Hybrid Modeling of a DC-DC Series Resonant Converter: Direct Piecewise Affine Approach

A dc-dc resonant converter has the advantage of overcoming switching losses and electromagnetic interference which are the main limitations of high frequency power converters. Nevertheless, the modeling and stability analysis of dc-dc resonant converters are considerably more complex than pulsewidth modulation counterparts. The conventional averaged linearized model of the resonant converter has limitations due to averaging and linearization. First of all, the linearized model has large modeling error in presence of large variations of reference voltage and input voltage. Furthermore, Converging area for stabilizing controllers is smaller in the averaged model. In order to overcome these limitations, this paper presents a novel framework for modeling of dc-dc resonant converters. As dc-dc resonant converters are naturally switched systems with affine subsystems, a piecewise affine model is derived directly from the converter model. The new model is based on analysis of the resonant converter on state plane trajectories. It is also suitable for precise simulation and high performance controller design of resonant converters. In addition, a stability analysis theorem is provided for the proposed model. The simulation and experimental results on a dc-dc series resonant converter show the effectiveness of this modeling approach.