Direct Stability Analysis of Electric Power Systems Using Energy Functions: Theory, Applications, and Perspective

Proceedings of the IEEE

Volumn 83, Issue 11, 1995, Pages 1497-1529

  Chiang, Hsiao Dong ^a   Chu, Chia Chi ^a   Cauley, Gerry ^b  

^a School of Electrical Engineering Cornell University ^*  (United States)

^b ELECTRIC POWER RESEARCH INSTITUTE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; COMPUTATIONAL METHODS; ELECTRIC LOADS; MATHEMATICAL MODELS; SYSTEM STABILITY; SYSTEMS ENGINEERING; TRANSIENTS;

ENERGY FUNCTIONS; NETWORK PRESERVING POWER SYSTEM; NETWORK REDUCTION POWER SYSTEM; ON LINE TRANSIENT STABILITY ASSESSMENTS;

ELECTRIC POWER SYSTEMS;

EID: 0029403498     PISSN: 00189219     EISSN: 15582256     Source Type: Journal    
DOI: 10.1109/5.481632     Document Type: Article

References (90)

1. R. Abraham, J. E. Marsden, and T. Ratiu, “Manifolds, tensor analysis, and applications,” in Applied Mathematical Sciences, vol. 75. New York: Springer-Verlag, 1988.
2. M. M. Abu-Elnaga, M. A. El-Kady, and R. D. Findlay, “Sparse formulation of the transient energy function method using sparse formulation to large-scale power systems,” IEEE Trans. Power Syst., vol. 3, pp. 1648-1654, Dec. 1988.
3. M. M. Abu-Elnaga, M. A. El-Kady, and R. D. Findlay, “Stability assessment of highly stressed power systems using sparse formulation of the direct method,” IEEE Trans. Power Syst., vol. 3, pp. 1655-1661, Dec. 1988.
4. P. M. Anderson and A. A. Fouad, Power System Control and Stability. New York: IEEE Press, 1994.
5. A. Arapostathis, S. S. Sastry, and P. Varaiya, “Global analysis of swing dynamics,” IEEE Trans. Circ. and Syst., vol. CAS-29, pp. 673-679, 1982.
6. D. K. Arrowsmith and C. M. Place, An Introduction to Dynamical Systems. Cambridge, UK: Cambridge Univ. Press, 1990.
7. T. Athay, R. Podmore, and S. Virmani, “A practical method for the direct analysis of transient stability,” IEEE Trans. Power Apparatus and Syst., vol. PAS-98, no. 2, pp. 573-584, 1979.
8. P. D. Aylett, “The energy integral-criterion of transient stability limits of power systems,” Proc. IEE, vol. 105c, no. 8, pp. 527-536, Sept. 1958.
9. A. R. Bergen and D. J. Hill, “A structure preserving model for power system stability analysis,” IEEE Trans. Power Apparatus and Syst., vol. PAS-100, pp. 25-35, 1981.
10. A. R. Bergen, D. J. Hill, and C. L. De Marco, “Lyapunov function for multimachine power systems with generator flux decay and voltage dependent loads,” Int. J. Electrical Power and Energy Syst., vol. 8, no. 1, pp. 2-10, 1986.
11. K. E. Brenan, S. L. Campbell, and L. R. Petzold, Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations. Amsterdam: Elsevier, 1989.
12. U. Di Caprio, “Accounting for transfer conductance effects in Lyapunov transient stability analysis of a multimachine power system,” Int. J. Electrical Power and Energy Syst., vol. 8, no. 1, pp. 27-41, 1986.
13. H. D. Chiang, “Study of the existence of energy functions for power systems with losses,” IEEE Trans. Circ. and Syst., vol. 36, pp. 1423-1429, Nov. 1989.
14. H. D. Chiang, “Analytical results on the direct methods for power system transient stability analysis,” in Control and Dynamic Systems: Advances in Theory and Application. New York: Academic, 1991, vol. 43, pp. 275-334.
