Energy communities (ECs) enable prosumers, consumers, and distributed energy resources (DERs) to jointly manage energy in a coordinated and economically efficient manner. In this work, we propose an energy management system (EMS) for ECs that integrates a demand response (DR) program with a peer-to-peer (P2P) market based on sealed-bid auctions and continuous Stackelberg dynamics. The buyers determine prices according to their energy demand and risk aversion, and generators decide on the amount of energy to sell based on the rewards received and their associated costs. Methodologically, we develop three algorithms to maximize the welfare of the community. The first algorithm incorporates a DR program and generation constraints to keep the EC competitive with grid prices over time. The second and third algorithms use replicator dynamics (RD) to find equilibria that optimize the system’s welfare, using Lagrangian relaxation (LR) to handle the model constraints. We integrate the models for sellers and buyers via a system of differential equations that simulate a Stackelberg game. Additionally, a filtering mechanism is employed to improve convergence and reduce computation time. We validate the EMS in a case study, showing that the proposed approach achieves greater self-sufficiency compared to a system without demand response and enables better resource management, enhanced fairness, and a more equitable distribution of benefits compared to a non-hierarchical and decoupled model.
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