A study on Hopf bifurcations for power system stability analysis

Hopf bifurcations are well known as a kind of local bifurcation that can occur in power system dynamics causing the nominal equilibrium of the system to lose their structural stability as the parameters pass through the bifurcation points. In this paper, based on the so far developments in this field, a study on Hopf bifurcations is presented for power system stability analysis. First, Hopf bifurcations in dynamic systems are demonstrated by mathematical equations. Then, varieties of phenomena in power systems, which may lead in Hopf bifurcations, are investigated. In addition, identifying of Hopf bifurcations are studied and various methodologies to analyze and control them are considered. Furthermore, different modeling levels with their relevant differential-algebraic equations are studied and Hopf bifurcation analysis of different order models of system considering induction motors and impedance load conditions supplied by under-load tap-changer transformers (ULTC) are taken into account.