We propose and experimentally validate a process to dispatch the operation of a distribution feeder with heterogeneous prosumers according to a trajectory with 5 minutes resolution, called dispatch plan, established the day before operation. The controllable element is a utility scale grid-connected battery energy storage system (BESS) integrated with a minimally pervasive monitoring infrastructure. The process consists of two stages: day-ahead, where the dispatch plan is determined by using forecast of the aggregated consumption and local distributed generation (prosumption), and real-time operation, where the mismatch between the actual prosumption realization and dispatch plan is corrected by adjusting the real power injections of the BESS with model predictive control (MPC). MPC accounts for BESS operational constraints thanks to reduced order dynamic grey-box models identified from on-line measurements. The experimental validation is performed by using a grid connected 720 kVA/500 kWh BESS to dispatch the operation of a 20 kV distribution feeder of the EPFL campus with both conventional consumption and distributed PV generation.