The ongoing increase of PhotoVoltaic (PV) microgeneration, pointing to high levels of penetration, can lead to the occurrence of overvoltages. Moreover, the inherent unbalanced nature of the LV distribution grid is a difficulty that must be considered when designing countermeasures. On the other hand, storage systems are suitable devices that can help the process of voltage control. This paper proposes a control system for a real-time energy management system, using Multi-Objective Particle Swarm Optimization (MOPSO) on a highly unbalanced LV distribution network, with batteries and a high share of PV. The purpose of the control system is the optimization of four objectives: Voltage Unbalance Factor (VUF), voltage deviation, active power losses and PV curtailment, wherein four scenarios were considered for assessment. This study is conducted using an unbalanced three-phase power flow algorithm. A comparison of residential and community storage is performed. The results show that the inclusion of storage devices near the prosumers’ PV systems is the recommended solution to enhance voltage stability and balance. Moreover, a significant reduction of active power losses in the LV network is observed.