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Energy-Efficient Train Driving Based on Optimal Control Theory

Author

Listed:
  • Wolfram Heineken

    (Fraunhofer Institute for Factory Operation and Automation IFF, Sandtorstraße 22, 39106 Magdeburg, Germany)

  • Marc Richter

    (Fraunhofer Institute for Factory Operation and Automation IFF, Sandtorstraße 22, 39106 Magdeburg, Germany)

  • Torsten Birth-Reichert

    (Fraunhofer Institute for Factory Operation and Automation IFF, Sandtorstraße 22, 39106 Magdeburg, Germany
    Hochschule für Angewandte Wissenschaften, Berliner Tor 5, 20099 Hamburg, Germany)

Abstract

Efficient train driving plays a vital role in reducing the overall energy consumption in the railway sector. An energy minimising control strategy can be computed using the framework given by optimal control theory; in particular, the Pontryagin maximum principle can be used. Our optimisation approach is based on an algorithm presented by Khmelnitsky that considers electric trains equipped with regenerative braking. A derivation of Khmelnitsky’s theory from a more general formulation of the maximum principle is given in this article, and a complete list of switching cases between different driving regimes is included that is essential for practical application. A number of numerical examples are added to visualise the various switching cases. Energy consumption data from real-life operation of passenger trains are compared to the calculated energy minimum. In the presented study, the optimised strategy was able to save 37 percent of the average energy demand of the train in operation. The sensitivity of the energy consumption to deviations of the train speed from the optimum speed profile is studied in an example. Another example illustrates that the efficiency of regenerative braking has an effect on the optimum speed profile.

Suggested Citation

  • Wolfram Heineken & Marc Richter & Torsten Birth-Reichert, 2023. "Energy-Efficient Train Driving Based on Optimal Control Theory," Energies, MDPI, vol. 16(18), pages 1-40, September.
    • Handle: RePEc:gam:jeners:v:16:y:2023:i:18:p:6712-:d:1243431
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    References listed on IDEAS

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    1. Janusz Szkopiński & Andrzej Kochan, 2021. "Energy Efficiency and Smooth Running of a Train on the Route While Approaching Another Train," Energies, MDPI, vol. 14(22), pages 1-27, November.
    2. Scheepmaker, Gerben M. & Goverde, Rob M.P. & Kroon, Leo G., 2017. "Review of energy-efficient train control and timetabling," European Journal of Operational Research, Elsevier, vol. 257(2), pages 355-376.
    3. Liu, Rongfang (Rachel) & Golovitcher, Iakov M., 2003. "Energy-efficient operation of rail vehicles," Transportation Research Part A: Policy and Practice, Elsevier, vol. 37(10), pages 917-932, December.
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