Renewable energy communities, where citizens, businesses, and institutions produce, consume, store, and share energy, are increasingly pivotal in energy markets. The use of shared community batteries introduces the challenge of adapting control strategies to community needs, which remains an open question in energy management. This study presents a two-layer optimal control model for managing community Battery Energy Storage Systems in low-voltage networks to self-dispatch, engage in energy arbitrage and maximize collective self-consumption, as well as preserving battery lifespan. The scheduling layer calculates the optimal dispatch plan and battery trajectories to maximize profits based on long-term forecasts. The real-time control layer minimizes dispatch errors based on real-time data and short-term forecasts. The key contribution of this work is the experimental validation of a novel model that, for the first time in the literature, integrates dispatch, energy arbitrage, and collective self-consumption services. This model is the result of adapting and enhancing an existing framework, which had previously been limited to mathematical formulation and simulation. Here, it is experimentally validated in a real-scale microgrid, demonstrating its applicability and effectiveness in managing these services.