Decentralized coordinated planning model for integrated energy systems under seasonal distribution and source–load uncertainties: A two-stage multi-layer robust optimization and Nash bargaining approach

Effective equipment capacity planning and energy scheduling are vital for improving the economic efficiency, energy savings, and carbon reduction of integrated energy systems (IES). The current independent IES planning overlooks interactions among multi-stakeholders across regions, resulting in suboptimal designs. Coordinated planning of multi-regional IESs can leverage spatial–temporal characteristics and resource complementarities to improve efficiency and allocation. However, uncertainties in both supply and demand introduce fluctuations that threaten system stability, and the absence of an effective energy-sharing mechanism complicates optimal configuration and scheduling. To address these challenges, we propose a decentralized framework for coordinating multi-regional IES configuration and scheduling under uncertainty through energy sharing. This framework incorporates uncertainties in supply-side output, load demand, and seasonal distributions, constructing a two-stage three-layer robust optimization model. A decentralized coordinated optimization framework, based on cooperative games, facilitates supply–demand interactions among regional IESs, with the Nash bargaining method for benefit allocation. The solution process uses the Column-and-Constraint Generation algorithm to decouple the main problem and subproblem for faster computation, while the Alternating Direction Method of Multipliers algorithm ensures distributed solving and protects participant privacy. Results demonstrate that the model mitigates uncertainty impacts, enhances the energy system’s economic and environmental performance, and fosters long-term stakeholder cooperation.