Load Modeling for Voltage Stability Studies Kip Morison1
Hamid Hamadani1
—Voltage stability continues to be a limiting Abstract phenomenon phenomeno n in many power systems systems world-wide. world-wide. When combined with a continual growth in load, the lack of sufficient and optimally optimally located generation generation together together with the failure failure to build new transmission facilities has lead many systems to be vulnerable vulnerable to situations situations of uncontr uncontrollable ollable system voltages. voltages. In its most most severe severe form, form, voltag voltagee instabil instability ity can resu result lt in localiz localized ed or even cascading system blackouts. To deal with this serious issue, many many utilit utilities ies have have mandat mandated ed the stud study y of voltage voltage stabi stabilit lity y as a normal normal comp compone onent nt in system system plann planning ing and and operat operation ion.. While While acceptable methods of voltage stability analysis have emerged in recent years, and comprehensive tools have been developed, the issue of load modeling remains a challenge. It can be argued that the details of load modeling are, because of the nature of the phenomena, phen omena, more critical critical for voltage stability stability than for other forms of stability, and this this has perhaps been been partially responsible for the the lack of of widely widely accept acceptabl ablee load modeli modeling ng practi practices ces.. This This paper discusses discusses some of the factors factors that that make load modelin modeling g for voltage stability a challenge and provides insight into key issues which must be considered when performing practical studies. Index Terms —Load
modeling, voltage stability, dynamic
simulation.
I. I NTRODUCTION
F
OR many many power power system systems, s, voltage voltage stability stability assessmen assessmentt has become one of the most important types of analysis performed as part of system planning, operational planning, and real-ti real-time me operat operation ions. s. Voltag Voltagee stabil stability ity is defi defined ned as the the ability of a power system to maintain steady acceptable voltages voltages at all buses buses in the system system under under normal normal operating operating conditions, conditions, and after being being subjected subjected to a disturbance disturbance [1]. Instability Instability may occur occur in the form of a progressiv progressivee fall of voltage voltage of some buses. buses. The main factor factor causing causing voltage voltage instab instabilit ility y is the inabil inability ity of the the powe powerr system system to main maintai tain n a proper balance of reactive power throughout the system and, therefore, therefore, it is often associated associated with systems systems with inadequate inadequate or poorly located generating sources and insufficient transmission facilities. Since reactive power requires a voltag voltagee gradie gradient nt to be tran transpo sporte rted d from from point point to to point point in in a power system, in order to provide sufficient voltage support, reactive sources, of which generators are the most most important, must be located near load centers, or connected to the load cent center erss via via stro strong ng tran transm smis issi sion on syst system ems. s. In many many powe power r systems, systems, deregulatio deregulation n has has lead to the reduction reduction in constructio construction n of new transmiss transmission ion facilities facilities and the “non-optim “non-optimal” al” location location
Lei Wang1
of generating generating plants. plants. In many many situations situations the inadequate inadequate transmission situation has has been exacerbated by the imposition of more stringent environmental requirements. Over the past past several several years, years, the increasing increasing concer concern n over voltag voltagee stabil stability ity has lead lead to an enorm enormous ous effo effort rt in indust industry ry to develop acceptable techniques and tools for analysis analysis of this phenomena [2-6]. Since voltage stability is characteristically diffe differe rent nt from from othe otherr form formss of stabi stabilit lity, y, such such as trans transie ient nt stability stability or small signal stability, stability, new analytica analyticall and modeling modeling approaches were were required. Both steady-state steady-state (static) analysis analysis methods methods (such as PV curves and modal modal analysis) analysis) and dynamic dynamic analys analysis is (suc (such h as as time time-do -doma main in sim simula ulatio tion) n) have have gained gained industry acceptance and are now widely widely used. An important important step step in the the devel developm opment ent of analy analysis sis meth methods ods involv involves es identifying identifying and developing developing models models for for system system componen components, ts, device devices, s, and contro controls ls which which are are key to the the voltag voltagee stabilit stability y phenomenon. These include such examples as the modeling of reactive reactive capability capability of generato generators rs including including over-excita over-excitation tion limiters, limiters, Static Var Systems, Systems, automatic automatic under-load under-load tapchanging changing transform transformers, ers, automatical automatically ly switched switched capacitors, capacitors, and load-s load-shed heddin ding g schem schemes. es. In genera general, l, these these can be considered considered “deter “determinis ministic” tic” modelin modeling g issues; issues; the the device device structures/functions are not explicitly time-varying time-varying and once once known, can be modeled with a reasonable degree of certainty. Howeve However, r, the drivin driving g force force for voltag voltagee instab instabilit ility y is usuall usually y the loads, which can be considered highly “statistical” in nature and, therefore, much more of a challenge when developing practical models which are generically applicable. Studies have shown that that the results of stability stability simulations can be drastically affected by variations in load models; this is particularly true for voltage stability studies in which loads may be subjec subjected ted to large large variations variations in in system voltages voltages and in which short-term short-term and long-term non-linear non-linear load characteristics characteristics may come come into play. While there has been significant attention given to load modeling modeling in industry industry [7-11], [7-11], including including numerous IEEE and CIGRE publications, for most engineers, it remains remains a challenge challenge to properly properly develop develop load models models which which can be used with confidence in practical day-to-day studies.
