Modelling and optimal switching pattern generation for AC to AC power converters

`Thin' power electronics concentrates on the design of minimal and cost effective power converters. Part of the research effort targets the direct processing of an AC input to an AC output without the use of an intermediate DC stage. Particular examples include the inverterless active filter and the controllable network transformer, both of which in their simplest form employ a buck switcher as the active element. Existing analysis of these circuits has dealt with a continuous approximation to the modulating function with applications to relatively high switching frequencies. This paper addresses the problem of selecting a low frequency switching pattern that achieves the correct transformation of an AC input composed of a set of arbitrary harmonics into an AC output containing a desired set of harmonics. This is achieved by constructing a model of the converter in the frequency domain so as to allow a systematic description of the interaction between linear filters and the buck converter via a set of non-linear equations that closely approximate the behaviour of the physical circuit. These equations are set in the form of a constrained optimization problem, the solution of which represents an optimal switching pattern that satisfies a set of harmonic constraints. The method is presented in a general way, facilitating direct application to other systems composed of linear filters and a buck converter. The inverterless active filter is considered as an example problem and the method is used to construct optimal switching patterns that provide harmonic correction of the current drawn by a three phase passive rectifier.