This paper presents a novel simplified method to implement the finite set -model predictive control technique for photovoltaic generation systems connected to the ac network. This method maintains the advantages of the conventional finite set -model predictive control, such as fast response, simple implementation, and easy understanding; but it also eliminates the use of a cost function and hence the weighting factors, instead, it finds the optimal operating state directly from the model and the discrete number of valid states of the converter. Although the proposed algorithm does not compute a cost function, it is able to select the inverter state that minimizes the tracking error by using a hexagonal convergence region. The main advantage of this technique is to reduce the computational cost in 43% of the algorithm that selects the best state, presenting a simple and complete algorithm without compromising the predictive control performance. The proposed algorithm properly operates under various conditions such as changes in the network frequency and changes in the system parameters.INDEX TERMS Predictive control, Solar power generation, ac-dc power converters, Fast MPC.