To accommodate China’s electricity market reforms integrating medium and long-term (MLT) transactions and spot transactions, and to boost renewable energy consumption through the spot market, this paper proposes an optimized cross-provincial electricity trading strategy model based on a two-layer game framework. The proposed model incorporates an MLT green certificate contract decomposition method, enabling nested optimization of green certificate contracts and scheduling plans for cross-provincial power transactions. To encourage broader participation, a bilateral green certificate trading framework is established, which globally optimizes green certificate allocation to increase benefits for market participants. A Nash-Stackelberg game model is introduced to address complex game interactions among multiple participants under the green certificate mechanism and the limitation of assuming complete rationality. The game model combines supply and demand sides with an embedded demand-side evolutionary game. Additionally, an improved Aquila optimization algorithm (IAOA) is developed to accurately calculate electricity supply and demand. The algorithm integrates a Circle chaotic map, Sobol sequence, random walk strategy, and filtering technology to enhance optimization capabilities and manage complex constraints. The algorithm is then embedded with a distributed iterative approach to achieve equilibrium strategies. A real-world case study was conducted to validate the feasibility and effectiveness of the proposed model. The results demonstrate that the proposed approach effectively achieves equilibrium, optimizes trading strategies, and fosters win-win, coordinated development among participants in the cross-provincial electricity market.
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