G-2026-66
Optimal energy trading in residential prosumer clusters via graphon mean field games
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BibTeX referenceIn this work, we address the optimal energy trading~(OET) problem in distribution grids operated by an energy grid operator (EGO) and a large number of prosumer households. We first introduce a cluster-of-clusters (CoC) architecture that partitions the grid into residential prosumer clusters (RPCs), each coordinated by an aggregator responsible for internal energy exchanges and external interactions with neighbouring clusters and the EGO. To optimize energy exchanges within and across clusters, we develop a new decentralized control approach based on major-minor graphon mean field game theory (MM-GMFG). This framework models the OET problem as a decentralized dynamic game, deriving optimal control strategies that minimize each prosumer’s individual energy cost (minor-agents) and optimal strategies for the EGO (major agent). Household (minor-agent) dynamics and cost functions are influenced by: (i) local aggregate effects within their RPC and global interactions across the interconnected CoC network, and (ii) the EGO decisions (major-agent strategies). EGO dynamics and cost function are, in turn, influenced by the aggregate effect of all the minor agents. We derive optimal control strategies interpreted as a Nash equilibrium for the formulated game and establish existence, uniqueness under a full-coupling Lasry-Lions monotonicity condition, and a finite-population \(\varepsilon_N\)-Nash approximation guarantee under finite-to-continuum cost-consistency conditions. Numerical experiments conducted on a dense energy network with 100 clusters, each containing 200 heterogeneous households, demonstrate the computational feasibility and economic performance of the proposed MM-GMFG approach.
Published October 2026 , 29 pages
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