Scanning the Issue-Special Issue on Nonlinear Phenomena in Power ...

Scanning the Issue Special Issue on Nonlinear Phenomena in Power Systems: Theory and Practical Implications Power systems are naturally modeled as highly nonlinear structured dynamical systems. Historically, real systems have generally been observed to have rather benign behavior except for very occasional collapses which can be attributed to some rare concurrence of events (From a consumer point of view, the lights are almost always on). However, these nonlinear models can be shown to exhibit a wide variety of complex behavior described mathematically in terms of the theories of Lyapunov stability, bifurcations, structural stability, and chaos. Moreover, problems in power systems have inspired improvements to these theories. Previous planning and operating practice has been able to proceed largely without deep concern for these more exotic aspects of system behavior. The future promises a different picture. Economic and environmental restrictions, along with the current trend to open access systems, will see operating margins reduced as systems become more heavily loaded. Consequently, system behavior will be more dependent on nonlinear characteristics and so more complex. Ultimately, there will be a greater dependence on control based capability rather than physical system expansion [ 11, but the benefits of continuing to use mainly linear control ideas do not appear adequate to handle the essentially nonlinear problems of large disturbance behavior. Before appropriate nonlinear control can be developed, there needs to be a greater understanding of the nonlinear phenomena. This special issue has been designed to present a state-ofthe-art of nonlinear phenomena in power systems. There are numerous sources of information which deal with related practical aspects. The emphasis chosen here was to provide a strong theoretical basis supplemented by related practical considerations. This dependence on a clear rigorous basis is felt to be vital in power systems analysis and control for the future. In fact, this issue is based on the belief that a nonlinear analytical view will be essential to derivation of techniques which extract the most effective use of power system assets. A widely appreciated theoretical basis seems to be less a feature of this subject than others such as robotics, manufacturing and information systems. Tutorial discussions of the main mathematical techniques and phenomena have been assembled. The industry viewpoint has been included via industry based coauthors. In addition, each university author, while highly credible theoretically, can claim extensive interactions with industry and in some cases work within industry.

The intention is that the papers will be of interest to a wide range of readers, including electrical engineers in the areas of control, circuits and systems, and computational methods, who deal with nonlinear problems and techniques, and mathematicians interested in nonlinear phenomena. It is worth reflecting on the highlights of the development of the subject of nonlinear phenomena in power systems. First, from a practical viewpoint, there are four major analytical problems: 1) power flows to compute equilibria; 2) angle stability (commonly called transient stability) to check preservation of generator synchronism; 3) oscillations (commonly treated as a linear issue); and 4) voltage instability to check the possibility of voltage collapse. The last one has attracted the most attention recently as it increasingly occurs in modern systems with high transfers between remote generation and load. Of course, theoretically they are all aspects of the one overall stability question, but it is possible to focus on each via appropriate modeling simplifications. The earliest contributions to power systems theory recognized the highly nonlinear nature of the subject in studies of system dynamics. Classic references [ 2 ] and all current texts for undergraduates deal with nonlinear views of power system stability via the well known equalarea criterion for assessing transient stability; multimachine extensions go back as far as the 1930’s in Russia and in the work of Gorev in particular. The so-called energy function methods have evolved to be a competitive analysis tool these days. However, most nonlinear thinking for power systems occurs in the context of numerical techniques. In some significant papers of the early 1970’s [3], [4], a new strand of nonlinear theory for power systems was initiated. These papers suggested rigorously looking at existence, uniqueness and enumeration issues in solution of power system equations and the influence on dynamical behavior. These sorts of questions require advanced mathematics and this was not typically available in the power system community. A significant opportunity came with the Systems Engineering for Power program managed by Fink [5] and which resulted in a significant series of Proceedings [6], [7]. Following this came a series of symposia on Bulk Power System Voltage Phenomena which continued the theme, with the most recent being reported in [8], and other publications

from the same community [9]. This program had the vision of bringing greater theoretical credibility to the analysis and