II. THE COMPLEXITY OF LOADS In general, general, load modeling modeling for power power system stability stability studies studies is challenging for a number of reasons as described below.
1
Powertech Labs Inc., Surrey, British Columbia, Canada
1-4244-0178-X/06/$20.00 ©2006 IEEE
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PSCE 2006
load and system controls (which can not be adequately represented in steady-state analysis) determine whether the system will be stable or unstable. Long-Term Voltage Instability
not necessary including ULTCs, switchable capacitors, and thermostatic loads. As it is not possible or practical to represent every device which makes up the load, the “aggregate” or “equivalent” representation as shown in Figure 1 is usually necessary. A practical approach for obtaining suitable models is provided in [12] in which various methods of load model acquisition are discussed including,
If a contingency is of insufficient magnitude to cause stalling of induction motors within a short period of time, voltage instability may still occur in a longer time frame. As voltages decline in a system, a number of controls will act to restore a) Simplified voltage dependent models based on voltages close to their pre-contingency levels. Such controls engineering judgment: This is the most widely applied include generators AVRs, static VAr systems (SVS), approach in which simple voltage (and possibly automatic switched capacitors, and automatic transformer frequency) dependent models are used based on under-load tap-changers (ULTCs). As the voltage is raised, approximate knowledge of how the systems loads loads begin to be restored to pre-contingency MW and MVAr respond to voltage (or frequency) variations. While easy levels. This increases the reactive losses through system to create and use, these models normally lack empirical elements and puts additional reactive demands on the already justification and because rotating dynamics are not weakened system. Eventually the ability to provide more included, are not suitable for the analysis of short-term reactive support will be curtailed as (a) generator overvoltage instability. excitation limiters act, (b) SVSs may reach their maximum outputs or (c) all available switchable capacitor banks will be b) Measurement based modeling: In this approach the exhausted. As the reactive supply is curtailed, the system system voltage is perturbed at a substation bus (a bus voltages will drop, further aggravating the condition since the represented by a load bus in the powerflow) and support from static capacitors will drop and induction motors measurements made to determine the response of P and Q will draw more reactive power, or actually stall. The time over time. The perturbation can be imposed by switching frame of long-term voltage instability depends on the system a capacitor or by changing a tap on a transformer. A initial conditions, the severity of the initial disturbance and the model is then fit to the measured responses. While controls and devices which come into play. Time frames possibly useful for benchmarking of existing models, the could extend from a few tens of seconds to many minutes. method does not provide adequate information for the Thermostatic load restoration may also bring on voltage development of induction motor models primarily instability in a very long time frame. Figure 4 shows an because the imposed disturbance can not be sufficiently example of long-term voltage instability occurring after large to drive the actual system loads into the non-linear approximately 120 seconds. region in which induction motor reactive behavior becomes apparent. IV. LOAD MODELING FOR SHORT-TERM VOLTAGE I NSTABILITY
c)
Component based modeling: In this approach a survey of the devices which make up the lumped load is made and, based on known characteristics of the individual devices, a composite load can be synthesized. The composite load can consist of induction motors, resistive loads, and other unique load types; in this regard the model may be more realistic than that achieved from measurement.
