Distributionally Robust Bi-Level Optimization of Distribution Network and Charging Stations for Sustainable Operation Under Climate–Charging Load Uncertainty

With the large-scale integration of electric vehicles (EVs), charging demand exhibits significant spatiotemporal variability, further intensified by climatic factors, which makes it difficult for existing uncertainty models to capture underlying dependency structures. To address this issue, this paper proposes a Copula–Wasserstein-based distributionally robust optimization (C-WDRO) framework for the coordinated operation of distribution networks and charging stations. A climate-sensitive physical mapping model of electric vehicle energy consumption is first developed to establish a coupled climate–energy–load mechanism. Copula functions are then used to characterize dependencies among temperature, precipitation, and charging demand, and are incorporated into a bi-level optimization formulation. The model is solved using Karush–Kuhn–Tucker (KKT) conditions and a column-and-constraint generation (C&CG) algorithm. Case studies on the IEEE 33-bus system show that the proposed method reduces total operating cost by 4.26% compared with robust optimization (RO), while maintaining economic efficiency, and reduces the load shedding rate by 0.14 percentage points compared with Wasserstein distributionally robust optimization (WDRO), while keeping voltage security. These results demonstrate that explicitly modeling dependency structures can enhance operational efficiency and support more sustainable and reliable power–transportation system operation under uncertainty.