Control for Stability in Interconnected Power Systems

ABSTRACT: The increase in size and com- plexity of interconnected power systems, coupled with industly’s commitment to max- imum security at minimum cost, has led to the development of many special control de- vices. These control devices ensure that the system is able to operate, without instability, under a wide range of system conditions. This paper describes the development of a number of stabilizing controls. The robust- ness of the overall power system is empha- sized along with modifications to the basic controls necessary to achieve this robust- ness. Analytical tools used in the design of practical power system controls are de- scribed. The importance of validation of modeling and simulation methods by planned system tests and by the analysis of naturally occurring faults is stressed. Likely future system developments are reviewed, includ- ing the implication on the type of controls that may be necessary.

Introduction In recent years, power systems, world-

wide, have grown markedly in size and com- plexity. In order to maximize efficiency of generation and distribution of electric power, the interconnections between individual util- ities have increased and the generators have been required to operate at maximum limits for extensive periods of time. In addition, the most economic sites for generation plants are often remote from load centers and the power must be transmitted over long dis- tances. The majority of power system inter- connections are made through AC transmis- sion lines and the interconnected generators run synchronously. In a large interconnected system, such as that in North America, there may be thousands of synchronous generators in service to supply the load. Each generator normally has separate controls that are used to regulate the real and reactive power sup- plied by the generator to the system.

Transients in power systems are analyzed using many levels of modeling detail. At one extreme is the study of electromagnetic tran-

Dr. Graham J. Rogers is with Ontario Hydro, 700 University Avenue, Toronto, Ontario M5G 1x6, Canada.

Graham J. Rogers

sients initiated by steep wavefront pulses (such as lightning strikes); at the other ex- treme is the study of long-term transients, with periods of several minutes or more, in- volving the interaction between slow auto- matic controls and manual control by system operators. And between is the study of elec- tromechanical oscillations between the syn- chronous generators within the system. Con- trol for the stability of the electromechanical oscillations is the subject of this paper. The time period of concern is from 1 to 40 sec following a disturbance, and the frequency range is from 0.1 to 2.0 Hz. Because of the separation between the frequency of the three types of transients, each can be studied using simplified dynamic models. In electrome- chanical oscillation studies, detailed models are used for machines, including their exci- tation and governing systems, but the high- frequency network transients are ignored as are the low-frequency steam turbine boiler dynamics and the slow system controls (such as on-load tap changers). The resulting sys- tem is governed by nonlinear differential equations, which describe the interchange of electromechanical energy between the gen- erators through the transmission network.

Because of their essential nonlinearity, the stability of power systems depends on the severity of the applied disturbances. Criteria for power system design specify the types of fault the system must be able to withstand without major loss of synchronism and con- sequent breakup. It is also critical that the power system remains stable while operating with no faults. Power system analysts refer to these separate, but related, stability prob- lems as transient stability and small-signal stability, respectively. In general, the system operating conditions are restricted most by the need to maintain transient stability. In recent years, however, as power systems have been operated with higher power trans- fer levels to meet economic constraints, small-signal stability problems have become apparent. In order to achieve the required high transfers of power, the controls asso- ciated with the generators have become crit- ical.

In special cases, asynchronous DC trans- mission is utilized with controlled rectifica- tion at one end and controlled inversion at

the other. In association with DC links, and in order to achieve a uniform voltage distri- bution through the power system, thyristor- controlled capacitors and reactors (static var compensators) have been found necessary. These devices provide additional local con- trols that have significant effects on power system stability.

The power system control designer must ensure that the power system is stable locally and globally. Global control is achieved through correct design and coordination of the local controls of the individual compo- nents of the power system and by restricting the allowable operating conditions of the system. In this paper, a number of stability problems and their solutions are described.

Local Generator Stability

The two most important controllers on modern synchronous generators are the speed governor and the automatic voltage regulator (AVR). In an interconnected system, neither fulfill their nominal function alone: the speed governor also controls the active power sup- plied by the generator to the system; the AVR controls the reactive power supplied by the generator to the system.

