Inter-area coordination approach for metro train regulation under localized bi-directional power supply shortage during peak periods

Faults in the traction power supply system of metro lines frequently cause Localized Bi-directional Power Supply Shortage (LBPSS) during peak periods, significantly restricting the traction power available to trains in the under-supplied area, and have knock-on impacts on train operations in other regions. To mitigate the impacts of LBPSS on the entire line, this paper proposes an inter-area coordination approach for the train regulation problem, dividing the global problem into three sequential sub-problems. In the first stage, a cooperative control approach optimizes the control strategies in the under-supplied area, restoring the balance between power supply and demand within the power supply capacity constraints. Building on these results, the second stage reschedules the train timetable in the well-supplied areas using multiple dispatching measures. Since synchronization of entry and exit times between different regions may not be fully achieved in the first two stages, the third stage fine tures hard-to-synchronize entry/exit times, and adjusts control strategies in the under-supplied area via feedback adjustment. To address the unique challenges of each sub-problem, this paper adopts the specific algorithms: Independent Deep Q-Networks (IDQN) for cooperative control, the GUROBI solver for timetable rescheduling, and Adaptive Large-scale Neighborhood Search (ALNS) for fine-tuning synchronization. Notably, for complex constraints associated with the feedback adjustment problem, an improved ALNS algorithm is introduced, which incorporating a constraint operator to enhance convergence speed and solution quality through heuristic rules. Finally, numerical experiments based on the Beijing Metro Yizhuang Line validate the effectiveness of the proposed approach. Results indicate that the solution quality improves by up to 20.0% and 2.8% compared to two previous train regulation approaches: the conservative approach based on maximum traction power and the two-stage approach for canceling hard-to-synchronize times.