Quasi-resonant FCS model predictive control for three phase grid connected highly intermittent PV-inverter with voltage support

•The approach enables FCS-MPC to generate a high gain at the grid frequency.•The qausi-resonant model offers improved tracking efficiency and reduced steady-state error.•The QR-FCS-MPC uses previous optimal parameters to implement a new future command signal.•The tracking error have been reduced from 0.35% to 0.057% that is six times, and provides improved harmonics suppression during distorted grid voltage.•Voltage support has been included to provide reactive power support during intermittency.