Conditional distributionally robust dispatch for integrated transmission-distribution systems via distributed optimization

With the growing penetration of renewable energy in power systems, its stochastic nature poses significant challenges to the reliable operation of integrated transmission-distribution systems (ITDSs). However, most existing approaches for handling uncertainty overlook the statistical relationship between the wind power forecast value and its associated forecast error, with the latter being a conditional distribution under the given prediction. Approaches that disregard the structural information of the true distribution often lead to overly conservative solutions and exhibit poor out-of-sample performance. This paper closes this gap by proposing a conditional distributionally robust optimization (DRO) method for ITDSs. Specifically, a novel ambiguity set is built by exploiting the dependence of the wind power forecast error on its forecast value, which differs from most of the existing ones. Consequently, a conditional DRO framework is developed for the ITDS dispatch problem under uncertainty. To ensure tractability, the model is reformulated into a linear programming problem through the duality theory-based transformation and Conditional Value-at-Risk (CVaR) approximation. Furthermore, a self-adaptive alternating direction method of multipliers (ADMM) is applied to enable a distributed solution to improve computational efficiency and preserve privacy. Case studies demonstrate that the proposed approach outperforms regular DRO in minimizing dispatch costs and satisfying reliability requirements due to the utilization of a more informed ambiguity set. Also, the distributed algorithm reduces solution time and scales well under various ITDSs.