Nonlinear analysis of a simple amplitude–phase motion equation for power-electronics-based power system

Abstract

With large-scale application of a large number of renewable energy sources, such as wind turbines, photovoltaics, and various power electronic equipment, the power electric system is becoming gradually more power-electronics-based, whose dynamical behavior becomes much complicated, compared to that of traditional power system. The recent developed theory of amplitude–phase motion equation provides a new framework for the general dynamic analysis of such a system. Based on this theory, we study a simple amplitude–phase motion equation, i.e., a single power-electronics device connected to an infinite-large system, but consider its nonlinear effect. With extensive and intensive theoretical analysis and numerical simulation, we find that basically the system shows some similarity with the classical second-order swing equation for a synchronous generator connected to an infinite bus, such as the two types of bifurcation including the saddle-node bifurcation and homoclinic bifurcation, and the dynamical behavior of stable fixed point, stable limit cycle, and their coexistence. In addition, we find that the Hopf bifurcation is possible, but for negative damping only. All these findings are expected to be helpful for further study of power-electronics-based power system, featured with nonlinearity of high-dimensional dynamic systems involved with not only a large timescale but also large space scale.