Energy-efficient train control (EETC) has been studied a lot over the last decades, because it contributes to cost savings and reduction of CO₂ emissions. The aim of EETC is to minimize total traction energy consumption of a train run given the running time in the timetable. Most research is focused to apply mechanical braking on this problem. However, current trains are able to use regenerative braking, which leads to another optimal driving strategy compared to mechanical braking. Research on EETC with a realistic nonlinear bounded model for regenerative braking or a combination between regenerative and mechanical braking is limited. The aim of this paper is to compare the difference between the EETC with regenerative and/or mechanical braking. First, we derive the optimal control structure for the problems with different braking combinations. Second, we apply the pseudospectral method on different scenarios where we investigate the effect of varying speed limits and gradients on the different driving strategies. Results indicate that compared to pure mechanical braking, combined regenerative and mechanical braking leads to a driving strategy with higher energy savings, a lower optimal cruising speed, a shorter coasting phase and a higher speed at the beginning of the braking phase. In addition, a nonlinear bounded regenerative braking curve leads to a different driving strategy compared to a constant braking rate that is commonly used in literature. We show that regenerative braking at a constant braking rate overestimates the total energy savings.

在过去的几十年中，对节能火车控制（EETC）进行了大量研究，因为它有助于节省成本和减少CO ₂排放。EETC的目标是在时间表中给出运行时间的情况下，将火车运行的总牵引能量消耗降至最低。大多数研究集中于将机械制动应用于此问题。但是，当前的火车能够使用再生制动，与机械制动相比，这导致了另一种最佳驾驶策略。利用用于再生制动或再生制动与机械制动的组合的逼真的非线性有界模型对EETC的研究是有限的。本文的目的是比较EETC与再生制动和/或机械制动之间的区别。首先，我们推导了针对不同制动组合问题的最优控制结构。其次，我们将伪谱方法应用于不同的场景，在其中我们研究了变化的速度限制和坡度对不同驾驶策略的影响。结果表明，与纯机械制动相比，再生制动和机械制动相结合可产生一种具有更高节能，更低最佳巡航速度的驾驶策略，在制动阶段开始时，滑行阶段更短，速度更高。此外，与文献中通常使用的恒定制动率相比，非线性有界再生制动曲线会导致不同的驱动策略。我们表明，以恒定制动速率进行再生制动会高估总的节能量。