Fully distributed expansion planning for cross-border energy systems using hierarchical dynamic game embedded with carbon emissions

The expansion planning of cross-border energy systems is essential for effectively integrating renewable energy sources on a broader spatial scale and addressing disparities in resource distribution. This paper presents a fully distributed expansion planning approach based on hierarchical dynamic games and multi-agent systems, accounting for data privacy and information interaction among multiple energy subsystems within cross-border energy networks. This study establishes both centralized cooperative and decentralized non-cooperative hierarchical dynamic game models. In the non-cooperative model, energy subsystems seek to maximize their own benefits in the light of neighboring agents' strategies, whereas in the cooperative model, they form alliances to minimize a joint cost. The model also incorporates the impact of carbon dioxide emissions, allowing for the analysis of future energy network evolution under dual carbon reduction goals. The proposed approach is validated through a modified cross-border energy system test case, demonstrating that the fully cooperative game model can maximize system-wide benefits. In the non-cooperative framework, with limited interaction involving coupling variable information, the optimal strategy converges to a Nash equilibrium, balancing the benefits of rational intelligent agents and maximizing energy data security.