Virtual energy flow-based carbon emission optimization and hybrid game model for multi-park integrated energy systems

To advance sustainable energy management in Park Integrated Energy Systems (PIESs), this paper proposes a hybrid game model among multiple PIESs to reduce carbon emissions under carbon emission quota (CEQ) policies. We introduce a virtual energy flow-based carbon emission optimization (VEF-CEO) method, where the virtual energy flow refers to an energy allocation determined by trading contracts rather than physical transmission paths. This approach linearizes emission calculations and resolves locational carbon price disparities. Within PIES, a Stackelberg game model transfers CEQ assessment costs to the load side, clarifying carbon reduction responsibilities and enhancing collaborative effects. Among PIESs, a cooperative game model improves CEQ satisfaction and economic benefits through coordination. The Karush-Kuhn-Tucker (KKT) conditions transform the Stackelberg model into a single-level model, and the Augmented Lagrange based Alternating Direction Inexact Newton (ALADIN) method is employed for non-convex model distributed solving. Case study demonstrates that cooperative strategies increase revenues by 21.4% and 51.3% for two PIESs respectively, and achieve complete wind power accommodation. The Stackelberg game successfully steers user consumption via price signals, and the VEF-CEO method outperforms traditional methods in fairness and computational efficiency. These findings validate the effectiveness of hybrid game approach, VEF-CEO method, and ALADIN algorithm for PIES optimization.