Automatic Voltage Regulator

The automatic voltage regulator plays an essential role in keeping the generator in synchronism with other generators on the system. In order to do this efficiently, it must be fast-acting. On a new plant in Ontario Hydro, high-gain electronic controls, with a controlled thyristor power output stage, are used to supply the field of the generator, pro- portionally to the difference between a ref- erence signal and the generator’s terminal voltage magnitude. The result is to produce a highly oscillatory, potentially unstable, mode of electromechanical energy inter- change between the local generator and the rest of the power system. The mode may be stabilized by feeding an additional signal into the AVR input. Most commonly, the signal is derived from the speed of the generator rotor, although the generator power and fre- quency also may be used [ 11, [ 2 ] .

A dynamic compensator is used to modify

0272-170818910100-0019 $01 00 G 1989 IEEE January 1989 19

the stabilizing signal to the AVR in such a way that the damping of the electromechan- ical mode is increased. The device is often referred to as a power system stabilizer. Al- though apparently straightforward, a number of practical difficulties with such devices have occurred.

One of the most serious difficulties expe- rienced with early power system stabilizers fitted to steam-turbine-driven generators was their interaction with the turbine-shaft dy- namics and consequent instability of the first torsional mode. The reason for the interac- tion was twofold. First, speed measurement at the generator rotor contains a strong com- ponent of this torsional mode. Second, the stabilizer compensation is essentially a phase- lead circuit, which increases the high-fre- quency gain of the stabilizer. A change in the location of the speed measurement trans- ducers to a node of the lowest torsional to- gether with tuned torsional filters was the first solution to this problem [ 2 ] . This, how- ever, led to additional “exciter modes,” which restricted the stabilizer gain and, hence, the achievable damping of the elec- tromechanical mode. The most recent sta- bilizers achieve rejection of the torsional modes by using a combination of generator power and speed (the Delta PIOmega sta- bilizer) [3]. With this device, the additional exciter mode introduced by the stabilizer is far less sensitive to the stabilizer gain and, thus, higher values of electromechanical mode damping may be obtained.

Under transient conditions following a se- vere fault, the action of a speed input power system stabilizer is often opposite to that re- quired. It is important that stabilizer output be restricted both in the positive and negative directions. The negative limit is the most critical. It is normally set to between -5 and -10 percent of the rated terminal voltage setting. The positive limit is normally set to 20 percent of the rated terminal voltage set- ting.

Practically, the stabilizer acts by modulat- ing the voltage in the vicinity of the gener- ator in such a way that the generator elec- trical torque has a component in phase with the generator rotor speed change. During se- vere swings, the voltage may be forced to dangerously high levels if uncontrolled. A terminal voltage limit signal is thus required, which opposes the stabilizer signal for ter- minal voltages higher than the maximum safe level. In general, the limiter takes the form of a high-gain terminal voltage control loop, biased off for normal voltage. When oper- ating, torsional modes present in the terminal voltage signal may become unstable; it is important to limit the high-frequency loop

gain of the voltage limit circuit to avoid in- stability.

Governor

The governor’s time response is slow compared to the frequency of the local elec- tromechanical oscillation, and its dynamics have little effect on this mode’s stability. Modern steam turbines, with very fast elec- trohydraulic governor valve drives, are now being used, which have been found to give rise to torsional instabilities similar to those caused by early power system stabilizers. Torsional filters have proved effective in controlling this type of instability [4].

With hydraulic generators, the governor auxiliary controls, which set the transient droop and reset time, require careful tuning to assure stability of the generator both when running in isolation from the rest of the sys- tem and when synchronized to the system [5] . With the introduction of electrohy- draulic gate controls in modern hydraulic turbine governors, there is scope for the in- troduction of more radical control design.

Interarea Stability Following both small and large distur-

bances, a power system experiences low-fre- quency oscillations, which are associated with groups of synchronous generators swinging against other groups of synchro- nous generators through weak transmission connections. The frequencies of these inter- area modes are lower than those of the local modes. In general, interarea modal frequen- cies lie in the range of 0.1 to 0.8 Hz, whereas the local modal frequency range is from 0.8 to 2.0 Hz. The lower modal frequency and the fact that many machines participate in the mode make interarea oscillations more difficult to control than local oscillations. Nonetheless, it has not yet been found nec- essary to use centralized controls to stabilize these modes.

