Joint optimization of multi-train cooperative driving profiles and timetables for energy-efficient urban rail operations

Punctuality and energy consumption are two critical performance indicators for urban rail systems to provide cost-efficient and high-quality service. This paper presents a novel energy-efficient optimization method for dynamic scheduling of urban rails with wayside energy storage devices (WESD). Specifically, the delays and net traction energy (i.e. total energy imported from grid) in disruptions are minimized by jointly optimizing multiple trains' arrival/departure time at stations, speed profiles and traction/braking force, so that the direct utilization of a braking train's regenerative energy for other accelerating trains can be improved and the excessive energy to be stored in WESD is reduced. First, a heuristic method is used to obtain a preliminary timetable for the purpose of recovering delays. The priority of the train is then determined according to the departure time of the train, and each iteration only optimizes the operation process of the train with the highest priority until the operation of all trains within the specified time window is optimized. A weighted sum approach is adopted to transform the problem into a single-objective nonlinear optimization model, which is then solved using the EsDEr_NR algorithm. Simulation verification was conducted using the Beijing Yizhuang Line. The results show that this method reduces the net traction energy consumption 51.31% when recovering from delays. Additionally, the capacity requirements of WESD can be reduced by 11.12%.