Multi-objective hybrid game-theoretic framework with distributionally robust chance constraints for multi-energy microgrid energy management

Multi-energy microgrids (MEMGs) have emerged as pivotal enablers for constructing low-carbon, intelligent energy systems, owing to their distinct advantages in multi-energy complementarity and synergistic source-load-storage coordination. Nevertheless, the energy management decision-making process within MEMGs is characterized by escalating complexity. This intricacy stems from the divergent profit-seeking objectives of multiple stakeholders, the pervasive influence of multifaceted uncertainties, and the dual operational imperatives of enhancing energy efficiency while promoting environmental sustainability. This research analyzes the economic and energy flows between the microgrid (MG) and photovoltaic prosumers (PVPs) from both vertical and horizontal perspectives, proposing a MEMG energy management strategy based on Distributionally Robust Chance-Constrained (DRCC) optimization and a multi-objective hybrid game-theoretic approach. Vertically, a Stackelberg game framework is employed to integrate the lower-level PVPs into the upper-level MG model, thereby balancing the economic interests between the operator and the prosumers. Horizontally, a cooperative game model, founded on Nash bargaining theory, is established among the lower-level PVPs. The Alternating Direction Method of Multipliers algorithm is utilized to achieve distributed operational optimization for each entity while preserving privacy. Concurrently, a DRCC optimization methodology, leveraging the Wasserstein metric, is adopted to manage the multifaceted uncertainties inherent in MEMGs, such as renewable energy fluctuations, by adjusting the system's robustness through the Wasserstein radius. Furthermore, an improved Technique for Order Preference by Similarity to Ideal Solution, incorporating Grey Relational Analysis for weight determination and Mahalanobis distance, is proposed to facilitate a coordinated and globally optimal balance between economic and environmental objectives for the MEMG. Numerical case studies and simulations verify that the proposed hybrid game-theoretic model significantly enhances the overall economic benefits and energy utilization efficiency of the MEMG.