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

Abstract

Inverters connected to the grid can become unstable under specific grid impedance conditions. In order to find a solution to this problem, it is possible to ensure system stability and their robustness to R-L type grid impedances by satisfying two conditions. The first condition is to ensure that the closed-loop poles of the system are in stable positions to variations in the grid impedance. The second condition is reliant on the admittance model of the equivalent circuit. Specifically, the product of this admittance and the grid impedance must adhere to the Nyquist stability criterion. In this work, the stability of the converter connected to the grid through an LCL filter is analysed. For this purpose, the output admittance is modelled in the Laplace domain taking into account the behaviour of the discrete controller. In addition, to ensure that the closed-loop poles are in stable positions, the system open-loop response is analysed. These two conditions are examined across scenarios where system states are partially or completely fed back, for different system parameter values. Consequently, a robust controller is designed for variations of the R-L type grid impedance.