Energy-Efficient Driving for a Single Train
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(Published version)
Date
2023
Authors
Pudney, P.
Editors
Su, S.
Tian, Z.
Goverde, R.M.P.
Tian, Z.
Goverde, R.M.P.
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Book chapter
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Lecture Notes in Mobility, 2023 / Su, S., Tian, Z., Goverde, R.M.P. (ed./s), vol.Part F814, Ch.3, pp.41-67
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Abstract
There are infinitely many speed profiles that a train could follow between one station and the next, even if the total journey duration is fixed. Finding the most energy-efficient way to drive a train between stops can be formulated, and solved, as an optimal control problem. The motion of the train is described by a pair of differential equations, with parameters including the tractive and braking effort curves of the train, resistance forces, track gradient forces and track curvature forces. Speed limits and timing requirements impose constraints on the motion. The optimal driving strategy has only five driving modes: power, hold, coast, regen and brake. Furthermore, the necessary conditions for an optimal control can be used to determine the optimal sequence of control modes for a journey, and when the control should be switched between modes. Optimal journey profiles can be calculated quickly enough to provide driving advice that adapts in real-time to changing conditions on a rail network.
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Copyright 2023 The Author(s), under exclusive license to Springer Nature Switzerland
Access Condition Notes: Accepted manuscript available after 1 October 2025