Saddle-Node Bifurcation Associated with Parasitic Inductor Resistance in Boost Converters

TL;DR

This paper analyzes saddle-node bifurcation in boost converters caused by parasitic inductor resistance, deriving conditions for its occurrence and highlighting its impact on steady-state solutions and control design.

Contribution

It provides the first closed-form critical conditions for saddle-node bifurcation in boost converters considering parasitic resistance, clarifying when it occurs in different control modes.

Findings

Saddle-node bifurcation occurs with parasitic resistance in voltage and current mode control with voltage loop closed.

Without modeling parasitic resistance, the bifurcation does not occur, leading to potential misinterpretation of dynamics.

Design limitations can prevent bifurcation effects in practical applications.

Abstract

Saddle-node bifurcation occurs in a boost converter when parasitic inductor resistance is modeled. Closed-form critical conditions of the bifurcation are derived. If the parasitic inductor resistance is modeled, the saddle-node bifurcation occurs in the voltage mode control or in the current mode control with the voltage loop closed, but not in the current mode control with the voltage loop open. If the parasitic inductor resistance is not modeled, the saddle-node bifurcation does not occur, and one may be misled by the wrong dynamics and the wrong steady-state solutions. The saddle-node bifurcation still exists even in a boost converter with a popular type-III compensator. When the saddle-node bifurcation occurs, multiple steady-state solutions may coexist. The converter may operate with a voltage jump from one solution to another. Care should be taken in the compensator design to ensure that only the desired solution is stabilized. In industry practice, the solution with a higher duty cycle (and thus the saddle-node bifurcation) may be prevented by placing a limitation on the maximum duty cycle.