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Nonlinear Analysis of Limit Cycles in Power System Models

Juan Li

出版	Washington State University, 2001
URL	http://books.google.com.hk/books?id=pseHNwAACAAJ&hl=&source=gbs_api

註釋

The focus of the dissertation is on the study and analysis of limit cycles and Hopf bifurcations in power system models. Both analytical and computational results are pursued for different power system models. Analysis of Hopf bifurcations is extended to a four equation SMIB model with excitation control. Under the assumptions of a fast high gain exciter, singular perturbation theory is applied to reduce the original four equation system onto a two-equation slow model. Thus Hopf bifurcation coefficient a can be calculated analytically. The sign of the coefficient a gives the supercritical or subcritical nature of the Hopf bifurcations, thus predict the existence of stable or unstable limit cycle. Formulas are derived for estimating the size of the limit cycles analytically. Hopf bifurcation coefficient a along the Hopf bifurcation locus of the SMIB model is computed numerically. We observe that the Hopf bifurcations are mostly subcritical. When the exciter control is a fast high gain control and when the Thevenin equivalent transmission line impedance is high, the Hopf bifurcation can become supercritical leading to birth of stable limit cycles locus on the SMIB system which verified the analytical results.