Robust Controller Design for a Grid-Connected VSI via an LCL Filter in the Presence of Unknown Grid Impedance

Abstract

Grid-connected inverters may become unstable under specific grid impedance conditions. To address this issue, system stability and robustness against grid impedances of the R-L type can be ensured by satisfying two conditions. The first condition is to ensure that the closed-loop poles of the system remain stable despite variations in grid impedance. The second condition relies on the admittance model of the equivalent circuit. Specifically, the product of this admittance and the grid impedance must satisfy the Nyquist stability criterion. In this work, the stability of a converter connected to the grid through an LCL filter is analyzed. To this end, the output admittance is modeled in the Laplace domain, taking into account the behavior of the discrete controller. In addition, to ensure that the closed-loop poles remain stable, the system's open-loop response is analyzed. These two conditions are examined in scenarios where system states are partially or fully fed back, under different system parameter values. Consequently, a robust controller is designed for variations in R-L type grid impedance.