Bi-Level Coordinated Optimal Operation of a Multi-Microgrid System with Shared Energy Storage

To improve sustainable operation of multi-microgrid (MMG) systems with high penetration of renewable energy, this paper proposes a bi-level coordinated optimization method based on Stackelberg and cooperative games to address wind–photovoltaic output fluctuations, stakeholder coordination, and low-carbon dispatch under shared energy storage (SES). At the upper level, the shared energy storage operator (SESO) acts as the leader and the MMG coalition as the follower, forming a Stackelberg model for time-of-use service pricing and coordinated response. At the lower level, the coalition dispatch integrates tiered carbon trading, power-to-gas (P2G), and carbon capture and storage (CCS), together with a time-correlated continuous-budget uncertainty set and a two-stage robust scheduling model for wind power, photovoltaic output, and electricity prices. Marginal economic contribution is defined by the change in total system cost caused by an MG joining the coalition and is used to construct an asymmetric Nash benefit-allocation mechanism. Particle swarm optimization (PSO), the alternating direction method of multipliers (ADMMs), and column-and-constraint generation (C&CG) form a hierarchical nested solution framework: PSO searches the upper-level service prices, ADMM coordinates the coalition’s continuous coupling variables, and C&CG generates adverse scenarios for the coalition-level two-stage robust problem. Tests on the IEEE 33-bus system show that, relative to deterministic optimization, robust scheduling incurs an 11.33% nominal operating-cost premium but reduces carbon emissions from 1478.55 to 1318.46 kg and improves adaptability under uncertain scenarios. The marginal-contribution-based Nash allocation keeps every MG’s allocated cost below its stand-alone cost. The proposed method, therefore, balances operating economy, robustness, low-carbon performance, and stakeholder benefits.