Computational Methods for Nonlinear Analysis of Hopf Bifurcations in Power System Models

Hopf bifurcations can occur in power systems when a system mode experiences low damping because of changes in system operating conditions and they can lead to the emergence of limit cycles and oscillations. There are two types of Hopf bifurcations, namely, supercritical and subcritical, and they are determined by the sign of a cubic normal form coefficient. This paper discusses the two types of Hopf phenomena in test power system models where both types could be seen under changes in system and control parameters. The paper proposes an efficient computational method for carrying out the higher-order center manifold and normal form calculations for a general power system model and discusses the implications of the normal form coefficients for power system dynamics. Distinguishing between subcritical versus supercritical is important since they lead to very different types of oscillatory phenomena, divergence versus sustained oscillations, respectively.