Power system stabilizers on large gener- ating units can be designed to help damp interarea modes in which the generators are significant participants [6]. Thus, it is im- portant that the dynamic compensator asso- ciated with each power system stabilizer is designed to ensure a positive contribution to damping of all modes having frequencies be- tween 0.1 and 2.0 Hz. This may entail a slight reduction in the damping of the higher- frequency local modes.

At the lower end of the interarea mode frequency range, both hydraulic and steam turbine dynamics can affect the damping of the mode. The nonminimum-phase charac- teristic of the hydraulic turbine can cause the

turbine torque to increase with increasing speed rather than decrease, as required to damp system oscillations. In steam turbines, the reheater stage time constant is the critical element, which may introduce a phase lag and reduce the low-frequency damping. In both types of turbine, a simple phase-lead compensator may be used in the governor to ensure that the turbine characteristics do not increase the risk of low-frequency, interarea instability [7], [8].

Transient Stability Following large system disturbances, some

synchronous generators may swing suffi- ciently to lose synchronism with the system. This is prevented, for a wide range of spec- ified, severe system faults by the provision of an adequate transmission system, with rapid fault clearance facilities, and by setting system operating limits. The system design and its operating limits are based on exten- sive simulation of the nonlinear system elec- tromechanical dynamics. The stability of the system following a severe fault can be aided significantly by the installation of fast-acting AVRs on major generating units. As noted previously, fast-acting AVRs generally re- quire power system stabilizers to give ade- quate small-disturbance stability. The power system stabilizers may not produce the cor- rect control input to the AVR following a large system disturbance, and additional ovemding nonlinear controls may be nec- essary. In Ontario, the Transient System Ex- citation Control (TSEC) [9] is used to force up the voltage at the terminals for generators accelerating following a fault. The maxi- mum voltage is limited by a special fast- acting, bang-bang voltage limiter system. TSEC is operative for only the first swing of the system oscillation following the fault.

Direct Current Transmission Thus far, synchronous generator controls

and their influence on different aspects of the stability of power systems have been dis- cussed. As a result of various system con- straints, some technical and some economic, DC transmission is being used more and more.

The characteristics of the firing angle con- trols (pole controls) at the rectifier and in- verter interfaces between the DC transmis- sion and the AC transmission can have a significant impact on both local and global stability. The pole controls can affect the sta- bility of nearby generators; it is usual to sup- ply supplementary controls to prevent insta- bility. The pole controls generally have a

20 IEEE Control Systems Magazine

high bandwidth and interaction between the controls, and the shaft torsional dynamics of nearby steam turbines have produced tor- sional instability that was stabilized by mod- ifying the high-frequency characteristics of the current control loop and adding a notch filter to the power modulation control [ 101.

Because the DC transmission can control significant amounts of power, its effect on the damping of interarea modes can be con- siderable. The need for an AC system whose voltage is relatively insensitive to changes in the power transmitted through the DC sys- tem has led to additional voltage control de- vices, such as static var compensators and synchronous condensers, being placed in the AC system close to the DC transmission ter- minals.

Thus far, the controls for each DC trans- mission system have been designed individ- ually. There are insufficient DC links in ser- vice to draw generic conclusions about the type of control needed to ensure global as well as local stability. As the transmission capability of DC links is growing, there is little doubt that their interaction with the sys- tem is likely to be more severe in future sys- tems and that special consideration will have to be given to the effect that their control design has on the global stability of the sys- tem [ l l ] .

Analysis Tools Because of the size of power system

models being used in stability analysis, spe- cially developed computer programs are used. Step-by-step integration of nonlinear equations of the system is used in the study of transient stability. For small-signal sta- bility studies, equations are linearized about an operating point, and eigenvalue and ei- genvector techniques are used to perform modal analysis of the system. Ontario Hydro currently uses programs in which systems having up to 12,000 AC network nodes and 1500 synchronous machines may be repre- sented. Up to 1000 of the synchronous ma- chines may be modeled, in detail, with AVR and governor, leading to, potentially, 15,000 dynamic states [ 121. Clearly, the consistency of data for such system models is as much a concern as the mathematical techniques of modeling and analysis [ 131.

