A Distributed MILP-ADMM Framework for Italian Energy Communities: Shared Energy Incentives, Renewables, and Shiftable Loads

In this paper, we propose a distributed optimization framework for Italian energy communities that take advantage of state incentives linked to the amount of shared energy consumed. The framework models the collective use of renewable energy generated by community members, allowing those without direct access to renewable sources to benefit from energy at a reduced cost, in line with regulatory incentives. We formulate the problem as a Mixed-Integer Linear Program (MILP) that considers different user configurations, including those with renewable energy sources and battery energy storage systems (BESS). A key feature of our approach is the integration of shiftable loads, enabling flexible energy consumption adjustments to optimize overall system performance. To solve this problem, we employ a distributed optimization approach combining MILP with the Alternating Direction Method of Multipliers (ADMM), facilitating decentralized decision-making, enhancing data privacy, and reducing computational complexity. This makes the solution more scalable and efficient for larger communities. Numerical results show that our approach significantly reduces the community's overall energy costs and demonstrates the effectiveness of cooperative BESS management and dynamic energy consumption optimization through shiftable loads.