Optimal Siting of Electric Ship Battery Swap Stations and Economic Speed Optimization Considering Time-of-Use Electricity Pricing

High energy replenishment cost and low navigation efficiency in inland electric vessels are caused by decoupled decisions on battery swap station siting and cruising speed selection. To address this issue, a coordinated optimization method for swap station layout and sailing speed under time-of-use electricity pricing is investigated. A bi-level multi-objective optimization model is established to describe the coupling between infrastructure planning and vessel operation. At the upper level, the construction and operation costs of battery swap stations are minimized while maximizing the proportion of energy replenishment completed during off-peak electricity periods, using binary siting variables and inter-station distance constraints. At the lower level, given the siting results, cruising speeds on each route segment are continuously optimized to minimize total sailing time and energy replenishment cost. Considering the practical cost transmission characteristics of time-of-use pricing under containerized battery swapping, a charging time-window conversion mechanism is introduced. Electricity prices are converted from vessel arrival times to equivalent settlement prices based on station-side historical charging behavior, thereby revising the conventional energy-cost relationship in speed optimization. Constraints on battery capacity updating, maximum depth of discharge, swap triggering conditions, and segmented speed limits are incorporated to ensure engineering feasibility and navigational compliance. A case study on the Yangtze River involving three representative pure electric vessels is conducted. Results show that, while satisfying endurance and safety speed constraints, the coordinated scheme reduces one swap station and decreases single-voyage replenishment cost by 4000 to 7000 CNY, with an average reduction of 14%, while total sailing time is shortened by 15 to 23 hours. Compared with fixed-speed operation, the optimized speed strategy further reduces replenishment cost by 25 000 to 80 000 CNY, with an average reduction of 45%, and shortens sailing time by 16 to 21.5 hours. Across different vessel types and departure times, the system-level average sailing time is reduced by 19.5 hours and replenishment cost is reduced by approximately 55%. The results confirm that siting-speed coordinated optimization under time-of-use electricity pricing effectively improves the economic performance and operational efficiency of inland electric vessel battery swapping systems.