Dynamic and Steady-State Analysis of Switching Power Converters Made Easy: Complementarity Formalism

Power electronics converters represent an interesting class of switched nonlinear circuits. Switchings of electronic devices 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 behaviours are difficult to be obtained. In this chapter it is shown how linear complementarity systems can be used to model the behaviour of a wide class of power converters. The complementarity framework is suitable for modelling piecewise-linear characteristics of diodes and controlled electronic switches. The combination of such models with a state-space representation of the circuit allows to obtain a model of the power converter which is valid for any operating mode. The discretization of such model allows to formulate a static complementarity problem whose solution provides the steady-state oscillation of the converter, either in open or closed-loop. Throughout the chapter the usefulness of the complementarity formalism for the analysis of power converters is shown by considering three challenging examples: a DC–DC voltage–mode pulse-width modulated boost converter, a resonant converter and a switched capacitors converter are used as examples.