An integrated energy-efficient train operation approach based on the space-time-speed network methodology

Document Type

Journal Article

Publication Date


Subject Area

mode - subway/metro, planning - methods, operations - scheduling


Energy reduction, Regenerative energy, Space-Time-Speed network methodology, Dynamic programming, Discrete differential dynamic programming


Reduction on the traction energy and increasing of the reused regenerative energy are two main ways for saving energy in metro systems, which are related to the driving strategy as well as the train timetable. To minimize the systematic energy, this paper proposes an integrated energy-efficient train operation method in which the driving strategy and the train timetable are jointly optimized. Firstly, the models of calculating the traction energy and the reuse of the regenerate energy are introduced with the constraints of the train operation. Then, the systematical optimization model is formulated by taking the net energy (i.e., the difference between the traction energy and the reused regenerate energy) as the objective function. Based on the Space–-Time-Speed network methodology, the optimization model is transformed into a discrete decision problem. Next, two algorithms are used to solve the problem. The dynamic programming algorithm is used to obtain the global optimal solution, and the discrete differential dynamic programming algorithm is applied to get the approximate optimal solution to reduce the computing time. Finally, two numeral examples are conducted to illustrate the effectiveness of the proposed method on energy saving. The method can reduce the net energy consumption by up to 25.0% compared to the result without optimization and by up to 8.7% compared to the result by using the two-stage method.


Permission to publish the abstract has been given by Elsevier, copyright remains with them.


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