Fair Cost Allocation in Energy Communities: A DLMP-based Bilevel Optimization with a Shapley Value Approach

TL;DR

The paper tackles fair cost allocation in energy communities where coordinated DER operations affect Distribution Locational Marginal Prices (DLMPs). It develops a DLMP-based bilevel optimization between a Community Energy Aggregator (CEA) and a Distribution System Operator (DSO), reformulated into a single-level MILP via KKT conditions and strong duality. fairness is achieved by applying the Shapley value to allocate total cooperative savings among ECs, with a signature-based approximation to scale to larger numbers of communities. Numerical studies on CIGRE 19-bus, IEEE 69-bus, and IEEE 123-bus networks demonstrate that the proposed approach yields allocations that reflect each EC’s marginal contribution while reducing system-wide costs, and that the approximation substantially reduces computational burden without sacrificing fairness fidelity. This framework provides incentive-compatible guidance for DLMP-aware distribution-market design and DER participation in energy communities.

Abstract

Energy communities (ECs) are emerging as a promising decentralized model for managing cooperative distributed energy resources (DERs). As these communities expand and their operations become increasingly integrated into the grid, ensuring fairness in allocating operating costs among participants becomes a challenge. In distribution networks, DER operations at the community level can influence Distribution Locational Marginal Prices (DLMPs), which in turn affect system's operation cost. This interdependence between local decisions and system-level pricing introduces new challenges for fair and transparent cost allocation. Despite growing interest in fairness-aware methods, most methods do not account for the impact of DLMPs. To fill this gap, we propose a bilevel optimization model in which a Community Energy Aggregator (CEA) schedules DERs across multiple ECs while a Distribution System Operator (DSO) determines DLMPs through network-constrained dispatch. Leveraging the Karush-Kuhn-Tucker (KKT) conditions and strong duality, the bilevel model is reformulated into a tractable single-level problem. We achieve fairness in the cost allocation by applying the Shapley value to quantify each community's marginal contribution to system-wide cost savings. The effectiveness of the proposed method is validated through simulations on several benchmark distribution systems.

Figures (9)

• Figure 1: Bilevel optimization framework between the CEA and the DSO, and its duality-based single-level reformulation.
• Figure 2: CIGRE low voltage benchmark network.
• Figure 3: Individual cost, Shapley-based savings, and final cost for each community bus in the CIGRE system, under Shapley and base allocation methods. The Shapley-based final cost reflects each community's marginal contribution, while the base method directly applies DLMPs and dispatch results without fairness considerations.
• Figure 4: Active power DLMP distributions at the community nodes under individual activation and grand coalition participation.
• Figure 5: 3D box-plot of non-participating buses’ cost distribution across different numbers of participating communities.