A Complementarity Model for Closed-Loop Power Converters

At a certain level of abstraction, power converters can be represented as linear circuits connected to diodes and controlled electronic switches. The evolutions of the electrical variables are determined by the state-dependent switchings, which complicate the mathematical modeling of controlled power converters. Differently from the complementarity models previously presented in the literature, the model proposed in this paper allows to represent as a linear complementarity system also closed-loop power converters, without requiring the a priori knowledge of the converter modes. A model construction procedure, not dependent on the specific converter topology, is presented. The discretization of the continuous-time model allows to formulate mixed linear complementarity problems for the computation of the control-to-output frequency response and the evolutions of both transient and steady-state currents and voltages. As illustrative examples, Z-source, boost, and buck dc-dc power converters under voltage-mode control and current-mode control operating both in continuous and discontinuous conduction modes are considered.