Distributed robust cooperative optimization of multi-integrated energy systems based on variational inequality-driven non-cooperative game theory

In integrated energy system (IES), multiple uncertainties exist regarding renewable energy output and electricity prices, while traditional electric hydrogen module model fail to accurately characterize the operational states of electrolyzer. Additionally, complex coupling and competitive interests among multi-integrated energy system (MIES) pose significant challenges for effective management. To address these challenges, this paper integrates non-cooperative game theory with distributionally robust optimization (DRO) to propose an efficient and robust operational strategy for MIES. Firstly, a DRO model for IES is established using Wasserstein distance, allowing for a refined modeling of the electric hydrogen module. Subsequently, a non-cooperative game equilibrium model based on variational inequalities (VI) is constructed to describe the interactions among MIES, leading to the development of a VI-driven equilibrium model for non-cooperative games in MIES under distributionally robust optimization. To achieve efficient equilibrium while safeguarding the privacy of each IES, an AOP-BL-ADMM algorithm is developed. Finally, the effectiveness of the proposed method is validated through case analysis.