Stability analysis of power systems using network decomposition and local gain analysis

Proceedings of IREP Symposium: Bulk Power System Dynamics and Control - IX Optimization, Security and Control of the Emerging Power Grid, IREP 2013

Volumn , Issue , 2013, Pages

  Anghel, Marian ^a   Anderson, James ^b   Papachristodoulou, Antonis ^b  

^a LOS ALAMOS NATIONAL LABORATORY   (United States)

^b UNIVERSITY OF OXFORD   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

DISTURBANCE ANALYSIS; EXTERNAL DISTURBANCES; LARGE-SCALE POWER SYSTEMS; NETWORK DECOMPOSITION; REGION OF ATTRACTION; STABILITY ANALYSIS; SUM-OF-SQUARES PROGRAMMING; TRANSIENT STABILITY ANALYSIS;

LYAPUNOV FUNCTIONS; OPTIMIZATION; SYSTEM THEORY;

ELECTRIC POWER DISTRIBUTION;

EID: 84890527678     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/IREP.2013.6629365     Document Type: Conference Paper

References (36)

1. F. N. Bailey, "The application of Lyapunovs second method to interconnected systems," J. SIAM Control, vol. 3, no. 3, pp. 443-462, 1966.
2. J. C. Willems, "Dissipative dynamical systems. II. Linear systems with quadratic supply rates," Arch. Rational Mech. Anal., vol. 45, pp. 352-393, 1972.
3. M. Araki, "Stability of large-scale nonlinear systems-quadraticorder theory of composite-system method using M-matrices," IEEE Transactions on Automatic Control, vol. 23, no. 2, pp. 129-142, 1978.
4. P. J. Moylan and D. J. Hill, "Stability criteria of large-scale systems," IEEE Transactions on Automatic Control, vol. 23, no. 2, pp. 143-149, 1978.
5. H. R. Pota and P. J. Moylan, "A new Lyapunov function for interconnected power system," IEEE Transactions on Automatic Control, vol. 37, no. 8, pp. 1192-1196, Aug. 1992.
6. A. I. Ze?cevíc and D. D. ? Siljak, Control of Complex Systems: Structural Constraints and Uncertainty, ser. Communications and Control Engineering. New York: Springer, 2010.
7. J. Anderson and A. Papachristodoulou, "A decomposition technique for nonlinear dynamical system analysis," IEEE Transactions on Automatic Control, vol. 57, pp. 1516-1521, June 2012.
8. C. C. Chu and H. D. Chiang, "Boundary property of the BCU method for power system transient stability assessment," in Proceedings of the IEEE International Symposium on Circuits and Systems (ISCAS), May 2010, pp. 3453-3456.
9. H. D. Chiang, Direct Methods for Stability Analysis of Electric Power Systems. New Jersey: Wiley, 2011.
10. M. Anghel, F. Milano, and A. Papachristodoulou, "Algorithmic construction of lyapunov functions for power stability analysis," IEEE Transactions on Circuits and Systems-I: Fundamental Theory and Applications, 2013, in press.
11. P. A. Parrilo, "Structured semidefinite programs and semialgebraic geometry methods in robustness and optimization," Ph. D. dissertation, Caltech, Pasadena, CA, 2000.
12. A. Papachristodoulou and S. Prajna, "On the construction of Lyapunov functions using the sum of squares decomposition," in Proceedings of the IEEE Conference on Decision and Control, Dec. 2002, pp. 3482-3487.
13. Z. J. Wloszek, R. Feeley, W. Tan, K. Sun, and A. Packard, Positive Polynomials in Control. Berlin, Heidelberg: Springer-Verlag, 2005, ch. Control Applications of Sum of Squares Programming, pp. 3-22.
14. A. Papachristodoulou and S. Prajna, Positive Polynomials in Control. Berlin Heidelberg: Springer-Verlag, 2005, ch. Analysis of nonpolynomial systems using the sum of squares decomposition, pp. 23-43.
15. S. Prajna, A. Papachristodoulou, P. Seiler, and P. A. Parrilo, Positive Polynomials in Control. Berlin, Heidelberg: Springer-Verlag, 2005, ch. SOSTOOLS and Its Control Applications, pp. 273-292.
16. A. Papachristodoulou and S. Prajna, "A tutorial on sum of squares techniques for systems analysis," in Proceedings of the 2005 American Control Conference, June 2005, pp. 2686-2700.
