Analysis and Control of Period-Doubling Bifurcation in Buck Converters Using Harmonic Balance

TL;DR

This paper analyzes period doubling bifurcation in buck converters using harmonic balance, deriving conditions for bifurcation and designing control to prevent it, thereby enhancing stability and regulation.

Contribution

It introduces an exact harmonic balance method for analyzing bifurcation in buck converters and proposes a control strategy to eliminate it.

Findings

Derived a necessary and sufficient condition for bifurcation

Identified the bifurcation location precisely

Designed a control to eliminate bifurcation and improve regulation

Abstract

Period doubling bifurcation in buck converters is studied by using the harmonic balance method. A simple dynamic model of a buck converter in continuous conduction mode under voltage mode or current mode control is derived. This model consists of the feedback connection of a linear system and a nonlinear one. An exact harmonic balance analysis is used to obtain a necessary and sufficient condition for a period doubling bifurcation to occur. If such a bifurcation occurs, the analysis also provides information on its exact location. Using the condition for bifurcation, a feedforward control is designed to eliminate the period doubling bifurcation. This results in a wider range of allowed source voltage, and also in improved line regulation.