As global energy demands continue to rise and the need for sustainable development becomes more urgent, Cross-Border Integrated Energy Systems (CBIES) offer a crucial pathway to improving energy efficiency and security through international collaboration. This paper proposes a bi-level electricity and heat sharing model based on Nash game theory, which optimizes resource allocation and management in cross-border energy systems. The model addresses two sub-problems: maximizing the overall benefits of the alliance and ensuring fair redistribution of those benefits within the alliance. To tackle the complexities of these problems, the Alternating Direction Method of Multipliers (ADMM) is employed in a distributed manner. Additionally, the ARIMA-GARCH model is introduced to handle the uncertainties related to exchange rate volatility in cross-border energy transactions. Carbon capture and storage (CCS) and power-to-gas (P2G) technologies are also integrated into the cogeneration system to promote low-carbon energy production, aligning with environmental sustainability goals. The results show that the upper-level electricity sharing sub-problem reduced the total operational cost from 1,173,330 CNY to 875,582 CNY after 55 iterations, while the lower-level heat sharing sub-problem further optimized the cost to 687,356 CNY after 14 iterations. Post-cooperation cost comparisons showed that the costs for Country B and Country C were reduced by 207,828 CNY and 390,672 CNY, respectively, demonstrating the model’s effectiveness.
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