15. H. D. Chiang, “The BCU method for direct stability analysis of electric power systems: Theory and applications,” J. Chow, P. V. Kokotovic, and R. J. Thomas, Eds., in Systems Control Theory for Power Systems, vol. 64 of IMA Volumes in Mathematics and Its Applications. New York: Springer-Verlag, 1995, pp. 39-94.
16. H. D. Chiang and C. C. Chu, “Theoretical foundation of the BCU method for direct stability analysis of network-reduction power system model with small transfer conductances,” IEEE Trans. on Circuits and Systems-I: Fundamental Theory and Applications, vol. CAS-42, no. 5, pp. 252-265, May 1995.
17. H. D. Chiang and L. Fekih-Ahmed, “On the direct method for transient stability analysis of power system structure preserving models,” in IEEE Int. Symp. on Circ. and Syst., 1992, pp. 2545-2548.
18. H. D. Chiang, M. W. Hirsch, and F. F. Wu, “Stability region of nonlinear autonomous dynamical systems,” IEEE Trans. Auto. Control, vol. 33, pp. 16-27, Jan. 1988.
19. H. D. Chiang and J. S. Thorp, “The closest unstable equilibrium point method for power system dynamic security assessment,” IEEE Trans. Circ. and Syst., vol. 36, pp. 1187-1120, Sept. 1989.
20. H. D. Chiang, F. F. Wu, and P. P. Varaiya, “Foundations of direct methods for power system transient stability analysis,” IEEE Trans. Circ. and Syst., vol. CAS-34, pp. 160-173, Feb. 1987.
21. H. D. Chiang, F. F. Wu, and P. P. Varaiya, “Foundations of the potential energy boundary surface method for power system transient stability analysis,” IEEE Trans. Circ. and Syst., vol. 35, pp. 712-728, June 1988.
22. H. D. Chiang, F. F. Wu, and P. P. Varaiya, “A BCU method for direct analysis of power system transient stability,” IEEE Trans. Power Syst., vol. 9, pp. 1194-2000, Aug. 1994.
23. C. C. Chu, “Transient dynamics of electric power systems: Direct stability assessment and chaotic motions,” Ph.D. dissertation, Cornell Univ., Ithaca, NY, Jan. 1996.
24. C. C. Chu and H. D. Chiang, “Analytical energy functions for electric power systems with detailed generator and load models: Framework and developments,” to be published in IEEE Trans. Circ. and Syst.-I: Fund. Theory and Applic.
25. L. O. Chua and A. C. Deng, “Impasse points-part ii: Analytic aspects,” Int. J. Circuit Theory, vol. 17, no. 3, pp. 271-289, 1989.
26. CIGRE Task Force Rep., “Assessment of practical fast transient stability methods,” Convener S. Geeves, June 1992.
27. R. H. Craven and M. R. Michael, “Load characteristic measurements and representation of loads in the dynamic simulation of the Queensland power system,” in 1983 CIGRE and IFAC Symp., Florence, 1983, pp. 39-83.
28. C. L. De Marco and A. R. Bergen, “Application of singular perturbation techniques to power system transient stability analysis,” in IEEE Int. Symp. on Circ. and Syst., 1984, pp. 597-601.
29. C. L. De Marco and A. R. Bergen, “A security measure for random load disturbances in nonlinear power system models,” IEEE Trans. Circ. and Syst., vol. CAS-34, pp. 1546-1557, 1987.
30. A. H. El-Abiad and K. Nagappan, “Transient stability regions for multi-machine power systems,” IEEE Trans. Power Apparatus and Syst., vol. PAS-85, pp. 169-179, 1966.
31. M. A. El-kady et al., “Dynamic security assessment utilizing the transient energy function method,” IEEE Trans. Power Syst., vol. PS-1, pp. 284-291, Mar. 1986.
