A bi-level hybrid game framework for Stochastic Robust optimization in multi-integrated energy microgrids

Multi-Integrated Energy Microgrids (IEMs) facilitate efficient renewable energy utilization through coordinated scheduling across interconnected systems. However, the dynamic interactions between renewable energy sources and multi-energy loads result in complex benefit couplings and significant operational uncertainties, creating substantial challenges for scheduling optimization. To tackle these issues, this paper introduces an innovative hybrid game framework tailored for IEMs. Specifically, the framework employs a bi-level hybrid game structure, where IEMs act as leaders and multi-energy loads as followers. Additionally, profit allocation among IEMs is regulated through a Nash game mechanism, ensuring equitable and efficient resource distribution. This framework employs Two-Stage Stochastic Robust Optimization (TSSRO) to address uncertainties, including variations in renewable energy generation, multi-energy loads, and electricity pricing. Initial scenarios for uncertain variables are generated using Spectrally Normalized Conditional Generative Adversarial Networks (SNCGAN). Leveraging the Karush-Kuhn-Tucker (KKT) conditions, the bi-level game is transformed into a single-level optimization problem, enhancing computational efficiency. The solution approach combines the Alternating Direction Method of Multipliers (ADMM) with a Column and Constraint Generation Algorithm using an Alternating Iteration Strategy (C&CG-AIS), effectively optimizing IEM operational performance. Numerical validation demonstrates that the proposed framework significantly improves collaborative optimization in multi-IEM systems, showcasing enhanced stability and adaptability over conventional models.