there were no VCPI index appears due to their generation bus or P-V bus characteristics. As shown in column 3, proposed VCPI is simplified by stating small change in load reactive power to one (1), compared to the original VCPI introduced by Chen [2].

35 Table 4.6: Calculation of VCPI on heavy load state (IEEE 14-bus system) Load bus

  



1.31 1.41 1.56 1.54 1.29 1.13 1.21 1.59

1 1 1 1 1 1 1 1



1 2 3 4 5 6 7 8 9 10 11 12 13 14

       1.31 1.41 1.56 1.54 1.29 1.13 1.21 1.59

Table 4.7 shows the critical bus ranking using VCPI index. Eight rankings are  produced from the tabulated data above and load buses are ranked ascending from weak to strong. Load buses are ranked ascending from weak to strong from the calculated VCPI index above. Bus 14 appears as the weakest bus according to the index; follow by  bus 9, 10, 5, 4, 11, 13 and finally bus 12 as the strongest bus.

Table 4.7: Critical load bus ranking of IEEE 14-bus system using VCPI Critical bus ranking (weak to strong) 1 2 3 4 5 6 7 8

Load bus

14 9 10 5 4 11 13 12

36 4.2.1.3 Discussion

Table 4.8: Comparison of 3 proximity measures for contingency ranking of IEEE 14-

 bus system Rank (weakest to strongest) 1 2 3 4 5 6 7 8

CPF 14 10 12 11 9 13 5 4

Proximity measures VC 14 9 10 5 4 11 13 12

VCPI 14 9 10 5 4 11 13 12

Table 4.8 shows the load buses of IEEE 14-bus test system ordered from the weakest to strongest using continuous power flow (CPF) and relative voltage change index (VC), compared to voltage collapse proximity indicator (VCPI). All three indicator noted bus 14 as the weakest bus. For VC and VCPI, both of them produce the same rank of weak load buses, it is evidenced by their same choice of strongest bus in system, which is bus 12, followed by bus 13, bus 11, bus 4, bus 5, bus 10, bus 9 and finally bus 14. Besides the weakest bus, CPF screens different results compared to another two indices. Except ranking of bus 10 and bus 13 are similar to those shown by others, the remaining rank of buses deviate much, as it can be seen that CPF ranked bus 4 as the strongest bus while others ranked it as the fifth of weakest.

4.2.2

IEEE 30-bus test system

While for IEEE 30-bus system, it consists of 30 buses, 6 generators and 20 loads. The test system data can be viewed in Appendix A.

37

Figure 4.2: IEEE 30-bus system

Before the computation of VC and VCPI, critical loading condition is obtained for the test system, same as done for IEEE 14-bus test system. As shown in Table 4.9, heavy load state happens when the load is increased 80% from basecase, at the same time maintaining 0.9 p.u. to 1.1 p.u. of voltage magnitude on the load bus, which is 10% tolerance of the normal value. It appears when the minimum voltage magnitude is stressed to 0.907 p.u. for bus 8 is and maximum voltage magnitude is 1.000 p.u. for bus 1.

38 Table 4.9: Determination of critical loading condition for IEEE 30-bus system % of 0% 10% 20% 70% 90% …  increment 80% 0.961 0.955 0.949 0.915 0.899 Minimum 0.907  p.u. @  p.u. @  p.u. @  p.u. @ voltage p.u. @  p.u. @  bus 8  bus 8  bus 8  bus 8 …  bus 8 magnitude bus 8 1.000 1.000 1.000 1.000 1.000 Maximum 1.000  p.u. @  p.u. @  p.u. @  p.u. @ voltage p.u. @  p.u. @  bus 1  bus 1  bus 1  bus 1 …  bus 1 magnitude bus 1

4.2.2.1 Benchmark results

Benchmark results consist of VC and CPF. The calculation of the indices and the critical bus ranking are shown.

4.2.2.1.1

Relative Voltage-Change Method

Table 4.10 shows the calculation of VC on IEEE 30-bus system during critical loading condition. For load bus 1, 2, 13, 22, 23 and 27, the VC index appears as nil due to their generation bus or P-V bus characteristics, which will maintain their voltage magnitude in spite of load change. Bus 5, 6, 9, 11, 25 and 28 are not considered for the ranking as it is not a load bus, containing no load data for active and reactive power.

