Closed-Form Critical Conditions of Saddle-Node Bifurcations for Buck Converters

TL;DR

This paper derives a comprehensive closed-form condition for saddle-node bifurcations in buck converters, aiding designers in predicting and preventing jump instabilities and solution coexistence.

Contribution

It provides a generalized, exact critical condition applicable to various control schemes, unifying and extending previous results.

Findings

Derived a closed-form critical condition for saddle-node bifurcations.

Unified previous critical conditions as special cases.

Proposed a systematic procedure for different control schemes.

Abstract

A general and exact critical condition of saddle-node bifurcation is derived in closed form for the buck converter. The critical condition is helpful for the converter designers to predict or prevent some jump instabilities or coexistence of multiple solutions associated with the saddle-node bifurcation. Some previously known critical conditions become special cases in this generalized framework. Given an arbitrary control scheme, a systematic procedure is proposed to derive the critical condition for that control scheme.