Trajectory Sensitivity Theory in Nonlinear Dynamical Systems: Some Power System Applications

  • M. A. Pai
  • Trong B. Nguyen
Part of the Control Engineering book series (CONTRENGIN)

Abstract

Trajectory sensitivity analysis (TSA) has been applied in control system problems for a long time in such areas as optimization and adaptive control. Applications in power systems in conjunction with Lyapunov/transient energy functions first appeared in the 1980s. More recently, TSA has found applications on its own by defining a suitable metric on the trajectory sensitivities with respect to the parameters of interest. In this chapter we present theoretical as well as practical applications of TSA for dynamic security applications in power systems. We also discuss the technique to compute critical values of any parameter that induces stability in the system using trajectory sensitivities.

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References

  1. [1]
    G. L. Wilson and P. Zarakas, “Anatomy of a blackout,” IEEE Spectrum vol. 15, no. 2, pp. 38–46, Feb. 1978.Google Scholar
  2. [2]
    O. Alsac and B. Stott, “Optimal load flow with steady state security,” IEEE Trans. Power Apparatus and Systems, vol. PAS-93, pp. 745–754, 1974.CrossRefGoogle Scholar
  3. [3]
    M. A. Pai, Energy Function Analysis for Power System Stability Kluwer, Norwell, MA, 1989.CrossRefGoogle Scholar
  4. [4]
    A. A. Fouad and V. Vittal Power System Transient Stability Analysis Using the Transient Energy Function Method Prentice-Hall, Englewood Cliffs, NJ, 1991.Google Scholar
  5. [5]
    H. D. Chiang, C. C. Chu, and G. Cauley, “Direct stability analysis of electric power system using energy functions: Theory, applications, and perspective,” Proc. IEEE, vol. 83, no. 11, pp. 1497–1529, Nov. 1995.CrossRefGoogle Scholar
  6. [6]
    M. Pavella, D. Ernst, and D. Ruiz-Vega, Transient Stability of Power Systems: A Unified Approach to Assessment and Control, Kluwer, Norwell, MA, 2000.Google Scholar
  7. [7]
    K. W. Chan, A. R. Edwards, R. W. Dunn, and A. R. Daniels, “On-line dynamic security contingency screening using artificial neural networks,” IEE Proc. Generation, Transmission, and Distribution, vol. 147, no. 6, pp. 367–372, Nov. 2000.CrossRefGoogle Scholar
  8. [8]
    Y. Mansour, E. Vaahedi, and M. A. El-Sharkawi, “Dynamic security contingency screening and ranking using neural networks,” IEEE Trans. Neural Networks vol. 8, no. 4, pp. 942–950, July 1997.CrossRefGoogle Scholar
  9. [9]
    T. B. Nguyen, Dynamic Security Assessment of Power Systems using Trajectory Sensitivity Approach, Ph.D. Dissertation, University of Illinois, Urbana-Champaign, 2002.Google Scholar
  10. [10]
    T. B. Nguyen and M. A. Pai, “Dynamic security-constrained rescheduling of power systems using trajectory sensitivities,” IEEE Trans. Power Systems, to appear.Google Scholar
  11. [11]
    H. You, V. Vittal, and Z. Yang, “Self-healing in power systems: An approach using islanding and rate of frequency decline based load shedding,” IEEE Trans. Power Systems, to appear.Google Scholar
  12. [12]
    P. M. Frank, Introduction to System Sensitivity Theory, Academic Press, New York, 1978.MATHGoogle Scholar
  13. [13]
    M. Eslami, Theory of Sensitivity in Dynamic Systems, Springer-Verlag, New York, 1994.Google Scholar
  14. [14]
    H. W. Bode Network Analysis and Feedback Amplifier Design Van Nostrand, New York, 1945.Google Scholar
  15. [15]
