With the energy consumption rising in rail transport, the railway sector is showing increasing interest in the energy-efficient operation of freight trains. Freight trains require more complicated driving strategies than ordinary passenger trains do due to their heavy loads, especially in the long-distance steep downhill (LDSD) sections that are very common in freight rail lines in China. This paper studies the energy-efficient operation of a freight train considering LDSD sections. An optimal control model including regenerative and pneumatic braking is developed for the freight train. Then, when a train leaves/enters the LDSD section, we verify the uniqueness of control transitions and discuss the speed profile linkage between LDSD and its adjacent sections, which indicates that the periodic braking should be applied on LDSD sections for optimality. Additionally, given the same running time for the entire journey, our analysis shows that electrical braking-full braking strategy is more energy-efficient than coasting-full braking strategy on LDSD sections. Finally, a numerical algorithm for the optimal driving solution is proposed. The simulation results demonstrate that the driving strategies generated by the proposed algorithm performs better than those from fuzzy predictive control and field operation regarding energy saving.
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