A bifurcation analysis of subsynchronous oscillations in power systems

Abstract

A bifurcation analysis is used to investigate the complex dynamics of a heavily loaded turbine-generator system connected to an infinite busbar through a series capacitor-compensated transmission line. It reveals the existence of self-excited subsynchronous torsional oscillations of a 5-mass rotor, which may eventually lead to the destruction of the shaft or the loss of synchronism of the generator. Specifically, we show that, as the capacitor-compensation value increases and reaches a critical value, called supercritical Hopf bifurcation, the system around the operating point undergoes small single-period oscillations with constant amplitude. This in turn results in a small limit-cycle attractor. As the compensation level increases further, the amplitude of oscillation grows until a secondary Hopf bifurcation is reached. There, the oscillations characterize themselves by two incommensurate periods and bounded amplitudes, signifying the transformation of the limit cycle into two-period quasiperiodic motion called a two-torus attractor. When the capacitor-compensation level passes a third critical value, the amplitude of oscillations becomes unbounded following the destruction of the two-torus attractor and its basin of attraction in a so-called bluesky catastrophe. Interestingly, this scenario repeats itself in the vicinity of three supercritical Hopf bifurcations. The bifurcation analysis is validated with numerical solutions of the differential equations that govern the power system.