Optimal Energy Trading In Residential Prosumer Clusters Via Graphon Mean Field Games

In this work, we address the optimal energy trading (OET) problem in distribution grids with a large number of prosumer households. We first introduce a clustering architecture that partitions the grid into residential prosumer clusters (RPCs), each managed by an aggregator responsible for internal energy coordination and external interactions with neighbouring clusters and the distribution system operator. To optimize energy exchanges within and across clusters, we develop a novel decentralized control framework based on graphon mean field game theory. This framework models the OET as a decentralized dynamic game, deriving optimal control strategies that minimize each prosumer’s individual energy cost. Household dynamics and cost functions are influenced by both local aggregate effects within their RPC and global interactions across interconnected clusters. Numerical experiments conducted on a dense energy network with 100 clusters, each containing 200 uniform households, validate the effectiveness of the proposed method in achieving scalable and cost-efficient energy coordination.