Infrastructure planning of intra-city battery swapping stations considering demand uncertainty: a multi-pattern based distributionally robust approach

As intra-city battery swapping stations deployment expands, stakeholders are increasingly recognising the critical role of strategic infrastructure planning. However, the coupling of charging strategy and battery swapping demand uncertainty poses significant challenge for the stations planning. Considering the ambiguity and pattern of demand distribution, this paper develops a two-stage distributionally robust optimisation model to hedge against demand uncertainty with multi-pattern based Type-1 Wasserstein ambiguity set. In the planning stage, the station location and battery deployment decisions are made to minimise the expected total operation cost. In the operation stage, the battery charging strategies are optimised based on diverse demand distribution patterns and time-of-use electricity price structures. Due to its intractability, we provide a lower bound approximation based on support set restriction. And we also present an accelerated column-constraint generation algorithm to solve the problem exactly, by incorporating a family of valid inequalities and a lower bound approximation neighbourhood based heuristic warm-start strategy. Numerical results demonstrate the computational efficiency and effectiveness of our approach. Additionally, a case study in Shanghai demonstrates that the proposed method outperforms alternative approaches and reduces total operation cost by a median of 9.32% compared to the existing deployment.