A BIFURCATION-ANALYSIS OF SUBSYNCHRONOUS OSCILLATIONS IN POWER-SYSTEMS

A bifurcation analysis is used to investigate the complex dynamics of a heavily loaded turbine-generator system connected to an infinite bus bar through a series capacitor-compensated transmission line. It revea ls the existence of self-excited subsynchronous torsional oscillations of a 5-mass rotor, which may eventually lead to the destruction of th e 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 aro und the operating point undergoes small single-period oscillations wit h constant amplitude. This in turn results in a small limit-cycle attr actor. As the compensation level increases further, the amplitude of o scillation grows until a secondary Hopf bifurcation is reached. There, the oscillations characterize themselves by two incommensurate period s and bounded amplitudes, signifying the transformation of the limit c ycle 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 destruc tion of the two-torus attractor and its basin of attraction in a so-ca lled bluesky catastrophe. Interestingly, this scenario repeats itself in the vicinity of three supercritical Hopf bifurcations. The bifurcat ion analysis is validated with numerical solutions of the differential equations that govern the power system. (C) 1998 Elsevier Science S.A . All rights reserved.