This paper proposes and experimentally validates a control algorithm for a grid-connected battery energy storage system (BESS) to level the consumption of a group of prosumers and dispatch their aggregated operation. The control strategy is layered in a two-stage procedure: day-ahead and intra-day operation. During day-ahead operation, the load leveled power consumption profile is determined by applying a scenario-based robust optimization using historical measurements of the aggregated feeder power consumption. In the intra-day phase, the operation of the group of prosumers is dispatched according to the profile defined during the day-ahead stage, which becomes the so-called dispatch plan. The dispatch plan is tracked in real-time by properly adjusting the injections of the BESS using model predictive control (MPC). The proposed control process is experimentally validated using a 750 kW/500 kWh BESS.