A distributed optimization method for wind-storage systems with superlinear convergence

Distributed energy storage systems have been widely deployed to mitigate power generation fluctuations from wind farm clusters due to their flexible regulation capability. Distributed optimization is well-suited for managing these systems because of its lower communication overhead and enhanced robustness. However, conventional distributed methods often suffer from low computational efficiency and slow convergence. To address these limitations, this paper proposes a novel distributed optimization method that achieves both low communication costs and superlinear convergence. First, a bi-level optimization model is developed for wind-storage systems, incorporating global–local power coordination, equipment life-cycle cost, and the relative carbon payback period. The payback period is formulated using a high-order Taylor series expansion to enhance numerical accuracy. Secondly, a distributed optimization algorithm based on optimal control theory is proposed. By leveraging Pontryagin’s maximum principle and forward–backward difference equations, the method avoids Hessian inversion while guaranteeing this accelerated convergence rate. Finally, comprehensive simulations verify that the proposed approach reduces carbon emissions and enhances system robustness. Compared to the distributed gradient descent and network Newton algorithms, the proposed method achieves computational efficiency that is 2.92 and 51.37 times higher, respectively, while also improving solution accuracy. • A bi-level distributed energy storage system optimization model is developed to coordinate global power dispatch with local objectives, including life-cycle cost and relative carbon payback period. • The relative carbon payback period is formulated via a high-order Taylor series expansion to capture the time-varying nature of carbon intensity. • An optimal control-based distributed optimization method is proposed to efficiently solve the high-order model with low communication cost. • Comparative results demonstrate higher solution accuracy, shorter computation time, and better adaptability to complex wind-storage systems.