Carbon-Centric Hybrid-Game Robust Planning of Multiple Integrated Energy Systems Considering Higher-Order Uncertainty

With the growing focus on carbon neutrality, integrated energy systems (IESs) have become vital for low-carbon transitions. However, conventional multi-IES planning remains energy-centric, overlooking inter- and intra-system interactions of carbon trading and carbon-based pricing. Therefore, this paper proposes a carbon-centric hybrid-game robust planning model for multi-IESs under higher-order uncertainties (HOUs). The proposed model integrates an inter-IES Nash bargaining game to enhance system-wide coordination with dynamic carbon trading, and an intra-IES Stackelberg game to improve supplier-user interaction via carbon-based energy pricing. A novel low-carbon flexible retrofitted CHP structure, alongside its extended carbon emission flow (ECEF) model, is developed to provide physical support for dynamic carbon attribution. Additionally, to address HOUs in renewable outputs, a confidence band-based ambiguity set is constructed, considering both parameter and distributional variations for system robust planning. A decomposition algorithm combining adaptive ADMM and parallel C&CG is implemented to ensure computational tractability. Finally, case studies on a real-world system in Southern China validate the effectiveness of the proposed model in improving emission reduction, operational flexibility, and planning robustness.