Building energy management systems (BEMSs), dedicated to sustainable buildings, may have additional duties, such as hosting efficient energy management systems (EMSs) algorithms. This duty can become crucial when operating renewable energy sources (RES) and eventual electric energy storage systems (ESSs). Sophisticated EMS approaches that aim to manage RES and ESSs in real time may need high computing capabilities that BEMSs typically cannot provide. This article addresses and validates a fuzzy logic-based EMS for the optimal management of photovoltaic (PV) systems with lead-acid ESSs using an edge computing technology. The proposed method is tested on a real smart grid prototype in comparison with a classical rule-based EMS for different weather conditions. The goal is to investigate the efficacy of islanding the building local network as a control command, along with ESS power control. The results show the implementation feasibility and performance of the fuzzy algorithm in the optimal management of ESSs in both operation modes: grid-connected and islanded modes.