Impedance network inverters are a good alternative for voltage-source and current-source inverters. The shoot-through solution and the boosting capability of such converters make them an excellent solution for photovoltaic (PV) application. Furthermore, energy storage integration in these inverters does not require any additional components in the converter; indeed, a battery can be directly connected in parallel with one of the capacitors of the Z- or quasi Z-network. However, for an optimal control of these converters, complex control and modulation strategies are required. Model Predictive Control (MPC) provides high control performance at the expense of the computational effort. In this paper, a low computational control method where both MPC and proportional resonant (PR) controller are combined, is proposed. This makes the proposed controller perform two iterations only instead of iterating for all the available switching states. As shown in the obtained results, the proposed controller conserves the high performance of the conventional MPC with 50% less computational burden
