Abstract
In this paper, an introduction to the bifurcation theory and its applicability to the study of sub-synchronous resonance (SSR) phenomenon in power system are presented. The continuation and bifurcation analysis software AUTO97 is adopted to investigate SSR for a single-machine-infinite-bus power system with series capacitor compensation. The investigation results show that SSR is the result of unstable limit cycle after bifurcation. When the system exhibits SSR, some complex periodical orbit bifurcations, such as torus bifurcation and periodical fold bifurcation, may happen with the variation of limit cycle. Furthermore, the initial operation condition may greatly influence the ultimate state of the system. The time-domain simulation is carried out to verify the effectiveness of the results obtained from the bifurcation analysis.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
IEEE Committee Report by Subsynchronous Resonance Working Group of the System Dynamic Performance Subcommittee. Reader’s guide to subsynchronous resonance. IEEE Trans Power Syst, 1992, 7:150–157
Ajjarapu V, Lee B. Bifurcation theory and its application to nonlinear dynamical phenomena in an electrical power system. IEEE Trans Power Syst, 1992, 7: 424–431
Iravani M R, Semlyen A. Hopf bifurcations in torsional dynamics. IEEE Trans Power Syst, 1992, 7: 28–36
Zhu W, Mohler R R, Spee R, et al. Hopf bifurcations in a SMIB power system with SSR. IEEE Trans Power Syst, 1996, 11: 1579–1584
Nayfeh A H, Harb A M, Chin C M, et al. A bifurcation analysis of subsynchronous oscillation in power systems. Electr Power Syst Res, 1998, 47: 21–28
Nayfeh A H, Harb A M, Chin C M, et al. Application of bifurcation theory to subsynchronous resonance in power systems. Int J Bifurc Chaos, 1998, 8: 157–172
Mitani Y, Tsuji K, Varghese M, et al. Bifurcations associated with sub-synchronous resonance. IEEE Trans Power Syst, 1998, 13: 139–144
Niu X Z, Qiu J J. Investigation of torsional instability, bifurcation and chaos of a generator set. IEEE Trans Energy Conversion, 2002, 17:164–168
Hassard B D, Kazarinoff N D, Wan Y H. Theory and Application of Hopf Bifurcation. Cambridge: Cambridge University Press, 1981
Seydel R. From equilibrium to Chaos: Practical Bifurcation and Stability Analysis. New York: Elsevier Science Publishing Co., 1988
Guckenheimer J, Holmes P. Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields. New York: Springer-Verlag, 1983
Yu Y N. Electric Power System Dynamics. New York: Academic Press, 1983
Kundur P. Power System Stability and Control. New York: McGraw-Hill, 1994
Doedel E J, Champneys A R, Fairgrieve T F, et al. AUTO97: continuation and bifurcation software for ordinary differential equations (with HomCont). Montreal: Concordia University, 1998
Author information
Authors and Affiliations
Corresponding author
Additional information
Supported by the National Basic Research Program of China (“973” Projects) (Grant Nos. 1998020319 and 2004CB217906)
Rights and permissions
About this article
Cite this article
Duan, X., Wen, J. & Cheng, S. Bifurcation analysis for an SMIB power system with series capacitor compensation associated with sub-synchronous resonance. Sci. China Ser. E-Technol. Sci. 52, 436–441 (2009). https://doi.org/10.1007/s11431-008-0202-x
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11431-008-0202-x