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control of power systems. The participants in the program included some with strong theoretical backgrounds from the systems and control research community. These people picked up on ideas in the earlier pioneering work and turned them into fundamental theories. For instance, the local and global questions of existence and uniqueness raised by [3], [4] were studied using algebraic geometry, bifurcation, and geometric methods. Following this were major investigations of stability boundaries, theory of direct methods, nonlinear oscillations, chaos, structural stability and collapse phenomena. These are the topics covered in this Special Issue. Particularly significant in the theoretical development of these topics were projects undertaken at several US universities; the influence of these is clear to see in the papers of this issue. The tools of bifurcation analysis, Lyapunov theory, geometric ideas, and classical mechanics have clearly had a tremendous impact on the theoretical understanding of this subject. There have of course been numerous contributions by researchers to this subject from all over the world. In particular, it is worth pointing out that many interesting contributions to nonlinear analysis and control have occurred in Eastem Europe (and Russia in particular). This tradition was focussed on developing working emergency control schemes which cope with very low reserve margins. Unfortunately, it was not possible to arrange a contribution to the Special Issue which could feature this work. There are seven papers in this Special Issue. They are arranged to cover the main topics from a motivational starting point through major theoretical ideas supplemented by more practical viewpoints. The first paper, “Voltage Instability: Mechanisms and Control Strategies,” by Vu, Liu, Taylor, and Jimma introduces many nonlinear aspects of power systems via the topic of voltage stability. The overview goes from basic power system modeling to theory for collapse mechanisms, remedial control and a substantial practical illustration of concepts. The role of differential algebraic (DA) models and bifurcations is introduced along the way. This introduction leads naturally to the second paper, “Local Bifurcation in Power Systems: Theory, Computation and Application,” by Kwatny, Fischl, and Nwankpa which gives an extensive tutorial overview of local bifurcations in DA models of power systems. This paper really inspires the idea that large system capability can be thoroughly assessed using computational bifurcation techniques. The third paper, “Bifurcation, Chaos and Voltage Collapse in

The first three papers have some emphasis towards voltage collapse phenomena as reflects the current research activities. The fourth paper, “Direct Stability Analysis of Electric Power Systems Using Energy Functions: Theory, Applications and Perspective,” by Chiang, Chu, and Cauley tums attention mainly to large disturbance angle stability. So-called direct methods are descended from a variety of ideas inspired by Lyapunov stability theory and have been developed as a practical tool. They are particularly appealing for assessing margins of stability and systematically deriving emergency control actions; however there have been some longstanding basic theoretical questions which were for a long time bypassed with various ad hoc ideas. In this paper, a modern theoretical basis for these techniques is presented along with associated practical insights. The ultimate nonlinear analysis tool would simultaneously consider all the basic dynamics questions as part of a larger system problem. A fundamental starting point is complete characterization of all boundaries (stability, bifurcation, feasibility). The fifth paper, “A Taxonomy of the Dynamics of Large Constrained Nonlinear Systems,” by Venkatasubramanian, Schattler, and Zaborszky picks up on many issues discussed in earlier papers to present a taxonomy of behavior in DA models; in particular, boundaries in state and parameter spaces related to dynamical behavior are clearly characterized. The last two papers have more emphasis on modeling and practical issues. The paper “Static and Dynamic Nonlinear Loads and Structural Stability in Power Systems,” by Pai, Sauer, and Lesieutre continues the idea of structural stability (and connections to bifurcation theory) within the context of more complete models of generators and loads. It is shown how models of dynamic loads can greatly influence qualitative behavior. This is very important since loads are typically not modeled accurately compared to other components, especially in a dynamic sense. If this issue becomes a problem in heavily loaded systems, much more attention will need to be given to a systematic methodology of identifying loads according to their importance to a particular phenomenon. The final paper, “Analysis Tools for Power Systems-Contending with Nonlinearities,” by Hiskens takes more of an industry analyst’s viewpoint and reflects on the full range of nonlinearities in practical power systems including some not yet fully addressed theoretically. The limitations of tools currently used in industry are discussed. There is clearly scope to usefully develop further tools using ideas presented in this Special

Power Systems,” by Tan, Varghese, Varaiya, and Wu takes

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the bifurcation possibilities further to study global bifurcations (cyclic fold, period doubling, homoclinic chaos). This is done in an illustrative way mainly via showing these bifurcations occur in a simple three‘ bus system. The possibilities here for general computational techniques are limited, but such investigations show the richness of nonlinear phenomena in power system models. The paper points to there needing to be more theoretical and experimental work to determine which complicated behaviors are characteristic of real power systems.