39 Table 4.10: Calculation of VCi on heavy load state (IEEE 30-bus system) Load bus





1 2 3 4 5* 6* 7 8 9* 10 11* 12 13 14 15 16 17 18 19 20 21 22 23 24 25* 26 27 28* 29 30

1 1 0.983 0.98 0.982 0.973 0.967 0.961 0.981 0.984 0.981 0.985 1 0.977 0.98 0.977 0.977 0.968 0.965 0.969 0.993 1 1 0.989 0.99 0.972 1 0.975 0.98 0.968

1 1 0.952 0.946 0.956 0.932 0.923 0.907 0.957 0.972 0.957 0.97 1 0.955 0.961 0.957 0.957 0.94 0.935 0.942 0.988 1 1 0.978 0.981 0.948 1 0.932 0.961 0.939

           0 0 0.032563 0.035941 0.027197 0.043991 0.047671 0.059537 0.025078 0.012346 0.025078 0.015464 0 0.023037 0.019771 0.020899 0.020899 0.029787 0.032086 0.028662 0.005061 0 0 0.011247 0.009174 0.025316 0 0.046137 0.019771 0.030884

* Bus 5, 6, 9, 11, 25 and 28 were neglected from ranking as it is not a P-Q bus

Table 4.11 shows the critical bus ranking using VC index. Eighteen rankings are  produced from the tabulated data above and load buses are ranked ascending from weak to strong. The top three weakest buses appear as bus 8, 7 and 4, while the top three strongest buses are bus 21, 24 and 10.

40

Table 4.11: Critical load bus ranking of IEEE 30-bus system using VCi Critical bus ranking (weak to strong) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

4.2.2.1.2

Load bus

8 7 4 3 19 30 18 20 26 14 16 17 15 29 12 10 24 21

Continuation Power Flow (CPF) Based Method

Table 4.12 shows the tabulated real power and voltage magnitude from CPF on IEEE 30-bus system. Only pure load bus is considered for the plotting of CPF, therefore there is no data for bus 1, 2, 5, 6, 9, 11, 13, 22, 23, 25, 27 and 28.

41 Table 4.12: Real power and voltage magnitude of P-Q bus at voltage collapse point from PV curve (IEEE 30-bus system) Load bus 3 4 7 8 10 12 14 15 16 17 18 19 20 21* 24 26 29 30

P (p.u.) 3.702 5.676 2.586 2.254 3.307 2.850 1.337 2.544 1.523 2.048 1.297 1.277 1.400 2.600 1.930 0.352 0.754 0.748

V (p.u.) 0.5237 0.5995 0.5166 0.4937 0.7693 0.6237 0.5350 0.5963 0.5495 0.5601 0.5229 0.5208 0.5366 0.9388 0.5212 0.4964 0.5364 0.5463

Table 4.13 shows the critical bus ranking using CPF. Eighteen rankings are  produced from the tabulated data above and load buses are ranked ascending from weak to strong. The top three weakest buses appear as bus 26, 30 and 29, while the top three strongest buses are bus 4, 3 and 10. PV curve for bus 21 is not plotted accurately as it does not showed a full swing curve as others, thus the lowest point of the curve is adopted for the research.

42 Table 4.13: Critical load bus ranking of IEEE 30-bus system using voltage collapse  point from PV curve Critical bus ranking (weak to strong) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

Load bus

26 30 29 19 18 14 20 16 24 17 8 15 7 21* 12 10 3 4

*PV curve for bus 21 was not plotted accurately

4.2.2.2 Critical bus ranking by VCPI

Table 4.14 shows the calculation of VCPI on IEEE 30-bus system during critical loading condition. For load bus 1, 2, 5, 6, 9, 11, 13, 22, 23, 25, 27 and 28, there are no VCPI index appeared due to their generation bus or P-V bus characteristics. As shown in column 3, proposed VCPI is simplified by stating small change in load reactive power to one (1), compared to the original VCPI introduced by Chen [2].

43 Table 4.14: Calculation of VCPI on heavy load state (IEEE 30-bus system) Load bus

  



1.00 1.10 1.11 1.15 1.19 1.07 1.09 1.10 1.08 1.10 1.10 1.11 1.12 1.11 1.02 1.00 1.04 1.09 1.04 1.06

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

       1.00 1.10 1.11 1.15 1.19 1.07 1.09 1.10 1.08 1.10 1.10 1.11 1.12 1.11 1.02 1.00 1.04 1.09 1.04 1.06

Table 4.15 shows the critical bus ranking using VCPI index. Twenty rankings are  produced from the tabulated data above and load buses are ranked ascending from weak to strong. Load buses are ranked ascending from weak to strong from the calculated VCPI index above. The top three weakest buses appear as bus 8, 7 and 19, while the top three strongest buses are bus 23, 2 and 21.

44 Table 4.15: Critical load bus ranking of IEEE 30-bus system using VCPI Critical bus ranking (weak to strong) 1 2 3 4 4 4 7 7 7 7 11 11 13 14 15 16 16 18 19 19

Load bus

8 7 19 4 18 20 3 14 16 17 12 26 15 10 30 24 29 21 2 23

45 4.2.2.3 Discussion

Table 4.16: Comparison of 3 proximity measures for contingency ranking of IEEE 30-

 bus system Rank (weakest to strongest) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