While it is not possible to predict apriori whether a system will be prone to short-term or long-term voltage instability, it is clear that, if only short-term instability is of interest, devices and controls that are key include induction motors, motor protections, and possibly generator OELs. Induction motors must be represented in order to capture the speed/reactive From experience, it has been found that a practical approach power characteristic which results in the drawing of large to derive the basic load models for short-term voltage stability amounts of reactive power as motors stall. Induction motor studies is to use a “load composition” based approach to protections must also be considered since some motors may develop models for dynamic simulations. This method uses drop out and provide load relief, although this may be load surveys similar to that proposed in (c) above although individual devices are not surveyed, but rather load cl asses. temporary if the protections allow for reconnection of the motors after voltage recovery. Generator OELs should be In this approach, the portion of a load at each bus which can considered if the characteristics are such that a severe over be attributed to capacitors/reactors is extracted from the loads excitation can cause a very fast reduction of generator reactive and represented explicitly as impedances. Then the remaining output. Depending on the design and settings, it may also be load at each bus is split into Resistive, Small Motor, Large necessary to represent special protection schemes such as Motor, Discharge Lighting, and other components based on under-voltage load shedding schemes. However, many device the load classification (percentage of Residential, Commercial models required for the analysis of long-term instability are and Industrial) and composition (percentage of each
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component in each load class) obtained from survey as shown in Table 1. Typical models and data are available from various sources for many of the components such as induction motors and other components. Unless better information is available, this typical data can be used in deriving the overall load model. Table : Load Composition
Many motors are equipped with protections which cause them to disconnect when terminal voltages drop below a threshold value for a specific period of time. Such action provides load relief and may cause an otherwise unstable situation to remain stable. Figure 5 shows the same example as shown in Figure 4 except that 10% of induction motors are allowed to drop off as a result of motor protections. It can be seen that the system recovers and remain stable.
Load Composition (%) Load Class
R es ide nt ia l
Co mme rc ia l
I nd us tri al
Resistive
25
14
5
Small Motor
75
51
20
Large Motor
0
0
56
Discharge Lighting
0
35
19
Bus voltage magnitude 1.200
0.960
0.720
V. THE NEED FOR SENSITIVITY A NALYSIS 0.480
Regardless of the rigor used to construct load models the complexity and time varying nature of actual loads, as discussed earlier, always introduces some uncertainty in the validity of the model for use in studying any given condition. To deal with this uncertainty, sensitivity analysis is always recommended in order to assess the effect of variations in model parameters on system stability. Some of the sensitivities which should be considered include,
0.240
0.000 0
48
96
144
192
240
Time in seconds
Figure 5 Response with motor tripping
The percentage of induction motors in the aggregate load model The induction motor parameters. If stability limits are being computed as part of a study, it may The characteristic of the induction motor driven load be prudent to assess the sensitivity of parametric variations on The effect of motor protections the limits. An example from a practical study is given in Table 2 which illustrates that varying the load characteristic Figure 4 shows a system response in which induction motors modestly may have a significant impact on margins computed. are modeled but motor protections are not. In this example, it can be seen that the voltages drop after the disturbance and Table 2 : Sensitivity of Voltage Stability Limits to Parameters remains suppressed indefinitely; a result of a number of stalled Modification Change in VS Margin No motors 2.2 % induction motors.
