Piecewise-Linear Map for Studying Border Collision Phenomena in DC/AC Converters

Abstract

Recently, while studying the dynamics of power electronic DC/AC converters we have demonstrated that the behavior of these systems can be modeled by piecewise-smooth maps which belong to a specific class of models not investigated before. The characteristic feature of these maps is the presence of a very high number of switching manifolds (border points in 1D). Obviously, the multitude of control strategies applied in the modern power electronics leads to different maps belonging to this class of models. However, in this paper we show that several models can be studied using the same piecewise-linear approximation, so that the bifurcation phenomena which can be observed in this approximation are generic for many models. Based on the results obtained before for piecewise-smooth models with different kinds of nonlinearities resulting from the corresponding control strategies, in the present paper we discuss the generic bifurcation patterns in the underlying piecewise-linear map.