CPF 26 30 29 19 18 14 20 16 24 17 8 15 7 21* 12 10 3 4 -

Proximity measures VC 8 7 4 3 19 30 18 20 26 14 16 17 15 29 12 10 24 21 -

VCPI 8 7 19 4 18 20 3 14 16 17 12 26 15 10 30 24 29 21 2 23

Table 4.16 shows the load buses of IEEE 30-bus test system ordered from the weakest to strongest using continuous power flow (CPF) and relative voltage change index (VC), compared to voltage collapse proximity indicator (VCPI). In overall, VC and VCPI produce similar ranking of weak load buses while CPF shows an irrelevant ranking compared to others. VC and VCPI indicate bus 8 as the weakest bus while CPF votes for bus 26. For the strongest bus, both of them choose bus 12 but CPF goes for bus 4. When zooming into the difference of results by both VC and VCPI indices, their ranking of load buses deviate not more than three (3) position of rank. For CPF, the ranking is better at the middle rank. It is proofed that rank 5 and 10 for CPF is exactly same as VCPI and ranking for bus 19, 14, 20, 16, 15, 12 and 10 are similar to what VC and VCPI have ranked.

46

The deviation of results produced by CPF is explained by the critical loading condition set for VC and VCPI. Results of VC and VCPI are influenced by the assumption of heavy load state, where their voltage magnitude of all load buses has to lie between 0.9 p.u. to 1.1 p.u.. The increment of load with constant power factor stops at 80% from basecase. For CPF, the results are obtained from PV curve plotted using Continuation Power Flow program included in MATPOWER software package. It can  be seen from the PV curves that the system is stressed to the condition where the bus voltage magnitudes are suppressed down to 0.57 p.u. in 14-bus system, even 0.49 p.u. in 30-bus system.

In terms of computation time, CPF and VCPI require one complete load flow solution per load bus. CPF method need to plot the PV curve per load bus and obtain the voltage collapse point, while it is vital for VCPI to obtain small increase in generation and load reactive power. For VC, it requires two complete power flow solutions to obtain the load bus voltage magnitude for initial and critical state. Table 4.17 shows the computation time per power flow and table shows the overall computation time of all indices. Stopwatch time function in MATLAB utilizing “tic and toc” code is used in the

analysis.

47 Table 4.17: Comparison of 3 proximity measures in terms of computation time per load

flow for both test systems Test system

IEEE 14-bus

IEEE 30-bus

Run attempt 1 2 3 4 5 Average

1 2 3 4 5 Average

Computation time per load flow (second) CPF (on bus 4) VC VCPI 0.381236 0.018805 0.018805 0.384566 0.018985 0.018985 0.385031 0.018978 0.018978 0.391615 0.017533 0.017533 0.385207 0.018658 0.018658 0.385531 0.018592 0.018592

0.412958 0.417074 0.421429 0.411697 0.409544 0.41454

0.029133 0.028265 0.026094 0.025931 0.027766 0.027438

0.029133 0.028265 0.026094 0.025931 0.027766 0.027438

From Table 4.18, it can be seen that CPF has the longest computation time compared to another two indices, and VC appears to be the fastest indices to compute. For IEEE 14-bus test system, VCPI is seven (7) times slower than VC while twenty (20) times faster than CPF. For IEEE 30-bus test system, VCPI is seven (7) times slower than VC while fifteen (15) times faster than CPF. The assumption made for the analysis is the  power flow is attempted on bus 4 solely for CPF, and the power flow process for VC and VCPI is the same. All the computation time tabulated is based on pure CPU calculation time, neglecting time delay by user interaction. In comparison, VC has the shortest computation time compared to another two indices.

Table 4.18: Comparison of 3 proximity measures in terms of overall computation time

for both test systems Test system

IEEE 14-bus IEEE 30-bus

Overall computation time CPF (on bus 4) VC VCPI 5.38743 0.037184 0.260288 5.80356 0.054876 0.384132

48 For the overall performance of proposed VCPI, it can be rated as satisfactory as the result produced in both 14-bus and 30-bus test system are similar. The drawback is it has longer computation time than VC. With the advancement of computer technology nowadays, solution for a power flow by computer is less than one second and the  problem is minimized.

4.3

Summary

This chapter has discussed the comparison of three indices to indicate weak load  buses in the power system, tested on IEEE 14-bus test system and 30-bus test system. Two benchmark methods are adopted which were VC and CPF. The proposed VCPI is rated as satisfactory in terms of accuracy, but has longer computation time compared to  performance of VC. While for comparison with CPF, their ranking results deviate much due to the assumption of critical loading condition on VCPI index calculation, and VCPI is superior to CPF from the perspective of computation time.

49

CHAPTER 5

CONCLUSIONS & RECOMMENDATIONS

5.1

Introduction

In this chapter, conclusions are presented to address the stated objectives, implication of the findings, and limitations related to the proposed approach. Recommendations and future research work related to the current method are also highlighted.

5.2

Conclusions

This research has presented a comparative study and analysis of the performance of some static voltage collapse indices. The objectives for the research are archived: to develop an indicator to perform contingency screening and ranking  –   part of Voltage Security Assessment on standard IEEE test system using MATLAB language and to compare the results obtained from the VCPI to two benchmark results, which are VC and CPF. The software used to analysis primary data included Matpower and Matlab. Data collected is then analyzed by spreadsheet software Microsoft® Office Excel.

