Boundaries between fast- and slow-scale bifurcations in parallel-connected buck converters

This paper studies a system of parallel-connected dc/dc buck converters under master-slave current sharing and proportional-integral (PI) PWM control. Two distinct types of bifurcations can be identified. Depending on the value of the integral control time constant, the system exhibits either a slow-scale bifurcation (Neimark-Sacker bifurcation) or a fast-scale bifurcation (period doubling). Extensive simulations are used to capture the behaviour. Trajectories and Poincare sections before and after these bifurcations are shown. The boundaries between these two types of bifurcations are located. In particular, the parameter spaces of the controllers for these bifurcations are totally different. A detailed analysis is performed, based on examining the Jacobian and characteristic multipliers of the describing discrete-time map. Copyright (c) 2007 John Wiley & Sons, Ltd.