Stability Analysis of the Proportional-Resonant Controller in Single Phase Converters

Abstract

The proportional-resonant control (PR-control) is a simple and efficient control, which has the ability to eliminate error in linear time varying signals. This type of control is typically used in applications such as the integration of solar panels, energy storage and electric vehicles among others. Despite having non-linear dynamics, the analysis of the PR-control is usually performed using linear systems theory. This paper proposes a non-linear stability analysis based on Lyapunov theory which formalizes the main stability results on these controls that are standard in industrial applications. The proposed approach is general and independent of the structure of the phase-locked loop which is considered as a vanishing perturbation. This approach allows a better understanding of the control from a non-linear perspective. In addition, it gives an exact criteria for tuning the parameters of the controller. Numerical simulation results in a wide range of scenarios complement the analysis and validate them.