For the results, all the indices VC, CPF and VCPI point bus 14 as the weakest  bus in the system for IEEE 14-bus test system, and VC and VCPI produce the exact

50 ranking from each other. While for IEEE 30-bus test system, VC and VCPI produce similar ranking as well, rate bus 8 as the weakest bus but ranking of CPF deviates much, it rates bus 26 which is ranked 12 by VCPI. The researcher believes that the deviation is due to the critical loading condition assumption for calculation of VC and VCPI. In terms of computation time, VC is the best among three indices, followed by VCPI and CPF.

The results of this study indicate that the proposed VCPI is rated as satisfactory in terms of accuracy, but has longer computation time compared to performance of VC. While for comparison with CPF, their ranking results deviate much due to the assumption of critical loading condition, and VCPI is superior to CPF from the  perspective of computation time. Compared to the original VCPI by Chen [2], proposed VCPI is simplified by stating the small increase of load reactive power, ΔQi to one (1).

However, these findings are only applicable to contingency screening and ranking process as the part of Voltage Stability Assessment (VSA) discussed in Chapter 2. The research utilized static voltage collapse indices, and only applicable to offline  power system.

5.3

Recommendations

Based on the findings and conclusion of the study, here are several recommendations to be considered:

1.

User Interface  –   development of VCPI to Matlab program or incorporating Graphic User Interface (GUI). This will ease the user on the analysis. By calling certain function in Matlab, critical loading condition could be obtained and CPF, VC and VCPI could be tabulated nicely on the screen.

51 2.

Complex power VCPI  –   proposed VCPI is applicable for load with sufficient reactive power, obviously it would produce inaccurate index for unity power factor loads. Therefore a complex power index will be a better indicator. Further development of the index could refer to [22].

3.

Precision on critical loading condition –  to obtain more precise of critical loading condition, a smaller step size such as 5% or 1% can be adopted instead of 10% that was used in this research.

5.4

Future Research Work

This study should be conducted with large buses test system such as 57-bus or 118-bus to increase the validity of the research. Researchers should do more reading on the topic of voltage security assessment and previous methods of voltage collapse  proximity indicators and indices to identify weak load buses in power system.

Source of the information should not depend solely on internet articles. Journals and newspaper archive should also be taken into consideration. Methods of analyzing data collected should not be restricted on reactive power and voltage magnitude, but from more complex method such as right singular vector by Chen [2].

More advanced method should be implemented in order to increase the validity of the research, such as utilizing software like PowerWorld, Power System Analysis Toolbox (PSAT), Voltage Stability Toolbox (VST) and many more.

52

REFERENCES

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241 1992. 5.

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16, No. 5, pp.241-248, October 2002. 6.

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Akorede, M.F.; Hizam, H.; Aris, I.; Kadir, M.Z.A.; , "Contingency evaluation for voltage security assessment of power systems,"  Research and Development (SCOReD), 2009 IEEE Student Conference on , vol., no., pp.345-348, 16-18 Nov.

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53 10.

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flow margin using the modified continuation power flow in voltage stability analysis”, IEE Proc. Gen. Transm. Distrib. 148 (2) (2001) 128 – 132.

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General Meeting, 2009 IEEE, pp. 1-7, July 26-30 2009. 13.

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March 2009 14.

A.C. Zambroni, “Identifying a vanishing eigenvalue in voltage collapse analysis with consideration of limits”. IEE Proc. Gen. Transm. Distrib. 148 2 (2001), pp.

263 – 267. 15.

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17.

S. Greene, I. Dobson, and F. L. Alvarado, "Contingency ranking for voltage collapse via sensitivities from a single nose curve,"  IEEE Transactions on Power Systems, vol. 14, pp. 232-240, 1999.

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54 20.

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55 Appendix A1 IEEE 14-bus system MATLAB M-file

