Energy-efficient train control using nonlinear bounded regenerative braking

Gerben M. Scheepmaker, Rob M.P. Goverde

Research output: Contribution to journalArticleScientificpeer-review

28 Citations (Scopus)
42 Downloads (Pure)


Energy-efficient train control (EETC) has been studied a lot over the last decades, because it contributes to cost savings and reduction of CO2 emissions. The aim of EETC is to minimize total traction energy consumption of a train run given the running time in the timetable. Most research is focused to apply mechanical braking on this problem. However, current trains are able to use regenerative braking, which leads to another optimal driving strategy compared to mechanical braking. Research on EETC with a realistic nonlinear bounded model for regenerative braking or a combination between regenerative and mechanical braking is limited. The aim of this paper is to compare the difference between the EETC with regenerative and/or mechanical braking. First, we derive the optimal control structure for the problems with different braking combinations. Second, we apply the pseudospectral method on different scenarios where we investigate the effect of varying speed limits and gradients on the different driving strategies. Results indicate that compared to pure mechanical braking, combined regenerative and mechanical braking leads to a driving strategy with higher energy savings, a lower optimal cruising speed, a shorter coasting phase and a higher speed at the beginning of the braking phase. In addition, a nonlinear bounded regenerative braking curve leads to a different driving strategy compared to a constant braking rate that is commonly used in literature. We show that regenerative braking at a constant braking rate overestimates the total energy savings.

Original languageEnglish
Article number102852
Number of pages20
JournalTransportation Research Part C: Emerging Technologies
Publication statusPublished - 2020


  • Energy minimization
  • Optimal train control
  • Pseudospectral method
  • Regenerative braking
  • Trajectory optimization


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  • Energy-efficient Train Timetabling

    Scheepmaker, G. M., 2022, Trail / TU Delft. 250 p.

    Research output: ThesisDissertation (TU Delft)

    Open Access
    204 Downloads (Pure)

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