32. D. N. Ewart, “Whys and wherefores of power system blackouts,” IEEE Spectrum, vol. 15, pp. 36-41, 1978.
33. L. Fekih-Ahmed, “Theoretical results on the stability regions and bifurcations of nonlinear dynamical systems and their applications to electric power system analysis,” Ph.D. dissertation, Cornell Univ., Ithaca, NY, Aug. 1991.
34. R. Fischl, F. Mercede, F. F. Wu, and H. D. Chiang, “Comparison of dynamic security indices based on direct methods,” Int. J. Electrical Power and Energy Syst., vol. 10, no. 4, pp. 210-232, 1988.
35. A. A. Fouad and S. E. Stanton, “Transient stability of a multimachine power systems. Part i: Investigation of system trajectories,” IEEE Trans. Power Apparatus and Syst., vol. PAS-100, pp. 3408-3414, July 1981.
36. A. A. Fouad and V. Vittal, “The transient energy function method,” Int. J. Electrical Power and Energy Syst., vol. 10, no. 4, pp. 233-246, 1988.
37. A. A. Fouad and V. Vittal, Power System Transient Stability Analysis: Using the Transient Energy Function Method. Englewood Cliffs, NJ: Prentice-Hall, 1991.
38. G. E. Gless, “Direct method of Lyapunov applied to transient power system stability,” IEEE Trans. Power Apparatus and Syst., vol. PAS-85, pp. 164-179, 1966.
39. J. Guckenheimer and P. Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, Applied Mathematical Sciences Series No. 42. New York: Springer-Verlag, 1983.
40. U. Guadra, “A general Liapunov function for multi-machine power systems with transfer conductances,” Int. J. Control, vol. 21, no. 2, pp. 333-343, 1975.
41. D. J. Hill and I. M. Y. Mareels, “Stability theory for differential/algebraic systems with application to power systems,” IEEE Trans. Circ. and Syst., vol. 37, pp. 1416-1422, 1990.
42. M. Hirsch and S. Smale, Differential Equations, Dynamical Systems and Linear Algebra. New York: Academic, 1974.
43. I. A. Hiskens and D. J. Hill, “Energy functions, transient stability and voltage behavior in power systems with nonlinear loads,” IEEE Trans. Power Syst., vol. 4, pp. 1525-1533, 1989.
44. N. Kakimoto, Y. Ohsawa, and M. Hayashi, “Transient stability analysis of electric power system via lure-type Lyapunov function,” Trans. IEE of Japan, vol. 98, pp. 566-604, 1978.
45. H. K. Khalil, Nonlinear Systems. New York: Macmillan, 1992.
46. J. Kim, “On-line transient stability calculator,” Final Rep. RP2206-1, EPRI, Palo Alto, CA, Mar. 1994.
47. D. H. Kuo and A. Bose, “A generation rescheduling method to increase the dynamics security of power systems,” IEEE Trans. Power Syst., vol. 10, pp. 68-76, Jan. 1995.
48. H. G. Kwatny, L. Y. Bahar, and A. K. Pasrija, “Energy-like Lyapunov functions for power system stability analysis,” IEEE Trans. Circ. and Syst., vol. CAS-32, pp. 1140-1149, Nov. 1985.
49. A. Llamas et al., “Clarifications of the BCU method for transient stability analysis,” IEEE Trans. Power Syst., vol. 10, pp. 210-219, Jan. 1995.
50. W. W. Lemmon, K. R. C. Mamandur, and W. R. Barcelo, “Transient stability prediction and control in real-time by quasi-unstable equilibrium point (QUEP) methods,” IEEE Trans. Power Syst., vol. 4, pp. 44-52, Jan. 1989.
51. P. C. Magnusson, “Transient energy method of calculating stability,” AIEE Trans., vol. 66, pp. 747-755, 1947.
52. G. A. Maria, C. Tang, and J. Kim, “Hybrid transient stability analysis,” IEEE Trans. Power Syst., vol. 5, pp. 384-393, Feb. 1990.