function mpc = case14 %CASE14 Power flow data for IEEE 14 bus test case. % Please see CASEFORMAT for details on the case file format. % This data was converted from IEEE Common Data Format % (ieee14cdf.txt) on 20-Sep-2004 by cdf2matp, rev. 1.11 % See end of file for warnings generated during conversion. % % Converted from IEEE CDF file from: % http://www.ee.washington.edu/research/pstca/ % % 08/19/93 UW ARCHIVE 100.0 1962 W IEEE 14 Bus Test Case % MATPOWER % $Id: case14.m,v 1.11 2010/03/10 18:08:15 ray Exp $ %% MATPOWER Case Format : Version 2 mpc.version = '2'; %%----- Power Flow Data -----%% %% system MVA base mpc.baseMVA = 100; %% bus data % bus_i type Pd Qd Gs Bs area Vm Va baseKV zone Vmax mpc.bus = [ 1 3 0 0 0 0 1 1.06 0 0 1 1.06 0.94; 2 2 21.7 12.7 0 0 1 1.045 -4.98 0 1 1.06 0.94; 3 2 94.2 19 0 0 1 1.01 -12.72 0 1 1.06 0.94; 4 1 47.8 -3.9 0 0 1 1.019 -10.33 0 1 1.06 0.94; 5 1 7.6 1.6 0 0 1 1.02 -8.78 0 1 1.06 0.94; 6 2 11.2 7.5 0 0 1 1.07 -14.22 0 1 1.06 0.94; 7 1 0 0 0 0 1 1.062 -13.37 0 1 1.06 0.94; 8 2 0 0 0 0 1 1.09 -13.36 0 1 1.06 0.94; 9 1 29.5 16.6 0 19 1 1.056 -14.94 0 1 1.06 0.94; 10 1 9 5.8 0 0 1 1.051 -15.1 0 1 1.06 0.94; 11 1 3.5 1.8 0 0 1 1.057 -14.79 0 1 1.06 0.94; 12 1 6.1 1.6 0 0 1 1.055 -15.07 0 1 1.06 0.94; 13 1 13.5 5.8 0 0 1 1.05 -15.16 0 1 1.06 0.94; 14 1 14.9 5 0 0 1 1.036 -16.04 0 1 1.06 0.94; ];

Vmin

%% generator data % bus Pg Qg Qmax Qmin Vg mBase status Pmax Pmin Pc1 Pc2 Qc1min Qc1max Qc2min Qc2max ramp_agc ramp_10 ramp_30 ramp_q apf

56 mpc.gen = [ 1 232.4 -16.9 10 0 1.06 100 1 332.4 0 0 0 0 0 0 0 0 0 0 0 0; 2 40 42.4 50 -40 1.045 100 1 140 0 0 0 0 0 0 0 0 0 0 0 0; 3 0 23.4 40 0 1.01 100 1 100 0 0 0 0 0 0 0 0 0 0 0 0; 6 0 12.2 24 -6 1.07 100 1 100 0 0 0 0 0 0 0 0 0 0 0 0; 8 0 17.4 24 -6 1.09 100 1 100 0 0 0 0 0 0 0 0 0 0 0 0; ]; %% branch data % fbus tbus r x b rateA rateB rateC ratio angle status angmin angmax mpc.branch = [ 1 2 0.01938 0.05917 0.0528 9900 0 0 0 0 1 -360 360; 1 5 0.05403 0.22304 0.0492 9900 0 0 0 0 1 -360 360; 2 3 0.04699 0.19797 0.0438 9900 0 0 0 0 1 -360 360; 2 4 0.05811 0.17632 0.034 9900 0 0 0 0 1 -360 360; 2 5 0.05695 0.17388 0.0346 9900 0 0 0 0 1 -360 360; 3 4 0.06701 0.17103 0.0128 9900 0 0 0 0 1 -360 360; 4 5 0.01335 0.04211 0 9900 0 0 0 0 1 -360 360; 4 7 0 0.20912 0 9900 0 0 0.978 0 1 -360 360; 4 9 0 0.55618 0 9900 0 0 0.969 0 1 -360 360; 5 6 0 0.25202 0 9900 0 0 0.932 0 1 -360 360; 6 11 0.09498 0.1989 0 9900 0 0 0 0 1 -360 360; 6 12 0.12291 0.25581 0 9900 0 0 0 0 1 -360 360; 6 13 0.06615 0.13027 0 9900 0 0 0 0 1 -360 360; 7 8 0 0.17615 0 9900 0 0 0 0 1 -360 360; 7 9 0 0.11001 0 9900 0 0 0 0 1 -360 360; 9 10 0.03181 0.0845 0 9900 0 0 0 0 1 -360 360; 9 14 0.12711 0.27038 0 9900 0 0 0 0 1 -360 360; 10 11 0.08205 0.19207 0 9900 0 0 0 0 1 -360 360; 12 13 0.22092 0.19988 0 9900 0 0 0 0 1 -360 360; 13 14 0.17093 0.34802 0 9900 0 0 0 0 1 -360 360; ]; %%----- OPF Data -----%% %% generator cost data % 1 startup shutdown n x1 y1 ... xn yn % 2 startup shutdown n c(n-1) ... c0 mpc.gencost = [ 2 0 0 3 0.0430293 20 0; 2 0 0 3 0.25 20 0; 2 0 0 3 0.01 40 0; 2 0 0 3 0.01 40 0; 2 0 0 3 0.01 40 0; ]; % Warnings from cdf2matp conversion: %

