Modeling and Simulation of DC-DC Power Converters in CCM and DCM Using the Switching Functions Approach: Application to the Buck and C ù k Converters

In this paper, new mathematical models of DC-DC switch-mode converters, which are valid under both continuous and discontinuous operating modes, are presented. The modeling technique is based on the switching functions concept. The obtained models are represented by time-variant state equations, which offer high simplicity for computer implementation. For illustration purpose, the proposed modeling approach is applied to the conventional buck and Cùk converters. The obtained models are then tested through computer implementation using the Simulink tool of Matlab.

1. Introduction

Reliable numerical models for power converters are increasingly required for both academic and industrial purposes. The aim is to elaborate highly precise mathematical representations of widely used converters. The usefulness of such virtual models could be emphasized in two aspects. Firstly, they allow a systematic design of well-tuned control systems that improve the time response of the converter. Secondly, a pre-evaluation of the static and dynamic performance of the converter can be made on the basis of these models, avoiding therefore the necessity to elaborate a laboratory prototype for the same purpose.