Increasing the regenerative braking energy for railway vehicles

Shaofeng Lu, Paul Weston, Stuart Hillmansen, Hoay Beng Gooi, Clive Roberts

Research output: Contribution to journalArticlepeer-review

108 Citations (Scopus)


Regenerative braking improves the energy efficiency of railway transportation by converting kinetic energy into electric energy. This paper proposes a method to apply the Bellman-Ford (BF) algorithm to search for the train braking speed trajectory to increase the total regenerative braking energy (RBE) in a blended braking mode with both electric and mechanical braking forces available. The BF algorithm is applied in a discretized train-state model. A typical suburban train has been modeled and studied under real engineering scenarios involving changing gradients, journey time, and speed limits. It is found that the searched braking speed trajectory is able to achieve a significant increase in the RBE, in comparison with the constant-braking-rate (CBR) method with only a minor difference in the total braking time. An RBE increment rate of 17.23% has been achieved. Verification of the proposed method using BF has been performed in a simplified scenario with zero gradient and without considering the constraints of braking time and speed limits. Linear programming (LP) is applied to search for a train trajectory with the maximum RBE and achieves solutions that can be used to verify the proposed method using BF. It is found that it is possible to achieve a near-optimal solution using BF and the solution can be further improved with a more complex search space. The proposed method takes advantage of robustness and simplicity of modeling in a complex engineering scenario, in which a number of nonlinear constraints are involved.

Original languageEnglish
Article number6818443
Pages (from-to)2506-2515
Number of pages10
JournalIEEE Transactions on Intelligent Transportation Systems
Issue number6
Publication statusPublished - 1 Dec 2014


  • Bellman-Ford (BF) algorithm
  • computation efficiency improvement
  • dynamic programming
  • energy-saving strategy
  • train braking energy increment


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