57 % ***** Qmax = Qmin at generator at bus 1 (Qmax set to Qmin + 10) % ***** area data conversion not yet implemented (creating dummy area data) % ***** MVA limit of branch 1 - 2 not given, set to 9900 % ***** MVA limit of branch 1 - 5 not given, set to 9900 % ***** MVA limit of branch 2 - 3 not given, set to 9900 % ***** MVA limit of branch 2 - 4 not given, set to 9900 % ***** MVA limit of branch 2 - 5 not given, set to 9900 % ***** MVA limit of branch 3 - 4 not given, set to 9900 % ***** MVA limit of branch 4 - 5 not given, set to 9900 % ***** MVA limit of branch 4 - 7 not given, set to 9900 % ***** MVA limit of branch 4 - 9 not given, set to 9900 % ***** MVA limit of branch 5 - 6 not given, set to 9900 % ***** MVA limit of branch 6 - 11 not given, set to 9900 % ***** MVA limit of branch 6 - 12 not given, set to 9900 % ***** MVA limit of branch 6 - 13 not given, set to 9900 % ***** MVA limit of branch 7 - 8 not given, set to 9900 % ***** MVA limit of branch 7 - 9 not given, set to 9900 % ***** MVA limit of branch 9 - 10 not given, set to 9900 % ***** MVA limit of branch 9 - 14 not given, set to 9900 % ***** MVA limit of branch 10 - 11 not given, set to 9900 % ***** MVA limit of branch 12 - 13 not given, set to 9900 % ***** MVA limit of branch 13 - 14 not given, set to 9900

58 Appendix A2 IEEE 30-bus system MATLAB M-file

function mpc = case30 %CASE30 Power flow data for 30 bus, 6 generator case. % Please see CASEFORMAT for details on the case file format. % % Based on data from ... % Alsac, O. & Stott, B., "Optimal Load Flow with Steady State Security", % IEEE Transactions on Power Apparatus and Systems, Vol. PAS 93, No. 3, % 1974, pp. 745-751. % ... with branch parameters rounded to nearest 0.01, shunt values divided % by 100 and shunt on bus 10 moved to bus 5, load at bus 5 zeroed out. % Generator locations, costs and limits and bus areas were taken from ... % Ferrero, R.W., Shahidehpour, S.M., Ramesh, V.C., "Transaction analysis % in deregulated power systems using game theory", IEEE Transactions on % Power Systems, Vol. 12, No. 3, Aug 1997, pp. 1340-1347. % Generator Q limits were derived from Alsac & Stott, using their Pmax % capacities. V limits and line |S| limits taken from Alsac & Stott. % MATPOWER % $Id: case30.m,v 1.12 2010/03/10 18:08:13 ray Exp $ %% MATPOWER Case Format : Version 2 mpc.version = '2'; %%----- Power Flow Data -----%% %% system MVA base mpc.baseMVA = 100; %% bus data % bus_i type Pd Qd Gs Bs area Vm Va baseKV zone mpc.bus = [ 1 3 0 0 0 0 1 1 0 135 1 1.05 0.95; 2 2 21.7 12.7 0 0 1 1 0 135 1 1.1 0.95; 3 1 2.4 1.2 0 0 1 1 0 135 1 1.05 0.95; 4 1 7.6 1.6 0 0 1 1 0 135 1 1.05 0.95; 5 1 0 0 0 0.19 1 1 0 135 1 1.05 0.95; 6 1 0 0 0 0 1 1 0 135 1 1.05 0.95; 7 1 22.8 10.9 0 0 1 1 0 135 1 1.05 0.95; 8 1 30 30 0 0 1 1 0 135 1 1.05 0.95; 9 1 0 0 0 0 1 1 0 135 1 1.05 0.95; 10 1 5.8 2 0 0 3 1 0 135 1 1.05 0.95; 11 1 0 0 0 0 1 1 0 135 1 1.05 0.95; 12 1 11.2 7.5 0 0 2 1 0 135 1 1.05 0.95; 13 2 0 0 0 0 2 1 0 135 1 1.1 0.95; 14 1 6.2 1.6 0 0 2 1 0 135 1 1.05 0.95;

Vmax

Vmin

59 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

1 1 1 1 1 1 1 2 2 1 1 1 2 1 1 1

8.2 2.5 0 0 2 1 0 135 1 1.05 0.95; 3.5 1.8 0 0 2 1 0 135 1 1.05 0.95; 9 5.8 0 0 2 1 0 135 1 1.05 0.95; 3.2 0.9 0 0 2 1 0 135 1 1.05 0.95; 9.5 3.4 0 0 2 1 0 135 1 1.05 0.95; 2.2 0.7 0 0 2 1 0 135 1 1.05 0.95; 17.5 11.2 0 0 3 1 0 135 1 1.05 0.95; 0 0 0 0 3 1 0 135 1 1.1 0.95; 3.2 1.6 0 0 2 1 0 135 1 1.1 0.95; 8.7 6.7 0 0.04 3 1 0 135 1 1.05 0.95; 0 0 0 0 3 1 0 135 1 1.05 0.95; 3.5 2.3 0 0 3 1 0 135 1 1.05 0.95; 0 0 0 0 3 1 0 135 1 1.1 0.95; 0 0 0 0 1 1 0 135 1 1.05 0.95; 2.4 0.9 0 0 3 1 0 135 1 1.05 0.95; 10.6 1.9 0 0 3 1 0 135 1 1.05 0.95;