5% reduction in motors 10% reduction in motor size Change in driven load characteristic
Bus voltage magnitude 1.200
0.960
0.5 % 3.3 % 4.0 %
VI. CONCLUSIONS
0.720
0.480
0.240
0.000 0.00 0
2 .0 00
4 .0 00
6.00 0
8.000
Time in seconds
10 .0 00
Voltage stability remains one of the most important aspects of power system analysis and one key factor in obtaining meaningful study results is the representation of loads. For the study of short-term voltage instability, load models which adequately represent induction motor characteristics are critical in order to capture the important motor reactive power behavior which is a driving force in short-term instability. However, the complexity of loads make it impossible to represent loads exactly, and therefore, uncertainty is present in any simplified or aggregate load models developed to represent load dispersed throughout distribution systems. To
Figure 4 Response without motor tripping
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assess the uncertainty, sensitivity analyses should be conducted which assess the impact of variations in the load parameters on both the system dynamic response and also stability limits. VII. R EFERENCES [1] P. Kundur, Power System Stability and Control, McGraw-Hill, 1994 [2] CIGRE TF 38-02-10, “Modeling of Voltage Collapse Including Dynamic Phenomena”, 1993. [3] IEEE Power System Stability Subcommittee, “Voltage Stability Assessment, Concepts, Practices, and Tools”, IEEE/PES Special Publication, August 2002. [4] G.K. Morison, B. Gao and P. Kundur, Voltage Stability Analysis Using Static and Dynamic Approaches, IEEE Transaction on Power Systems, Vol. 8, No. 3, August 1993, pp. 1159-1171 [5] C. W. Taylor, Power System Voltage Stability, McGrawHill Inc., 1994. [6] EPRI Project RP3578-01 Final Report TR-105214, “Assessment of Voltage Stability Methods and Tools”, October 1995 [7] IEEE Task Force on Load Representation for Dynamic Performance, “Standard load models for power flow and dynamic performance simulation”, IEEE Transactions on Power Systems, Vol. 10, No.3, pp1302-1313, August 1993. [8] IEEE Task Force on Load Representation for Dynamic Performance, “Load representation for dynamic performance analysis”, IEEE Transactions on Power Systems, Vol. 8, No.2, pp 472-482, May 1993. [9] EPRI Project 849-7 Final Report EL-5003, “Load Modeling for Power Flow and Transient Stability Computer Studies”, January 1987. [10] Canadian Electricity Association Report 113 T 1040 “Laboratory measurement of Modern Loads Subjected to Large Voltage Changes for Use in Voltage Stability Studies”, prepared by Ontario Hydro technologies, May 1996.
[11] W. Xu and Y. Mansour, “Voltage stability analysis using generic dynamic load models”, IEEE Transactions on Power System, Vol. 9, No. 1, pp. 479-486, February 1994. [12] K. Morison H. Hamadani, L. Wang, “Practical Issues i n Load Modeling for Voltage Stability Studies”, Pane; Paper at IEEE PES General Meeting, 2003. Kip Morison received his BaSc and MaSc degrees in Electrical Engineering from the University of Toronto in 1980 and 1985 respectively. From 1981 to 1993 he worked in the Analytical Methods and Specialized System Studies Department at Ontario Hydro in Toronto, Canada. In 1993 he joined Powertech Labs in Vancouver, where he is now Director of the Power System Studies Group which provides international consulting services and commercial power system software. His interests include power system stability and control and on-line dynamic security assessment and he has authored numerous publications on the subject. He is a registered professional engineer in the Provinces of Ontario and British Columbia and is a member of the IEEE. Hamid Hamadani (Hamadanizadeh) received his B.Sc. degree from Sharif (Arya-Mehr) University of Technology, Tehran, Iran, in 1978 and his M.A.Sc. degree from the University of Toronto in 1981, both in Electrical Engineering. Presently, he is a Specialist Engineer in the Power System Studies Group. Before joining Powertech in 1993, he was with the System Planning Division of Ontario Hydro for seven years and the Research Institute of Hydro Quebec (IREQ) for two years. His current interests include power system security (mainly Voltage Stability) and steady-state analysis. He has several years of experience in development of analytical tools (for off-line and on-line applications) and study of these and other aspects of power systems. Lei Wang received the B.A.Sc and M.A.Sc degrees from Shanghai Jiao Tong University, China in 1982 and 1984, respectively, and the Ph.D degree from the University of Toronto, Canada in 1991. He worked for Ontario Hydro from 1989 to 1993 as a system studies engineer. In 1993, he joined Powertech Labs Inc. where he is now a Principal engineer.
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