Abstract: [Objective]　With the deepening of the energy Internet strategy, the participation of renewable energy and multiple communities continues to rise, the uncertainties in the system increase significantly, and the cooperation and competition between the participating entities become more complex and volatile. Therefore, a hybrid game optimization scheduling method for a multi-community integrated energy system considering multiple uncertainties and electricity-carbon coupling trading is proposed. [Methods]　Firstly, a Stackelberg game model with community integrated energy system (CIES) operators as leaders and users as followers, as well as a two-layer hybrid game optimization model for electricity-carbon coupling trading between CIESs, are constructed. Then, the uncertainty models of grid electricity price and renewable energy output are constructed using fuzzy sets based on the Wasserstein distance. Finally, the alternating direction multiplier method (ADMM) combined with the duality principle is used to solve the model in a distributed manner, and the effectiveness of the model is verified through case studies. [Results]　The proposed model and method can effectively improve the benefits of participating entities and reduce the carbon emissions of the system. [Conclusions]　This method effectively coordinates the conflicts of interest of multi-community systems, realizes the coordinated optimization of electricity and carbon under multiple uncertainties, and is of great significance to promote the optimal operation of community systems with high penetration of renewable energy

Key words: distributionally robust optimization, community integrated energy system (CIES), Stackelberg game, cooperative game, bi-level optimization, electricity-carbon coupling trading, distributed algorithm, Wasserstein distance