]; %% generator data % bus Pg Qg Qmax Qmin Vg mBase status Pmax Pmin Pc1 Pc2 Qc1min Qc1max Qc2min Qc2max ramp_agc ramp_10 ramp_30 ramp_q apf mpc.gen = [ 1 23.54 0 150 -20 1 100 1 80 0 0 0 0 0 0 0 0 0 0 0 0; 2 60.97 0 60 -20 1 100 1 80 0 0 0 0 0 0 0 0 0 0 0 0; 22 21.59 0 62.5 -15 1 100 1 50 0 0 0 0 0 0 0 0 0 0 0 0; 27 26.91 0 48.7 -15 1 100 1 55 0 0 0 0 0 0 0 0 0 0 0 0; 23 19.2 0 40 -10 1 100 1 30 0 0 0 0 0 0 0 0 0 0 0 0; 13 37 0 44.7 -15 1 100 1 40 0 0 0 0 0 0 0 0 0 0 0 0; ]; %% branch data % fbus tbus r x b rateA rateB rateC ratio angle status angmin angmax mpc.branch = [ 1 2 0.02 0.06 0.03 130 130 130 0 0 1 -360 360; 1 3 0.05 0.19 0.02 130 130 130 0 0 1 -360 360; 2 4 0.06 0.17 0.02 65 65 65 0 0 1 -360 360; 3 4 0.01 0.04 0 130 130 130 0 0 1 -360 360; 2 5 0.05 0.2 0.02 130 130 130 0 0 1 -360 360; 2 6 0.06 0.18 0.02 65 65 65 0 0 1 -360 360; 4 6 0.01 0.04 0 90 90 90 0 0 1 -360 360; 5 7 0.05 0.12 0.01 70 70 70 0 0 1 -360 360; 6 7 0.03 0.08 0.01 130 130 130 0 0 1 -360 360; 6 8 0.01 0.04 0 32 32 32 0 0 1 -360 360; 6 9 0 0.21 0 65 65 65 0 0 1 -360 360; 6 10 0 0.56 0 32 32 32 0 0 1 -360 360; 9 11 0 0.21 0 65 65 65 0 0 1 -360 360; 9 10 0 0.11 0 65 65 65 0 0 1 -360 360;

60 4 12 0 0.26 0 65 65 65 0 0 1 -360 360; 12 13 0 0.14 0 65 65 65 0 0 1 -360 360; 12 14 0.12 0.26 0 32 32 32 0 0 1 -360 360; 12 15 0.07 0.13 0 32 32 32 0 0 1 -360 360; 12 16 0.09 0.2 0 32 32 32 0 0 1 -360 360; 14 15 0.22 0.2 0 16 16 16 0 0 1 -360 360; 16 17 0.08 0.19 0 16 16 16 0 0 1 -360 360; 15 18 0.11 0.22 0 16 16 16 0 0 1 -360 360; 18 19 0.06 0.13 0 16 16 16 0 0 1 -360 360; 19 20 0.03 0.07 0 32 32 32 0 0 1 -360 360; 10 20 0.09 0.21 0 32 32 32 0 0 1 -360 360; 10 17 0.03 0.08 0 32 32 32 0 0 1 -360 360; 10 21 0.03 0.07 0 32 32 32 0 0 1 -360 360; 10 22 0.07 0.15 0 32 32 32 0 0 1 -360 360; 21 22 0.01 0.02 0 32 32 32 0 0 1 -360 360; 15 23 0.1 0.2 0 16 16 16 0 0 1 -360 360; 22 24 0.12 0.18 0 16 16 16 0 0 1 -360 360; 23 24 0.13 0.27 0 16 16 16 0 0 1 -360 360; 24 25 0.19 0.33 0 16 16 16 0 0 1 -360 360; 25 26 0.25 0.38 0 16 16 16 0 0 1 -360 360; 25 27 0.11 0.21 0 16 16 16 0 0 1 -360 360; 28 27 0 0.4 0 65 65 65 0 0 1 -360 360; 27 29 0.22 0.42 0 16 16 16 0 0 1 -360 360; 27 30 0.32 0.6 0 16 16 16 0 0 1 -360 360; 29 30 0.24 0.45 0 16 16 16 0 0 1 -360 360; 8 28 0.06 0.2 0.02 32 32 32 0 0 1 -360 360; 6 28 0.02 0.06 0.01 32 32 32 0 0 1 -360 360; ]; %%----- OPF Data -----%% %% area data % area refbus mpc.areas = [ 1 8; 2 23; 3 26; ]; %% generator cost data % 1 startup shutdown n x1 y1 ... xn yn % 2 startup shutdown n c(n-1) ... c0 mpc.gencost = [ 2 0 0 3 0.02 2 0; 2 0 0 3 0.0175 1.75 0; 2 0 0 3 0.0625 1 0; 2 0 0 3 0.00834 3.25 0; 2 0 0 3 0.025 3 0;

