Distributed optimization scheduling of flexible resources considering distributionally robust chance constraints

With the widespread integration of flexible resources such as distributed energy storage and controllable loads, the scheduling of modern power systems faces new challenges. On the one hand, the emergence of new grid architectures, such as microgrids and regional autonomous grids, is driving a shift in scheduling model from traditional centralized management to distributed scheduling. On the other hand, the large-scale integration of uncertain renewable energy sources significantly increases the complexity of deterministic scheduling. Therefore, a distributed optimization scheduling strategy for flexible resources that accounts for the uncertainty of renewable energy sources is proposed. Firstly, based on the Wasserstein distance, a fuzzy set of forecast errors is established to provide an approximate quantification of renewable energy uncertainty. Secondly, distributionally robust chance constraints are constructed to characterize the impact of uncertainty on system operations. Then, a distributed scheduling model is developed that incorporates the operational characteristics of flexible resources, including energy storage systems, electric vehicles, and controllable loads. To address the adverse effects of discrete controllable loads on algorithmic convergence, an improved consensus alternating direction method of multipliers (C-ADMM) is proposed, incorporating a branch-and-bound framework. Finally, the effectiveness of the proposed method is verified using a modified IEEE 30-bus system. Case study results show that the proposed strategy reduces the maximum economic cost by 2.07% compared with robust optimization under different fuzzy set radii, and decreases the maximum average constraint violation probability by 56.86% compared with stochastic optimization under various wind power forecast error distributions. Compared with the traditional C-ADMM, the improved C-ADMM reduces the convergence metric from 1.14 to 0.015.