Singular Perturbation Theory for PWM AC/DC Converters: Cascade Nonlinear Control Design and Stability Analysis

Abstract

In this paper, the problem of controlling PWM single-phase AC/DC converters is addressed. The control objectives are twofold: (i) regulating the output voltage to a selected reference value, and (ii) ensuring a unitary power factor by forcing the grid current to be in phase with the grid voltage. To achieve these objectives, the singular perturbation technique is used to prove that the power factor correction can be done in the open-loop system with respect to certain conditions that are not likely to take place in reality. It is also applied to fulfill the control objectives in the closed-loop through a cascade nonlinear controller based on the three-time scale singular perturbation theory. Additionally, this study develops a rigorous and complete formal stability analysis, based on multi-time-scale singular perturbation and averaging theory, to examine the performance of the proposed controller. The theoretical results have been validated by numerical simulation in MATLAB/Simulink/SimPowerSystems environment.

Keywords

• singular perturbation
• pwm ac/dc converters
• nonlinear control
• power factor correction
• averaging theory
• stability analysis.