    R. Tomovic, Sensitivity Analysis of Dynamic Systems, McGraw-Hill, New York, 1963.Google Scholar
  16. [16]
    R. Tomovic and M. Vukobratovic, General Sensitivity Theory, Elsevier, New York, 1972.MATHGoogle Scholar
  17. [17]
    J. B. Cruz, Jr., Ed., System Sensitivity Analysis, Dowden, Hutchingson and Ross, Stroudsburg, PA, 1973.Google Scholar
  18. [18]
    G. C. Verghese, I. J. Perez-Arriaga, and F. C. Scheweppe, “Selective modal analysis with applications to electric power systems, Part I and II,” IEEE Trans. Power Apparatus and Systems, PAS-101, pp. 3117–3134, Sept. 1982.CrossRefGoogle Scholar
  19. [19]
    M. J. Laufenberg and M. A. Pai, “A new approach to dynamic security assessment using trajectory sensitivities,” IEEE Trans. Power Systems, vol. 13, no. 3, pp. 953–958, Aug. 1998.CrossRefGoogle Scholar
  20. [20]
    I. A. Hiskens and M. Akke, “Analysis of the Nordel power grid disturbance of January 1, 1997 using trajectory sensitivities,” IEEE Trans. Power Systems, vol. 14, no. 3, pp. 987–994, Aug. 1999.CrossRefGoogle Scholar
  21. [21]
    I. A. Hiskens and M. A. Pai, “Trajectory sensitivity analysis of hybrid systems,” IEEE Trans. Circuits and Systems Part I: Fundamental Theory and Applications vol. 47, no. 2, pp. 204–220, Feb. 2000.CrossRefGoogle Scholar
  22. [22]
    T. B. Nguyen, M. A. Pai, and I. A. Hiskens, “Sensitivity approaches for direct computation of critical parameters in a power system,” Int. J. Electrical Power and Energy Systems, vol. 24, no. 5, pp. 337–343, 2002.CrossRefGoogle Scholar
  23. [23]
    P. W. Sauer and M. A. Pai, Power System Dynamics and Stability, Prentice-Hall, Upper Saddle River, NJ, 1998.Google Scholar
  24. [24]
    K. R. Padiyar, Power System Dynamics Stability and Control, BS Publications, Hyderabad, India, 2002.Google Scholar
  25. [25]
    N. G. Hingorani and L. Gyugyi, Understanding FACTS Concepts and Technology of Flexible AC Transmission Systems, IEEE Press, New York, 2000.Google Scholar
  26. [26]
    D. Gan, R. J. Thomas, and R Zimmerman, “Stability-constrained optimal power flow,” IEEE Trans. Power Systems, vol. 15, pp. 535–540, May 2000.CrossRefGoogle Scholar
  27. [27]
    D. Chaniotis, M. A. Pai, and I. A. Hiskens, “Sensitivity analysis of differential-algebraic systems using the GMRES method—Application to power systems,” Proc. IEEE International Symposium on Circuits and Systems pp.117–120, Sydney, Australia, May 2001.Google Scholar
  28. [28]
    C. Singh and I. A. Hiskens, “Direct assessment of protection operation and non-viable transients,” IEEE Trans. Power Systems, vol. 16, no. 3, pp. 427–434, Aug. 2001.CrossRefGoogle Scholar
  29. [29]
    F. Dobraca, M. A. Pai, and P. W. Sauer, “Relay margins as a tool for dynamical security analysis,” Int. J. Electrical Power and Energy Systems, vol. 12, no. 4, pp. 226–234, Oct. 1990.CrossRefGoogle Scholar
  30. [30]
    J. S. Thorp and A. G. Phadke, “Protecting power systems in the post-restructuring era,” IEEE Computer Applications in Power vol. 12, no. 1, pp. 33–37, Jan. 1999.CrossRefGoogle Scholar
  31. [31]
    P. Kundur, Power System Stability and Control McGraw-Hill, New York, 1994.Google Scholar
  32. [32]
    A. N. Michel and B. Hu, “Toward a stability theory of general hybrid dynamical systems,” Automatica vol. 35, pp. 371–384,1999.MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2003

Authors and Affiliations

  • M. A. Pai
  • Trong B. Nguyen

There are no affiliations available

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