Fair Least Core: efficient, stable and unique game-theoretic reward allocation in Energy Communities by row-generation

Energy Communities are increasingly proposed as a tool to boost renewable penetration and maximize citizen participation in energy matters. These policies enable the formation of legal entities that bring together power system members, enabling collective investment and operation of energy assets. However, designing appropriate reward schemes is crucial to fairly foster individuals to join, as well to ensure collaborative and stable aggregation, maximizing community benefits. Cooperative Game Theory, emphasizing coordination among members, has been extensively proposed for ECs and microgrids; however, it is still perceived as obscure and difficult to compute due to its exponential computational requirements. This study proposes a novel framework for stable fair benefit allocation, named Fair Least Core, that provides uniqueness, reproducibility, stability and fairness. A novel row-generation algorithm is also proposed that allows to efficiently compute the imputations for coalitions of practical size. A case study of ECs with up to 100 members shows the stability, reproducibility, fairness and efficiency properties of proposed model. The results also highlight how the market power of individual users changes as the community grows larger, which can steer the development of practical reliable, robust and fair reward allocations for energy system applications