Jump power concepts and some theorems on switching

Abstract

Power-like functions based on Tellegen's theorem are important tools in the study of electrical networks. Networks containing power converters are nonlinear and/or time-variant. This fact continues to represent a challenge regarding both theoretical analysis and practical application. The topologies of existing converters are multiform and there is not one single general approach to them. In terms of circuit theory, a number of theorems regarding ideal switching can be derived. This paper proposes a novel power-like function to describe the switching phenomenon and thus contribute to principles underlying power converters. Specifically, it sets out theorems and describes certain empirical applications which clearly work in practice but for which no formal proof has yet been provided. It focuses in detail on hard commutation of switches and formulates a principle of correlation between active (i.e. externally fired) and passive hard switching. The paper concludes by presenting examples of applications in support of the theoretical results.