A tri-level cooperative optimization framework for electric vehicle charging via a mean-field reverse Stackelberg game

The rapid growth of electric vehicles (EVs) introduces significant operational challenges to power distribution networks (PDNs), particularly when uncoordinated charging exacerbates peak demand and violates grid constraints. Existing pricing-based or bi-level coordination schemes often suffer from limited scalability, weak incentive compatibility, and the inability to capture the hierarchical interactions among distribution network operators (DNOs), aggregators, and EV users. To address these limitations, this paper proposes a tri-level cooperative optimization framework that integrates mean-field game (MFG) theory with a reverse Stackelberg game (RSG) mechanism. The upper-level performs PDN dispatch to enforce network constraints, the middle-level embeds an RSG-based dynamic pricing strategy to ensure incentive-aligned user responses, and the lower-level models large-scale EV charging decisions via an MFG approximation. However, this hierarchical formulation tightly couples nonconvex network constraints with the mean-field RSG process, resulting in substantial computational difficulty. To overcome this challenge, a scalable hierarchical decomposition algorithm is developed to efficiently solve the integrated model. Simulation studies demonstrate that the proposed mechanism significantly improves system performance. Compared with a representative retail pricing benchmark, the proposed method achieves an 18.80% reduction in PDN peak cost, while increasing EV user utility by 34.5% and system social welfare by 16.6%, indicating improved grid operation efficiency and enhanced user participation.