53. H. Miyagi and A. R. Bergen, “Stability studies of multimachine power systems with the effects of automatic voltage regulators,” IEEE Trans. Auto. Contr., vol. AC-31, pp. 210-215, 1986.
54. S. Mokhtari, “Analytical methods for contingency selection and ranking for dynamic security assessment,” Final Rep. RP3103-3, EPRI, Palo Alto, CA, May 1994.
55. N. Narasimhamurthi, “On the existence of energy functions for power systems with transmission losses,” IEEE Trans. on Circuits and Systems, vol. CAS-31, pp. 199-203, 1984.
56. N. Narasimhamurthi and M. R. Musavi, “A general energy function for transient stability analysis of power systems,” IEEE Trans. Circ. and Syst., vol. CAS-31, pp. 637-645, 1984.
57. R. E. J. O'Malley, Singular Perturbation Methods for Ordinary Differential Equations, vol. 89, Applied Mathematical Sciences, Springer-Verlag, 1991.
58. K. R. Padiyar and K. K. Ghosh, “Direct stability evaluation of power systems with detailed generator models using structure-preserving energy functions,” Int. J. Electrical Power and Syst., vol. 11, no. 1, pp. 47-56, 1989.
59. M. A. Pai, Power System Stability. Amsterdam: North-Holland, 1981.
60. M. A. Pai, Energy Function Analysis for Power System Stability. Boston: Kluwer Academic Publishers, 1989.
61. M. A. Pai, P. W. Sauer, and K. D. Demaree, “Direct methods of stability analysis in dynamic security assessment,” in Proc. 9th IFAC World Congress, Budapest, July 1984.
62. J. Palis and W. De Melo, Geometric Theory of Dynamical Systems: An Introduction. New York: Spring-Verlag, 1982.
63. F. S. Prabhakara and A. H. El-Abiad, “A simplified determination of stability regions for Lyapunov method,” IEEE Trans. Power Apparatus and Syst., vol. PAS-94, pp. 672-689, 1975.
64. F. A. Rahimi, “Evaluation of transient energy function method software for dynamic security analysis,” Final Rep. RP 4000-18, EPRI, Palo Alto, CA, Dec. 1990.
65. F. A. Rahimi, M. G. Lauby, J. N. Wrubel, and K. L. Lee, “Evaluation of the transient energy function method for on-line dynamic security assessment,” IEEE Trans. Power Syst., vol. 8, pp. 497-507, 1993.
66. IEEE Committee Rep., “Excitation systems models for power system studies,” IEEE Trans. Power Apparatus and Syst., vol. PAS-97, pp. 494-509, 1981.
67. IEEE Committee Rep., “Transient stability test systems for direct stability methods,” IEEE Trans. Power Syst., vol. 7, pp. 37-43, 1992.
68. M. Ribbens-Pavella and F. J. Evans, “Direct methods for studying dynamics of large-scale electric power systems—A survey,” Automatica, vol. 21, no. 1, pp. 1-21, 1985.
69. M. Ribbens-Pavella and P. G. Murthy, Transient Stability of Power Systems: Theory and Practice. New York: Wiley, 1994.
70. M. Ribbens-Pavella, P. G. Murthy, and J. L. Horward, “The acceleration approach to practical transient stability domain estimation in power systems,” in IEEE Control and Decision Conf., San Diego, CA, Dec. 1981, vol. 1, pp. 471-476.
71. C. Robinson, Dynamical Systems: Stability, Symbolic Dynamics, and Chaos. Boca Raton, FL: CRC, 1994.
72. H. Sasaki, “An approximate incorporation of fields flux decay into transient stability analysis of multi-machine power systems by the second method of Lyapunov,” IEEE Trans. Power Apparatus and Syst., vol. PAS-98, pp. 473-483, Feb. 1979.