61 2 0 0 3 0.025 3 0; ];

62 Appendix B test_cpf MATLAB M-file

function test_cpf %TEST_CPF Test continuation power flow (CPF). % created by Rui Bo on 2007/11/12 % % % % % % % % % % % % % % % % % % % % % % % % % % % %

MATPOWER $Id: test_cpf.m,v 1.4 2010/04/26 19:45:26 ray Exp $ by Rui Bo Copyright (c) 2009-2010 by Rui Bo This file is part of MATPOWER. See http://www.pserc.cornell.edu/matpower/ for more info. MATPOWER is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version. MATPOWER is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with MATPOWER. If not, see . Additional permission under GNU GPL version 3 section 7 If you modify MATPOWER, or any covered work, to interface with other modules (such as MATLAB code and MEX-files) available in a MATLAB(R) or comparable environment containing parts covered under other licensing terms, the licensors of MATPOWER grant you additional permission to convey the resulting work.

casename = 'case30';%'case6bus'; %'case30' %% test cpf fprintf('\n------------testing continuation power flow (CPF) solver\n'); loadvarloc = 7;%6;%7 % bus number at which load changes sigmaForLambda = 0.2;%0.05; % stepsize for Lambda sigmaForVoltage = 0.05;%0.025; % stepsize for voltage [max_lambda, predicted_list, corrected_list, combined_list, success, et] = cpf(casename, loadvarloc, sigmaForLambda, sigmaForVoltage); fprintf('maximum lambda is %f\n\n', max_lambda);

63 %% draw PV curve flag_combinedCurve = true;  busesToDraw = [];%[3:6]; drawPVcurves(casename, loadvarloc, flag_combinedCurve, busesToDraw);

corrected_list,

combined_list,

64 Appendix C PV curves for each load bus in IEEE 14-bus system

Figure C(a): PV curve of IEEE 14-bus system, bus 4

Figure C(b): PV curve of IEEE 14-bus system, bus 5

Figure C(c): PV curve of IEEE 14-bus system, bus 9

Figure C(d): PV curve of IEEE 14-bus system, bus 10

Figure C(e): PV curve of IEEE 14-bus system, bus 11

Figure C(f): PV curve of IEEE 14-bus system, bus 12

65

Figure C(g): PV curve of IEEE 14-bus system, bus 13

Figure C(h): PV curve of IEEE 14-bus system, bus 14

66 Appendix D PV curves for each load bus in IEEE 30-bus system

Figure D(a): PV curve of IEEE 30-bus system, bus 3

Figure D(b): PV curve of IEEE 30-bus system, bus 4

Figure D(c): PV curve of IEEE 30-bus system, bus 7

Figure D(d): PV curve of IEEE 30-bus system, bus 8

Figure D(e): PV curve of IEEE 30-bus system, bus 10

Figure D(f): PV curve of IEEE 30-bus system, bus 12

67

Figure D(g): PV curve of IEEE 30-bus system, bus 14

Figure D(h): PV curve of IEEE 30-bus system, bus 15

Figure D(i): PV curve of IEEE 30-bus system, bus 16

Figure D(j): PV curve of IEEE 30-bus system, bus 17

Figure D(k): PV curve of IEEE 30-bus system, bus 18

Figure D(l): PV curve of IEEE 30-bus system, bus 19

68

Figure D(m): PV curve of IEEE 30-bus system, bus 20

Figure D(n): PV curve of IEEE 30-bus system, bus 21

Figure D(o): PV curve of IEEE 30-bus system, bus 24

Figure D(p): PV curve of IEEE 30-bus system, bus 26

Figure D(q): PV curve of IEEE 30-bus system, bus 29

Figure D(r): PV curve of IEEE 30-bus system, bus 30

69 Appendix E MATLAB command for constant power factor load increment (for 14-bus system, 180% increment)

define_constants; mpc = loadcase('case14'); mpc.bus(2, PD) = mpc.bus(3, PD) = mpc.bus(4, PD) = mpc.bus(5, PD) = mpc.bus(6, PD) = mpc.bus(9, PD) = mpc.bus(10, PD) = mpc.bus(11, PD) = mpc.bus(12, PD) = mpc.bus(13, PD) = mpc.bus(14, PD) = mpc.bus(2, QD) = mpc.bus(3, QD) = mpc.bus(4, QD) = mpc.bus(5, QD) = mpc.bus(6, QD) = mpc.bus(9, QD) = mpc.bus(10, QD) = mpc.bus(11, QD) = mpc.bus(12, QD) = mpc.bus(13, QD) = mpc.bus(14, QD) = runpf(mpc);

60.76 263.76 133.84 21.28 31.36 82.6 25.2 9.8 17.08 37.8 41.72 35.56 53.2 -10.92 4.48 21 46.48 16.24 5.04 4.48 16.24 14

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