Stability analysis of grid-connected voltage source inverters with LCL-filters using partial state feedback

This paper addresses the stability of discrete controlled grid connected voltage source inverters with LCL-filter usually found in wind power generation systems. First a theorem that relates the controllability of the discrete dynamic equation with the LCL-filter parameters and the sampling frequency is derived. Then, a robust partial state feedback design on the linear matrix inequalities framework guarantee the stability damping the LCL-filter resonance for a large set of grid conditions without requiring tuning procedures. Finally, an internal model controller is added to ensure asymptotic reference tracking and disturbance rejection, therefore reducing significantly the impact of grid background voltage distortion on the line currents. Simulation and experimental results are presented to support the theoretical analysis carried out and to demonstrate the system performance.