NONLINEAR RESONANCE IN BASIN PORTRAITS OF 2 COUPLED SWINGS UNDER PERIODIC FORCING

A model of a simple electric power supply network involving two genera tors connected by a transmission network to a bus is studied by numeri cal simulation. In this model, the bus is supposed to maintain a volta ge of fixed amplitude, but with a small periodic fluctuation in the ph ase angle. In such a case, traditional analysis using direct methods i s not applicable. The frequency of the periodic fluctuation is varied over a range of values near a nonlinear resonance of the two-generator network. When the bus fluctuation frequency is away from resonance, t he system has several attractors; one is a small-amplitude periodic os cillation corresponding to synchronized, quasi-normal operation (sligh tly swinging), while others are large amplitude periodic oscillations which, if realized, would correspond to one or both generators operati ng in a desynchronized steady state. When the bus fluctuation frequenc y approaches resonance, a new periodic attractor with large amplitude oscillations appears. Although it does correspond to a synchronized st eady state, this attractor has a disastrously large amplitude of oscil lation, and represents an unacceptable condition for the network. Basi n portraits show that this resonant attractor erodes large, complicate d regions of the basin of the safe operating condition. Under conditio ns of small periodic fluctuation in bus voltage, this basin erosion wo uld not be detected by traditional analysis using direct methods. Furt her understanding of such complicated basin structures will be essenti al to correctly predict the stability of electric power supply systems .