We present a distributed optimization method for energy communities having distributed renewable generation and storage units. We explain how the resulting optimization problem can be cast as a bi-level optimization problem where the followers solve mixed-integer linear programs. Given the difficulty of these problems, we develop a heuristic where incentives are sent to the followers. Specifically, to maximize the collective-self consumption rate, we exploit the notion of allocation key traditionally used a posteriori for economic gain sharing to build an a priori incentive to demand response. The proposed method returns high-quality solutions to the optimal centralized real-world benchmark instances constructed over a month with accurate historical data from our demonstrator in South France.