Fortunately, the stability problems en- countered in regular power system design are often more local in nature, and reduced-or- der models can be determined that ade- quately represent the system for their study. In particular, the design of AVRs, gover- nors, and power system stabilizers for small- signal stability often can be performed using

a model of a single generator connected via a transmission line to a constant voltage source (infinite bus). Large models of the system are, however, still necessary to check these locally designed controllers for their effect on the global stability of the power system [6]. For transmission system design and the determination of operating limits to ensure transient stability in the first few sec- onds following a fault, a reduced-order sys- tem may be simulated that retains detail in an area close to the fault, with distant gen- erators represented by aggregate models [ 141, [ 151. Low-frequency interarea oscillations excited by severe disturbances may lead to groups of generators losing synchronism after several periods. Accurate simulation of this phenomenon requires extensive system mod- eling beyond the immediate vicinity of the fault. Although it may be possible to produce reduced-order models, the concepts of close and distant areas may not be valid. Addi- tional work is required on system reduction techniques to allow the retention of the low- frequency modes, accurate in both frequency and damping, and which maintain the basic structure of the original power system model.

Validation of the simulation models is a continuing process. Field tests, which can be camed out with no risk to system perfor- mance, are used in Ontario Hydro to im- prove the detailed modeling of this particu- larly important plant. This leaves in question the accuracy of simulations following major system disturbances. Transients following naturally occumng faults are monitored and compared with simulations of the same events to provide pointers to the need for dynamic model refinement.

General Comments

The degree of stability of power systems is less important than in many other control problems. What is required is for the power system to remain stable over a wide range of operating conditions. Oscillations of about 1 Hz in frequency with a damping ratio of 0.05 are commonly encountered associated with synchronous machines having slow ex- citation systems and no power system sta- bilizers, and which give rise to no stability problems. There is little need, therefore, for optimal design of controllers in order to maximize damping. Indeed, because of the nonlinear nature of the system dynamics, the robustness of optimal controls, based on lin- ear analysis, is often suspect [16]. Any de- sign based on linear analysis of a reduced system should be checked extensively by nonlinear simulation of the full intercon- nected system [6].

The modes of oscillation involving the system as a whole, the interarea electrome- chanical oscillations, normally can be sta- bilized by decentralized controllers placed at those generating units that participate signif- icantly in the mode. However, the advent of multiterminal DC links imbedded within the AC system may well require centralized DC pole controls to ensure global system stability.

Robustness of power system control de- sign is important but has been approached in a very practical sense thus far. Lack of ro- bustness quickly shows when commission- ing and operating new plants and immediate steps are necessary to rectify problems en- countered. In some cases, quick solutions to local robustness problems have led to global stability problems as the power system has developed. For example, power system sta- bilizers designed for correct compensation at a single local mode natural frequency can destabilize lower-frequency interarea modes. Another extreme case could be that special controls designed for the protection of ex- pensive plants could cause the plant to be tripped from the system to the detriment of the stability of the overall power system. Co- ordination of control design is clearly nec- essary.

For the future, there is a need for contin- ued work in the dynamic simulation of very large systems. The development of efficient techniques that utilize the fundamental phys- ical properties of the power system, such as singular manifolds [ 171, are required to ease the computational burden of transient and small-disturbance stability studies. Methods for more systematic ways to ensure robust- ness, applicable at the design stage, would also be useful. However, as with all evolv- ing systems, there is always the possibility of new methods of control interacting in an unexpected way to introduce potentially unstable modes. Such developments are dif- ficult to forecast and indeed may be hidden by oversimplified modeling in the initial de- sign stages. Therefore, it is important that any assumptions made in the power system model must be realistic. Oversimplified models should be treated with extreme cau- tion and used to provide only qualitative re- sults of a general nature.

Conclusions Control is vital to maintain the stability of

modem interconnected power systems. Al- though a vast amount of experience has been accumulated in the last 20 years, the chang- ing nature of the power system continues to provide challenges to the system designer.

January 1989 21

Simulation and analysis methods are under constant revision and improvement to enable the designer to ensure that the system is ro- bust and may be operated in an economic manner. There remains considerable scope for new approaches that will reduce the com- putational burden involved in the simulation of large power systems.

