This paper proposes an optimal design for hybrid grid-connected Photovoltaic (PV) Battery Energy Storage Systems (BESSs). A smart grid consisting of PV generation units, stationary Energy Storage Systems (ESSs), and domestic loads develops a multi-objective optimization algorithm. The optimization aims at minimizing the Total Cost of Ownership (TCO) and the Voltage Deviation (VD) while considering the direct and indirect costs for the prosumer, and the system stability with regard to intermittent PV generation. The optimal solution for the optimization of the PV-battery system sizing with regard to economic viability and the stability of operation is found while using the Genetic Algorithm (GA) with the Pareto front. In addition, a fuzzy logic-based controller is developed to schedule the charging and discharging of batteries while considering the technical and economic aspects, such as battery State of Charge (SoC), voltage profile, and on/off-peak times to shave the consumption peaks. Thus, a hybrid approach that combines a Fuzzy Logic Controller (FLC) and the GA is developed for the optimal sizing of the combined Renewable Energy Sources (RESs) and ESSs, resulting in reductions of approximately 4% and 17% for the TCO and the VD, respectively. Furthermore, a sensitivity cost-effectiveness analysis of the complete system is conducted to highlight and assess the profitability and the high dependency of the optimal system configuration on battery prices.