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Nonlinear dynamic analysis of a single-machine infinite-bus power system. (English) Zbl 07139353
Summary: This study focuses on the nonlinear dynamic characteristics of a single-machine infinite-bus (SMIB) power system under a periodic load disturbance. The qualitative behavior of this system is described by the well-known ”swing equation”, which is a nonlinear second-order differential equation. Compared with the existing results, the generator damping in this paper, which is more close to the practical engineering, is related to the state variables of this system. In addition, Melnikov’s method is applied to obtain the threshold for the onset of chaos. The efficiency of the criteria for chaotic motion is verified via numerical simulations. Comparisons between the theoretical analysis and numerical simulation show good agreements. The results in this paper will contribute a better understanding of the nonlinear dynamic behaviors of the SMIB power system.
34C28 Complex behavior and chaotic systems of ordinary differential equations
70K55 Transition to stochasticity (chaotic behavior) for nonlinear problems in mechanics
Full Text: DOI
[1] Lu, Q.; Sun, Y. Z., Nonlinear Control of Power System (1993), China Science Press: China Science Press Beijing
[2] Gerardo, E. P.; Paul, M. O.; Arnau, D. C.; Jaime, M., Output-feed back IDA stabilisation of an SMIB system using a TCSC, Int. J. Control, 83, 12, 2471-2482 (2010)
[3] Shi, J.; Tang, Y.; Dai, T.; Ren, L.; Li, J.; Cheng, S., Determination of SMES capacity to enhance the dynamic stability of power system, Physica C, 470, 20, 1707-1710 (2010)
[4] Manjarekar, N. S.; Banavar, R. N.; Ortega, R., Application of interconnection and damping assignment to the stabilization of a synchronous generator with a controllable series capacitor, Int. J. Electr. Power Energy Syst., 32, 1, 63-70 (2010)
[5] Chendur Kumaran, R.; Venkatesh, T. G.; Swarup, K. S., Voltage stability - case study of saddle node bifurcation with stochastic load dynamics, Int. J. Electr. Power Energy Syst., 33, 8, 1384-1388 (2011)
[6] Duan, X. Z.; Wen, J. Y.; Cheng, S. J., Bifurcation analysis for an SMIB power system with series capacitor compensation associated with sub-synchronous resonance, Sci. China Ser. E, 52, 2, 436-441 (2009)
[7] Zhu, W.; Mohler, R. R., Hopf bifurcations in a SMIB power system with SSR, IEEE Trans. Power Syst., 11, 3, 1579-1584 (1996)
[8] Wei, D. Q.; Luo, X. S., Noise-induced chaos in single-machine infinite-bus power systems, Europhys. Lett., 86, 5 (2009)
[9] Wei, D. Q.; Zhang, Bo.; Qiu, D. Y.; Luo, X. S., Effect of noise on erosion of safe basin in power system, Nonlinear Dyn., 61, 477-482 (2010)
[10] Chen, H. K.; Lin, T. N.; Chen, J. H., Dynamic analysis, controlling chaos and chaotification of a SMIB power system, Chaos Solitons Fractals, 24, 1307-1315 (2005)
[11] Alberto, L. F.C.; Bretas, N. G., Application of Melnikovs method for computing heteroclinic orbits in a classical SMIB power system model, IEEE Trans. Circuits Syst. I, 47, 7, 1085-1089 (2000)
[12] Zhang, W. N.; Zhang, W. D., Chaotic oscillation of a nonlinear power system, Appl. Math. Mech., 20, 10, 1175-1183 (1999)
[13] Yuan, B.; Ma, W. X., Chaos in the almost periodic forcing electrical power systems, Autom. Electr. Power Syst., 18, 5, 26-30 (1994), (in Chinese)
[14] Chen, X. W.; Zhang, W. N.; Zhang, W. D., Chaotic and subharmonic oscillations of a nonlinear power system, IEEE Trans. Circuits Syst. II, 52, 12, 811-815 (2005)
[15] Nayfeh, M. A.; Hamdan, A. M.A.; Nayfeh, A. H., Chaos and instability in a power system: subharmonic-resonant case, Nonlinear Dyn., 2, 53-72 (1991)
[16] Nayfeh, M. A.; Hamdan, A. M.A.; Nayfeh, A. H., Chaos and instability in a power system: primary resonant case, Nonlinear Dyn., 1, 313-339 (1990)
[17] Abed, E. H.; Varalya, P. P., Nonlinear oscillations in power systems, Int. J. Electr. Power Energy Syst., 6, 1, 37-43 (1984)
[18] Liwschitz, M. M., Positive and negative damping in synchronous machines, AIEE Trans., 60, 210-213 (1941)
[19] Guckenheimer, J.; Holmes, P., Nonlinear Oscillations, Dynamical Systems, and Bifurcations Vector Fields (1983), Springer-Verlag: Springer-Verlag New York
[20] Nusse, H. E.; Yorke, J. A., Dynamics: Numerical Explorations (1997), Springer-Verlag: Springer-Verlag NewYork
[21] Wolf, A.; Swift, J. B.; Swinney, H. L.; Vastano, J. A., Determining Lyapunov exponents from a time series, Phys. D, 16, 285-317 (1985)
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