73. S. Sastry and C. A. Desoer, “Jump behavior of circuits and systems,” IEEE Trans. Circ. and Syst., vol. CAS-28, pp. 1109-1124, Dec. 1981.
74. S. Sastry and P. Varaiya, “Hierarchical stability and alert state steering control of interconnected power systems,” IEEE Trans. Circ. and Syst., vol. CAS-27, pp. 1102-1112, 1980.
75. P. W. Sauer et al., “Trajectory approximation for direct energy methods that use sustained faults with detailed power system models,” IEEE Trans. Power Syst., vol. 4, pp. 499-506, Feb. 1989.
76. P. W. Sauer, K. D. Demaree, and M. A. Pai, “Stability limited load supply and interchange capability,” IEEE Trans. Power Apparatus and Syst., vol. PAS-102, pp. 3637-3643, 1983.
77. C. K. Tang, C. E. Graham, M. El-Kady, and R. T. H. Alden, “Transient stability index from conventional time domain simulation,” IEEE Trans. Power Systems, vol. 9, pp. 1524-1530, Mar. 1994.
78. N. A. Tsolas, A. Arapostathis, and P. P. Varaiya, “A structure preserving energy function for power system transient stability analysis,” IEEE Trans. Circ. and Syst., vol. CAS-32, pp. 1041-1049, 1985.
79. P. P. Varaiya, F. F. Wu, and R.-L. Chen, “Direct methods for transient stability analysis of power systems: Recent results,” Proc. IEEE, vol. 73, pp. 1703-1715, 1985.
80. V. Venkatasubramanian, H. Schättler, and J. Zaborszky, “A taxonomy of the dynamics of the large power system with emphasis on its voltage stability,” in Proc., Bulk Power System Voltage Phenomena II: Voltage Stability and Security: An International Seminar, Deep Lake, MD, 1991, pp. 9-52.
81. V. Venkatasubramanian, H. Schättler, and J. Zaborszky, “Voltage dynamics: Study of a generator with voltage control, transmission, and matched MW load,” IEEE Trans. Autom. Contr., vol. 37, pp. 1717-1732, Nov. 1992.
82. V. Venkatasubramanian, H. Schättler, and J. Zaborszky, “Feasibility regions and bifurcation boundaries in constrained systems such as the large power system,” to be published in IEEE Trans. Auto. Control.
83. M. Vidyasagar, Nonlinear Systems Analysis, Networks Series. Englewood Cliffs, NJ: Prentice-Hall, 1978.
84. S. Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos, vol. 2 of Texts in Applied Mathematics. New York: Springer-Verlag.
85. J. L. Willems, “Direct methods for transient stability studies in power system analysis,” IEEE Trans. Auto. Contr., vol. AC-16, pp. 332-341, Apr. 1971.
86. Y. Xue, Th. Van Custem, and M. Ribbens-Pavella, “Real-time analytic sensitivity method for transient security assessment and prevent control,” Proc. IEEE, Pt. C, vol. 135, pp. 107-117, Mar. 1988.
87. Y. Xue, Th. Van Custem, and M. Ribbens-Pavella, “Extended equal area criterion justifications, generalizations, applications,” IEEE Trans. Power Syst., vol. 4, pp. 44-52, Jan. 1989.
88. Y. Xue et al., “Extended equal area criterion revised,” IEEE Trans. Power Syst., vol. PS-7, pp. 1012-1022, 1992.
89. H. Yee and B. D. Spalding, “Transient stability analysis of multimachine power systems by the method of hyperplanes,” IEEE Trans. Power Apparatus and Syst., vol. PAS-96, pp. 276-284, Jan. 1977.
90. J. Zaborszky, G. Huang, B. Zheng, and T. C. Leung, “On the phase portrait of a class of large nonlinear dynamic systems such as the power system,” IEEE Trans. Auto. Contr., vol. 33, pp. 4-15, Jan. 1988.