References

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[3] D. C. Lee, R. E. Beaulieu, and J . A. R . Service, “A Power System Stabilizer Using Speed and Electrical Power Inputs-Design and Field Experience,” IEEE Trans. PAS, vol. 100, pp. 41514157, 1981. D. C. Lee, R. E. Beaulieu, and G. J . Rog- ers, “Effects of Governor Characteristics on Turbogenerator Shaft Torsionals,” IEEE Trans. PAS, vol. 104, pp. 1255-1261, 1985. P. L. Dandeno, P. Kundur, and J . P. Bayne, “Hydraulic Unit Dynamic Performance Under Normal and Isolated Conditions- Analysis and Validation,” IEEE Trans.

P. Kundur, M. Klein, G. J . Rogers, and M. S. Zywno, “Application of Power Sys- tem Stabilizers for Enhancement of Overall System Stability,” to be presented at IEEE PES Summer Meeting, 1988.

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F. M. Hughes, “Improvement of Turbo- generator Transient Performance by Control Means,” Proc. IEE, vol. 120, pp. 233-240, 1973. J. P. Bayne, P. Kundur, and W. Watson, ‘‘Static Exciter Control to Improve Tran- sient Stability,’’ IEEE Trans. PAS, vol. 94,

[IO] M. Buhrman, E. V. Larsen, R. J . Puvko, and H. S . Patel, “Experience with HVDC- Turbine-Generator Torsional Interaction at Square Bute,” IEEE Trans. PAS, vol. 99, pp. 966-975, 1980. R. L. Cresap and J . F. Hauer, “Emergence of a New Swing Mode in the Western Power System,” IEEE Trans. PAS, vol. 100, pp. 2037-2043, 1981.

[I21 D. Y. Wong, G . J . Rogers, B. Porretta, and P. Kundur, “Eigenvalue Analysis of Very Large Power Systems,” IEEE Winter Power Meeting, New Orleans, LA, 1987. P. L. Dandeno, P. Kundur, A. T. Poray, and M. E. Coultes, “Validation of Turbo- generator Stability Models by Comparisons with Power System Tests,” IEEE Trans. PAS, vol. 100, pp. 1637-1643, 1981. R. Podmore, “A Comprehensive Program for Computing Coherency Based Dynamic Equivalents,” PICA-79 Conf: Proc., May 1979.

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Lightly Damped Oscillatory Modes-A Power System Stabilizer Example,” Proc. 26th Con$ on Decision and Control, Los Angeles, CA, Dec. 1987. B. D. Riedle and P. V. Kokotovic, “Inte- gral Manifolds of Slow Adaptation,” IEEE Trans. Automat. Contr., vol. 31, pp. 316- 324, 1986.

[I71

Graham Rogers was born in Birmingham, En- gland, in 1933. After completing an engineer- ing apprenticeship and national service in the Royal Air Force, he at- tended Southampton Uni- versity where he gradu- ated in 1961 with first- class honors in electrical engineering. From 1961 to 1964, he was a Con-

sultant Mathematician with AEI (Rugby) Ltd. From 1964 to 1978, he was Lecturer in electrical engineering at Southampton University where he taught Control Theory and did research into the dynamics and control of electrical machines. Since 1978, when he immigrated to Canada, he has been employed by Ontario Hydro, where he is currently System Design Engineer, Specialist-Controls in the System Planning Division. His responsibilities in- clude the development of techniques for system stability analysis and their application to special- ized power system problems. He also holds the appointment of Associate Professor (part time) at McMaster University. He is a Fellow of The In- stitute of Mathematics and its Applications and a Registered Professional Engineer in the Province of Ontario.

4 989 Conference on Neural Networks The IEEE Control Systems Society is

among the sponsors of the third IEEE Inter- national Conference on Neural Networks. The conference will be held in Washington, D.C., at the Washington Sheraton Hotel on June 19-22, 1989. The conference will in- clude exhibits of the latest neurocomputers, neural network software, and applications presented by some 40 companies and orga- nizations. Papers of eight pages or less are solicited on the following areas: optical and electronic neurocomputers, combinatorial optimization, network architectures, neural

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