Nash-Stackelberg-Nash three-layer mixed game optimal control strategy for multi-integrated energy systems considering multiple uncertainties

With the development of distributed energy technology, traditional energy users are transitioning to energy prosumer (EP) with independent power generation capacity. To further improve the absorption rate of renewable energy and the interactive benefits of each subject, and solve the problem of cooperative optimization operation of integrated energy system (IES) with multiple EPs in the same distribution network. In this paper, a multi-IES three-layer mixed game optimal control strategy considering multiple uncertainties is proposed. Chance constrained programming and robust optimization method are used to deal with the uncertainty of renewable energy and electricity price respectively. The upper level determines the electricity price and heat price to minimize the IES operating cost, and the lower level responds to the IES electric heating decision to maximize the EP benefit. Then, Karush-Kuhn-Tucker (KKT) condition is used to solve the Stackelberg game between IES and EP by combining Big-M and McCormick method, and the cooperative game between EP and IES is solved by combining alternating direction multiplier method (ADMM). Case shows that the strategy proposed can effectively solve the complex model with three-layer mixed game, significantly improves total system revenue by 4.97 % and reduces total carbon emissions by 20.69 %.