Energy-efficient speed profile approximation: An optimal switching region-based approach with adaptive resolution

Jie Yang, Limin Jia*, Shaofeng Lu, Yunxiao Fu, Ji Ge

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

21 Citations (Scopus)


Speed profile optimization plays an important role in optimal train control. Considering the characteristics of an electrical locomotive with regenerative braking, this paper proposes a new algorithm for target speed profile approximation. This paper makes the following three contributions: First, it proves that under a certain calculation precision, there is an optimal coast-brake switching region-not just a point where the train should be switched from coasting mode to braking mode. This is very useful in engineering applications. Second, the paper analyzes the influence of regenerative braking on the optimal coast-brake switching region and proposes an approximate linear relationship between the optimal switching region and the regeneration efficiency. Third, the paper presents an average speed equivalent algorithm for local speed profile optimization in steep sections. In addition, this paper simplifies the proof of the optimality of smooth running on a non-steep track in two steps. The effects on energy consumption from two important factors (optimal coast and running time) are systematically analyzed. Extensive simulations verify these points of view and demonstrate that the proposed approximation approach is computationally efficient and achieves sufficient engineering accuracy.

Original languageEnglish
Article number762
Issue number10
Publication statusPublished - Oct 2016


  • Adaptive resolution
  • Energy consumption
  • Simulation study
  • Speed profile approximation


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