Steady state analysis of power converters via a complementarity approach

Power electronics converters represent an interesting class of switched systems. They can be assumed to consist of linear elements, external sources, and electronic devices such as diodes and electronic switches. The behavior of the converter is obtained by the commutations of the electronic devices which determine the switchings among the different converter modes. In general it is difficult to know a priori the sequence of modes and also steady state behaviors are typically obtained through long time-stepping simulations or by introducing severe approximations in the spectrum of the electrical variables (averaging, fundamental mode approximation, etc.). In this paper the complementarity modeling framework is proposed as a possible approach for computing steady state oscillations in power converters. Given a converter topology it is shown how to obtain its switched complementarity model. The discretization of such model allows to formulate a static complementarity problem whose solution represents the `exact´ steady state behavior of the converter. A resonant converter and a dc/dc buck converter are used as examples in order to show the effectiveness of the approach.