Research on multi-microgrid interaction scheduling optimization based on an improved ADMM approach

Multi-microgrid systems face significant challenges in distributed optimization scheduling due to high computational complexity, slow convergence, and insufficient privacy protection. To address these issues, this paper proposes an improved alternating direction method of multipliers (Improved ADMM) for efficient and privacy-preserving coordination among multiple microgrids. The proposed method introduces three key enhancements: a residual-balanced adaptive penalty parameter adjustment to accelerate convergence, a proximal regularization term to suppress numerical oscillations, and an asynchronous communication framework with Nesterov acceleration to enhance parallelism and real-time performance. Furthermore, a hierarchical Lagrangian relaxation framework is incorporated to manage mixed-integer and nonconvex constraints, ensuring global feasibility and consistency. Simulation results demonstrate that the improved ADMM significantly outperforms the standard version in convergence speed, computational efficiency, and economic–environmental performance—achieving ∼39% cost reduction and 36% carbon emission reduction while maintaining stable multi-microgrid power coordination. The proposed algorithm provides an effective, scalable, and privacy-aware optimization framework for distributed scheduling in complex energy networks.