Modeling and Analysis of Three-phase Diode Bridge Rectifiers as Linear Complementarity Systems

Abstract

This article presents the use of complementarity formalism to derive compact representations of models for electrical circuits that contain resistors, capacitors, sources, and diodes. As an important application, models will be developed in order to describe the behavior of an important class of electric power components: the diode bridge rectifiers. There are two important advantages of complementarity models. First, the theory of the complementarity systems aims at providing a compact representation of many such systems, especially in comparison with conventionally used switched models. Second, complementarity modeling offers powerful methods for analysis. For instance, by using the well-developed theory of the linear complementarity problem from the optimization theory, one may prove strong results such as the existence and uniqueness of solutions. The article shows also that the steady state of diode bridge rectifiers can be computed directly by means of non-iterative methods, and its existence and uniqueness may be rigorously proven. For validation purposes, several simulation results are presented. In all case studies, the solutions obtained by the complementarity approach are compared with solutions obtained via commercially available software packages such as PSpice and MATLAB/Simulink.