Hopf bifurcations in torsional dynamics (turbine-generators)

The authors extend the analysis of torsional oscillations into the nonlinear range and investigate the Hopf bifurcation phenomenon of the torsional dynamics of a turbine generator in a series capacitor compensated power system. The transition of growing torsional oscillations into nonlinear oscillations with limit cycles is demonstrated. Based on physical reasoning, a set of approximate nonlinear differential equations which explain the fundamentals of nonlinear torsional dynamics and the associated bifurcation phenomenon is developed. The results from the nonlinear equations are verified by time-domain simulation studies, using the Electromagnetic Transients Program (EMTP). The studies indicate that because of the Hopf bifurcation phenomenon, the range of instability (growing oscillations) of torsional oscillations is noticeably narrower than the one which is predicted by an eigenanalysis method.>