Symmetry-Breaking Bifurcation in Series-Parallel Load Resonant DC-DC Converters

Abstract

This paper reports the occurrence of symmetry-breaking bifurcation in the series-parallel load-resonant dc-dc converter with L-C output filter. The constant frequency phase shift modulation technique is employed with proportional-integral controller in the output voltage regulation. The complexity of the system is contributed by the fact that a six dimensional state space is divided into twelve subsystems by six switching surfaces. It is shown that the dynamics are not only related to the resonant components but are also heavily dependent on the output filter design. The understanding of the dynamics resulting from the interaction between the resonant tank and the filter circuit helps in designing more reliable converters. We show that the first instability can be caused by Neimark-Sacker as well as symmetry-breaking bifurcations. Stable as well as unstable periodic orbits are identified, and their characteristic multipliers are computed by a newly developed algorithm based on a combination of Filippov's theory and shooting method with Newton-Raphson algorithm.