Energy minimization in dynamic train scheduling and control for metro rail operations

Since the passenger demands change frequently in daily metro rail operations, the headway, cycle time, timetable and speed profile for trains should be adjusted correspondingly to satisfy the passenger demands while minimizing energy consumption. In order to solve this problem, we propose a dynamic train scheduling and control framework. First, we forecast the passenger demand, and determine the headway and cycle time for the next cycle. Then we optimize the reference timetable and speed profile for trains at the next cycle subject to the headway and cycle time constraints. Finally, the automatic train control system is used to operate trains with real-life conditions based on the reference timetable and speed profile. In this paper, we focus on the optimization of the timetable and speed profile. Generally speaking, the former distributes the cycle time to different stations and inter-stations under the headway constraint, and the latter controls the trains' speeds at inter-stations to reduce the consumption on tractive energy and increase the storage on regenerative energy. In order to achieve a global optimality on energy saving, we formulate an integrated energy-efficient timetable and speed profile optimization model, which is transformed to a convex optimization problem by using the linear approximation method. We use the Kuhn-Tucker conditions to solve the optimal solution and present some numerical experiments based on the actual operation data of Beijing Metro Yizhuang Line of China, which shows that the integrated approach can reduce the net energy consumption around 11% than the practical timetable. Furthermore, with given passenger demand sequence at off-peak hours, the dynamic scheduling and integrated optimization approach with adaptive cycle time can reduce the net energy consumption around 7% than the static scheduling and integrated optimization approach with fixed cycle time.