Design of a Stable and Robust H ∞ Loop-Shaping Controller for LCL Filter Based Grid-Tied Inverter

The main problem that faces LCL filter based grid-tied inverter is the phenomena of resonance. Under certain conditions, the conventional control methods may not properly cope with disturbances and uncertainties in the parameters of the system. As a result, power regulation and stability of the system cannot be guaranteed. The objective of this paper is to design a controller that can achieve stable and robust control of the current flowing through the grid or, in other words, make the output follow a time varying reference with zero steady-state error. The proposed controller consists of a state feedback controller using Linear Quadratic Regulator (LQR), which damps the effect of the resonance frequency. In addition, Kalman filter is added to estimate the missing states by considering the available measurement, which results in a Linear Quadratic Gaussian (LQG) controller. Finally, $H$ ∞ loop-shaping is employed to improve the stability margin of the LQG controller. Simulation results verify the effectiveness of the proposed control approach in terms of stability, reference tracking, and disturbance rejection.