Equivalent converter method for analyzing complex DC–DC converting systems

This paper introduces a new approach for analyzing the dynamics of DC–DC converters. Currently, the primary widely accepted method for examining dynamic processes is the Small Signal Analysis technique. However, when applied to modern complex converters, this method poses additional challenges in formulating and solving systems of differential equations. The method proposed in this paper is based on its application to the analysis of dynamic modes of energy functions—Lagrangians. These functions make it possible to define simple criteria to describe the course of dynamic processes, and in the end define an equivalent (approximating) conventional converter identical to the original one with respect to the course of dynamics. If the magnetic and electrical energies in the Lagrangians of both the converters are equal, the outcome is practically identical transient processes. These findings were confirmed by both theoretical analysis and experimentally modelling the dynamics of the initial converter and an equivalent to it in the Matlab–Simscape program. An additional possibility of using the transfer functions of a conventional boost converter for the theoretical analysis of the converters of much greater orders is also discussed. The authors’ experiments confirm the correctness of their theoretical conclusions.