Computation of Steady-State Oscillations in Power Converters Through Complementarity

Computation of periodic steady state in nonlinear circuits is a key issue. Power electronics converters represent an interesting class of switched nonlinear circuits. The behavior of the converter is obtained by the commutations of the electronic devices which determine the switchings among the different converter modes. Switchings can be classified as external, if forced by directly manipulable control variables, and internal if determined by state dependent conditions. The presence of internal switchings makes it difficult to know a priori the sequence of modes and also open loop steady-state behaviors are difficult to be obtained. In this paper the complementarity modeling framework is proposed as a possible approach for computing periodic steady-state oscillations in power converters with internal switchings. It is shown how linear complementarity systems can be used to model the behavior of a wide class of power converters. The discretization of such model allows to formulate a static complementarity problem whose solution provides the steady-state oscillation of the converter. It is proved that the backward zero-order-hold technique preserves passivity through the discretization and allows to determine the unique solution of the complementarity problem. A resonant converter and a dc/dc voltage-mode controlled buck converter are used as examples.