A Potential-Game Framework for Co-Clearing Electricity, Carbon Allowance, and Tradable Green Certificate Markets

Under dual-carbon goals, the coupling of electricity, carbon allowance, and tradable green certificate (TGC) markets creates complex strategic interactions often overlooked by conventional models, leading to inaccurate policy simulations. Existing game-theoretic methods further struggle with high complexity, lack of equilibrium guarantees, and conflicting objectives. To address these issues, this paper proposes a potential-game-based co-clearing method for integrated electricity-carbon allowance-TGC markets. A unified potential function is constructed that jointly captures the maximization of social welfare (electricity market), the minimization of carbon allowance cost, and the maximization of TGC revenue. A penalty mechanism coordinates electricity, carbon allowance, and TGC prices by penalizing inter-market decision inconsistencies. The model rigorously ensures the existence and uniqueness of the Nash equilibrium, enhancing analytical reliability. Case studies on a five-bus system demonstrate that the method effectively captures multi-market interactions. Results confirm improved market coordination and provide a robust framework for evaluating policy impacts in coupled energy-environment systems.