Looking beyond the subject of this Special Issue, it is clear that increased understanding of nonlinear phenomena can lay a basis for large-disturbance control of power systems as illustrated in our first paper. The power systems problem is an ideal forum for study and comparison of techniques in systems analysis and control. Power systems models are typically large-scale nonlinear structured systems with clear sources of uncertainty, particularly in load modeling, structural configuration, and fault position. While this Special Issue is oriented to system analysis, we should

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anticipate increasing attention to use of nonlinear control techniques [lo]. Further it seems that power systems problems will motivate improvements to that subject. Successful application of techniques like feedback linearization [ 1I] have already been reported [ 121. One interesting question regards the extent to which such general techniques can exploit specific structures and so give higher performance and robustness properties. The application of techniques like linear adaptive control and neural networks would appear to have limitations that can be overcome with modeling, bifurcation analysis, and a scheme of global control which may combine features of several control techniques. Earlier work by Zaborszky [13], for instance, made extensive use of power system specific structure in deriving nonlinear control structures. Another major direction to develop further alongside the advances in nonlinear analysis and control is the associated computational techniques for large-scale systems. Finally, about the process of producing the Special Issue: some of the papers were specifically invited. Others were submitted in the usual way. Numerous specialists from universities and industry contributed considerable effort to a quite spirited review process which certainly improved the readability of the papers. It is hoped by the Guest Editor that the efforts of the authors and these reviewers will stimulate further interest in a subject which is both theoretically challenging and of high practical significance.

DAVIDJ. H ~ L L Guest Editor

REFERENCES [1] J. F. Hauer, “Robustness issues in stability control of large electric power systems,” in Proc 32nd Con8 on Decision and Contr., San Antonio, TX, Dec. 1993. [2] E. W. Kimbark, Power System Stability: Synchronous Machines. New York: Wiley, 1956. [3] C. J. Tivora and 0. J. M. Smith, “Equilibrium analysis of power systems,” IEEE Trans. Power Apparatus and Syst., vol. PAS-91, pp. 1131-1137, 1972. [4] A. J. Korsak, “On the question of uniqueness of stable loadflow solutions,” IEEE Trans. Power Apparatus and Syst., vol. PAS-91, pp. 1033-1100, 1972. [5] L. H. Fink, “Systems engineering challenges emerge as electric energy network increases in complexity,” PE Mag., Dec. 1976. [6] L. H. Fink and K. Carlsen, Eds., “Systems engineering for power: Status and prospects,” in Proc. Engineering Found. Conf., Henniker, NH, Aug. 1975. [7] L. H. Fink and T. A. Trygar, Eds., “Systems engineering for power: Emergency operating state control and organisational forms for large scale systems,” in Proc. Engineering Found. Conf, Davos, Switzerland, Sept.-Oct. 1979. [8] L. H. Fink, Ed., “Bulk power system voltage phenomena 111-Voltage stabilitv securitv and control.” in Proc. Int. Seminar, ECC”Inc., 1954. r91 J. H. Chow. P. V. Kokotovic. and R. J. Thomas. Eds.. Svstems and Control Theory for Power Systems. New York SphgerVerlag, 1995. [lo] D. J. Hill, I. A. Hiskens, and Y . Wang, “Robust, adaptive or nonlinear control for modern power systems,” Proc. 32nd Conf. on Decision and Contr., San Antonio, TX, Dec. 1993. [I11 A. Isidori. Nonlinear Control Systems. New York SoringerVerlag, 1989. [12] J. W. Chapman etal., “Stabilizinga multimachine power system via decentralized feedback linearizing excitation control,” IEEE Trans. Power Syst., vol. 8, pp. 830-1839, Aug. 1993. [13] J. Zaborszky, K. W. Whang, and K. Prasad, “Stabilizing control in emergencies: Part 1. Equilibrium point and state determination: Part 2. Control by local feedback,” IEEE Trans. Power Apparatus and Syst., vol. PAS-100, pp. 2374-2389, May 1981. -

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David J. Hill (Fellow, IEEE) received the B.E. degree in electrical engineering and the B.Sc. degreefrom the University of Queensland, Australia, in 1972 and 1974, respectively. He received the Ph.D. degree in electrical engineeringfrom the University of Newcastle, Australia, in 1976. Since 1994 he has held the Chair in Electrical Engineering at the University of Sydney. From 1982 to 1993 he held various academic positions at the University of Newcastle: during 1991-1993 he was Assistant Dean of Engineering (Graduate Studies), and was Assistant Director of the Centre for Industrial Control Science from 1988 to 1992. During 1986 he was a Guest Professor in the Department of Automatic Control, Lund Institute of Technology, Sweden. He held a research position in the Electronics Research Laboratory of the University of California at Berkeley from 1978 to 1980, and a Queen Elizabeth Research Fellowship in the Department of Electrical and Computer Engineering, University of Newcastle, from 1980 to 1982. His research interests are mainly in nonlinear systems and control, stability theory, and power system dynamics and security. His recent applied work consists of various projects in power system stabilization and power plant control carried out in collaboration with utilities in Australia and Sweden. He is a Communicating Editor for the Journal of Mathematical Systems, Estimation and Control. Dr. Hill is a Fellow of the Institution of Engineers, Australia.

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