The credible regions on the approximate stability boundaries of nonlinear dynamic systems

IEEE Transactions on Automatic Control

Volumn 52, Issue 8, 2007, Pages 1486-1491

  Min, Yong ^a   Chen, Lei ^a   Hou, Kaiyuan ^a,b   Song, Yunghua ^c  

^a TSINGHUA UNIVERSITY   (China)

^b Northeast China Grid Company Limited   (China)

^c UNIVERSITY OF LIVERPOOL   (United Kingdom)

Author keywords

Credible region; Invariant manifold; Stability boundary; Stability region; Stable manifold

Indexed keywords

APPROXIMATION THEORY; DYNAMICAL SYSTEMS; INVARIANCE; STABILITY;

CHARACTERISTIC INVARIANT MANIFOLD; CREDIBLE REGION; STABILITY BOUNDARY;

NONLINEAR SYSTEMS;

EID: 34548247236     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2007.902759     Document Type: Article

References (14)

1. H. D. Chiang, M. W. Hirsch, and F. F. Wu, "Stability region of nonlinear autonomous dynamical system," IEEE Trans. Autom. Control vol. 33, no. 1, pp. 16-27, Jan. 1988.
2. J. Zaborzsky, 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. Autom. Control, vol. 33, no. 1, pp. 4-15, Jan. 1988.
3. H. D. Chiang, C. C. Chu, and G. Cauley, "Direct stability analysis of electric power systems using energy functions: Theory, applications, and perspective," in Proc. IEEE, Nov. 1995, vol. 83, no. 11, pp. 1497-1529.
4. S. Ushiki, "Analytic expressions of unstable manifolds," Proc. Jpn Acad. Ser. A.-Math. Sci., vol. 56, no. 6, pp. 239-244, 1980.
5. F. M. A. Salam, A. Araposthathis, and P. P. Varaiya, "Analytic expressions for the unstable manifold at equilibrium points in dynamical systems of differential equations," in Proc. 22nd IEEE Conf. Decision Control, Dec. 1983, vol. 3, pp. 1389-1392.
6. S. Saha, A. A. Fouad, W. H. Kliemann, and V. Vittal, "Stability boundary approximation of a power system using the real normal form of vector fields," IEEE Trans. Power Syst., vol. 12, no. 2, pp. 797-802, 1997.
7. R. Qi, D. Cook, W. Kliemann, and V. Vittal, "Visualization of stable manifolds and multidimensional surfaces in the analysis of power system dynamics," J. Nonlin. Sci., vol. 10, pp. 175-195, 2000.
8. Z. Jing, Z. Jia, and Y. Gao, "Research of the stability region in a power system," IEEE Trans. Circuits Syst. I, Fundam. Theory Appl. vol. 50, no. 2, pp. 298-304, Feb. 2003.
9. P. A. Cook and A. M. Eskicioglu, "Transient stability analysis of electric power systems by the method of tangent hypersurfaces," in Inst. Elect. Eng. Proc.-Gener. Transm. Distrib., Jul. 1983, vol. 130, no. 4, pp. 183-193.
10. J. Zaborzsky, G. Huang, B. Zheng, and T. Leung, "New results on stability monitoring on the large electric power systems," in Proc. 26th IEEE Conf. Decision Control, 1987, pp. 30-40.
11. M. Djukanovic, D. Sobajic, and Y.-H. Pao, "Neural-net based tangent hypersurfaces for transient security assessment of electric power systems," Int. J. Electr. Power Energy Syst., vol. 16, no. 6, pp. 399-408, 1994.
12. V. Venkatasubramanian and W. Ji, "Numerical approximation of (n - 1)-dimensional stable manifolds in large systems such as the power system," Automatica, vol. 33, no. 10, pp. 1877-1883, Oct. 1997.
13. D. Cheng, J. Ma, Q. Lu, and S. Mei, "Quadratic form of stable submanifold for power systems," Int. J. Robust Nonlin. Contr., vol. 14, pp. 773-788, 2004.
14. N. Kazantzis, "Singular PDEs and the problem of finding invariant manifold for nonlinear dynamical system," Phys. Lett. A., vol. 272, no. 4, pp. 257-263, Jul. 2000.