Distributed EV scheduling in distribution networks with reserve market participation under ambiguous probability distribution

To address the uncertainties inherent in large-scale electric vehicle (EV) charging and renewable energy generation, this paper develops a distributionally robust joint chance-constrained (DRJCC) model under the ambiguous probability distribution measured by Kullback-Leibler divergence (KL-divergence) to jointly consider the energy and reserve markets. To overcome the intractability of the DRJCC model, an optimized Bonferroni approximation (OBA) method is introduced. This method marks a significant improvement over the traditional Bonferroni approximation (BA) by allowing the risk levels of individual chance constraints, which are decomposed from the joint chance constraint, to be treated as decision variables. This flexibility leads to a 10.6 % cost reduction compared to the BA approach by leveraging differences in cost-risk characteristics across multiple chance constraints, enabling more economical decisions. Unlike moment-based methods, the proposed approach leverages distributional information, allowing for a better balance between economics and systemic risk across different KL-divergence levels. Additionally, the residual balanced alternating direction multiplier method is employed to coordinate EV charging stations and the distribution network in a distributed manner, resulting in higher computational efficiency and better scalability. The model's effectiveness is demonstrated on modified IEEE 33-bus and 123-bus systems, showcasing its ability to efficiently balance operational costs and system risks.