17. J. Bochnak, M. Coste, and M.-F. Roy, Real Algebraic Geometry. Berlin Heidelberg New York: Springer, 1998.
18. M. A. Pai, Power System Stability: Analysis by the Direct Method of Lyapunov. New York: North-Holland, 1981.
19. M. Ribbens-Pavella and F. J. Evans, "Direct methods for studying dynamics of large-scale electric power systems-A survey," Automatica, vol. 21, pp. 1-21, Jan. 1985.
20. R. Genesio, M. Tartaglia, and A. Vicino, "On the estimation of asymptotic stability regions: State of the art and new proposals," IEEE Transactions on Automatic Control, vol. 30, no. 8, pp. 747-755, Aug. 1985.
21. L. Vandenberghe and S. Boyd, "Semidefinite programming," SIAM Review, vol. 38, no. 1, pp. 49-95, Mar. 1996.
22. S. Prajna, A. Papachristodoulou, and P. A. Parrilo, SOSTOOLS A Sum of Squares Optimization Toolbox, User's Guide, 2002, available at http://www. cds. caltech. edu/sostools.
23. J. F. Sturm, "Using SeDuMi 1. 02, a MATLAB toolbox for optimization over symmetric cones," Optimization Methods and Software, vol. 11-12, pp. 625-653, Dec. 1999, software available at http://fewcal. kub. nl/sturm/software/sedumi. html.
24. K. G. Murty and S. N. Kabadi, "Some NP-complete problems in quadratic and nonlinear programming," Mathematical Programming, vol. 39, no. 2, pp. 117-129, June 1987.
25. G. Karypis and V. Kumar, "A fast and high quality multilevel scheme for partitioning irregular graphs," SIAM J. Sci. Comput., vol. 20, no. 1, pp. 359-392, 1998.
26. Z. W. Jarvis-Wloszek, "Lyapunov based analysis and controller synthesis for polynomial systems using sum-of-squares optimization," Ph. D. dissertation, University of California, Berkeley, CA, 2003.
27. W. Tan, "Nonlinear control analysis and synthesis using sum-of-squares programming," Ph. D. dissertation, University of California, Berkeley, CA, 2006.
28. M. Ribens-Pavella and P. G. Murthy, Transient Stability of Power Systems: Theory and Practice. New York: John Wiley & Sons, 1994.
29. R. Ortega, M. Galaz, A. Astolfi, Y. Sun, and T. Shen, "Transient stabilization of multimachine power systems with nontrivial transfer conductances," IEEE Transactions on Automatic Control, vol. 50, pp. 60-75, Jan. 2005.
30. G. Chesi, "Estimating the domain of attraction for non-polynomial systems via LMI optimizations," Automatica, vol. 45, pp. 1536-1541, June 2009.
31. N. G. Bretas and L. F. C. Alberto, "Lyapunov function for power systems with transfer conductances: Extension of the invariance principle," IEEE Transactions on Power Systems, vol. 18, no. 2, pp. 769-777, May 2003.
32. D. J. Hill and A. R. Bergen, "Stability analysis of multimachine power networks with linear frequency dependent loads," IEEE Transactions on Circuits and Systems-I: Fundamental Theory and Applications, vol. 29, no. 12, pp. 840-848, Dec. 1982.
33. N. A. Tsolas, A. Arapostathis, and P. P. Varaiya, "A structure preserving energy function for power system transient stability analysis," IEEE Transactions on Circuits and Systems-I: Fundamental Theory and Applications, vol. 32, no. 10, pp. 1041-1049, Oct. 1985.
34. A. R. Bergen, D. J. Hill, and C. L. de Marcot, "Lyapunov function for multimachine power systems with generator flux decay and voltage dependent loads," International Journal of Electrical Power and Energy Systems, vol. 8, pp. 2-10, Jan. 1986.
35. R. J. Davy and I. A. Hiskens, "Lyapunov functions for multimachine power systems with dynamic loads," IEEE Transactions on Circuits and Systems-I: Fundamental Theory and Applications, vol. 44, pp. 796-812, Sep. 1997.
36. C. C. Chu and H. D. Chiang, "Constructing analytical energy functions for network-preserving power system models," Circuits Systems and Signal Processing, vol. 24, pp. 363-383, Aug. 2005.