Uniform approach for stability analysis of fast subsystem of two-time scale nonlinear systems

International Journal of Bifurcation and Chaos

Volumn 17, Issue 11, 2007, Pages 4195-4203

  Alberto, Luís F C ^a   Chiang, Hsiao Dong ^b  

^a UNIVERSITY OF SÃO PAULO   (Brazil)

^b 328 Rhodes Hall ^*  (United States)

Author keywords

Stability analysis; Two time scale nonlinear systems

Indexed keywords

HEURISTIC METHODS; SMALL POWER PLANTS; SYSTEM STABILITY; UNCERTAINTY ANALYSIS;

POWER SYSTEM STABILITY ANALYSIS; STABILITY ANALYSIS; TWO-TIME SCALE NONLINEAR SYSTEMS;

NONLINEAR SYSTEMS;

EID: 39449123631     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218127407019731     Document Type: Article

References (27)

1. Al-Ashoor, R. A. & Khorasani, K. [1999] "A decentralized indirect adaptive control for a class of two-time-scale nonlinear systems with application to flexible-joint manipulators," IEEE Trans. Industr. Electron. 46, 1019-1029.
2. Alberto, L. F. C. & Chiang, H.-D. [2006] "Two-time-scale energy functions for stability analysis of non-linear systems," submitted to IEEE Trans. Circuits Syst.-I.
3. Athay, T., Podmore, R. & Virmani, S. [1979] "A practical method for direct analysis of transient stability," IEEE Trans. Power Appar. Syst. 98, 573-584.
4. Bretas, N. G. & Alberto, L. F. C. [2003] "Lyapunov function for power systems with transfer conductances: Extension of the invariance principle," IEEE Trans. Power Syst. 18, 769-777.
5. Chiang, H. D. [1989] "Study of the existence of energy functions for power systems with losses," IEEE Trans. Circuits Syst. 36, 1423-1429.
6. Chiang, H.-D., Hirsch, M. W. & Wu, F. F. [1988a] "Stability region of nonlinear autonomous dynamical systems," IEEE Trans. Autom. Contr. 33, 16-27.
7. Chiang, H.-D., Wu, F. F. & Varaiya, P. P. [1988b] "Foundations of the potential energy boundary surface method for power system transient stability analysis," IEEE Trans. Circuits Syst. 35, 712-728.
8. Chiang, H.-D., Wu, F. F. & Varaiya, P. P. [1994] "A BCU method for direct analysis of power systems transient stability," IEEE Trans. Power Syst. 9, 1194-1208.
9. Chiang, H.-D., Chu, C. C. & Cauley, G. [1995] "Direct stability analysis of electric power systems using energy functions: Theory, applications and perspectives," Proc. IEEE 83, 1497-1529.
10. Chiang, H.-D. [1999] "Power system stability," in Wiley Encyclopedia of Electrical and Electronics Engineering, ed. Webster, J. G. (John Wiley & Sons, NY), pp. 104-137.
11. Chow, J. H., Winkelman, J. R., Pai, M. A. & Sawer, P. W. [1990] "Singular perturbation analysis of large-scale power systems," Electr. Power Energy Syst. 12, 117-126.
12. Davy, R. J. & Hiskens, I. A. [1997] "Lyapunov functions for multimachine power systems with dynamic loads," IEEE Trans. Circuits Syst-I: Fund. Th. Appl. 44, 796-812.
13. Fouad, A. A. et al. [1989] "Direct transient stability assessment with excitation control," IEEE Trans. Power Syst. 4, 75-82.
14. Gameiro, M. F. & Rodrigues, H. M. [2001] "Applications of robust synchronization to communication systems," Appl. Anal. 79, 21-45.
15. Guckenheimer, J. & Holmes, P. [1993] Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields (Springer-Verlag, NY).
16. Gusia, S., Labrique, F., Grenier, D. & Buyse, H. [2003] "'Two time scale global dynamical modeling of power electronic systems," Math. Comput. Simul. 63, 225-236.
17. Hiskens, I. A. & Davy, R. J. [1996] "Lyapunov function analysis of power systems with dynamic loads," Proc. 35th IEEE Conf. Decision and Control, Vol. 4, pp. 3870-3875.
18. Hiskens, I. A., Pal, M. A. & Nguyen, T. B. [2000] "Bounding uncertainty in power system dynamic simulations," Proc. IEEE Power Engin. Soc. Winter Meet 2, 1533-1537.
19. Khorasani, K. & Pai, M. A [1988] "Two time scale decomposition and stability analysis of power systems," IEE Proc. 135, 205-212.
20. Ramdani, S., Rosseto, B., Chua, L. O. & Lozi, R. [2000] "Slow manifolds of some chaotic systems with applications to laser systems," Int. J. Bifurcation and Chaos 10, 2729-2744.
21. Rodrigues, H. M., Alberto, L. F. C. & Bretas, N. G. [2001] "Uniform invariance principle and synchronization. Robustness with respect to parameter variation," J. Diff. Eqs. 169, 228-254.
22. Saberi, A. & Khalil, H. [1984] "Quadratic-type Lyapunov functions for singularly perturbed systems," IEEE Trans. Autom. Contr. AC-29, 542-550.
23. Sasaki, H. [1979] "An approximate incorporation of field flux decay into transient stability analysis of multimachine power systems by the second method of Lyapunov," IEEE Trans. Power Appar. Syst. 98, 473-183.
24. Sauer, P. W., Behera, A. K., Pai, M. A., Winkelman, J. R. & Chow, J. H. [1989] "Trajectory approximations for direct energy methods that use sustained faults with detailed power system models," IEEE Trans. Power Syst. 4, 499-506.
25. Siddiqee, M. W. [1968] "Transient stability of an a.c. generator by Lyapunov's direct method," Int. J. Contr. 8, 131-144.
26. Susuki, Y., Hikihara, T. & Chiang, H.-D. [2004] "Stability boundaries analysis of electric power system with D.C. transmission based on differential-algebraic equation system," IEICE Trans. Fund. Electron. Commun. Comput. Sci. E87-A, 2339-2346.
27. Ueda, Y., Hirano, M., Ohta, H. & Abraham, R. H. [2004] "Attractor and basin portraits of a double swing power system," Int. J. Bifurcation and Chaos 14, 3135-3152.