Study of Hopf bifurcations in a simple power system model

This paper studies the occurrence of Hopf bifurcations in a simple single-machine-infinite-bus power system model. Our interest is primarily on the subcritical or supercritical nature of the Hopf bifurcations under variations in operating parameters. 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 stable limit cycles. Two degenerate bifurcations, namely, one related to double zero eigenvalues, and the other related to Hopf normal form efficient becoming zero, give rise to homoclinic orbits and nested limit cycles respectively