A new look at the shape characteristics of optimal speed profile for energy-efficient train control considering multi-train power flow

The key point for the energy-efficient train control (EETC) in a multi-train system is effectively utilizing the output power of other trains. However, obtaining the optimal solution of the EETC problem considering multi-train power flow requires high-precision calculation of the adjoint variables, which is time-consuming. In this paper, we revisit the problem and introduce a speed volatility functional to analyze the shape of the optimal speed profile and the corresponding optimal control modes for the train under different external power and track gradients. Based on this analysis, a fast-solving algorithm is devised. Case studies are conducted to validate our theoretical results, and demonstrate that the proposed algorithm achieves a significant improvement in computational speed (over 99%) compared to the global optimal algorithm (Rao et al., 2023a) while ensuring the energy saving effectiveness.