**8. Conclusions**

The basis of eco-driving strategy is the substitution of the use of braking with coasting periods. Trains equipped with regenerative braking allow for recovering the kinetic energy during deceleration phases, which can be used by other trains or sent back to the utility grid in AC power supply systems or in DC systems equipped with reversible substations. In this context of high use of regenerated energy, it is necessary to analyze whether eco-driving design based on coast commands has an impact on energy savings. In this work, an eco-driving strategy has been compared to a standard driving strategy. The former one consists on holding a cruise speed without braking (if braking is needed to maintain that speed, it is not applied and the speed increases) and coasting before braking. The latter one consists of holding the cruise speed and braking if it is necessary to do so. A comparison has been performed in two real case studies by simulating a train on two high-speed Spanish lines. One of them is a section of the Madrid–Barcelona high-speed line, which is fed by a 2 × 25 kV power supply system. The other one is a section of the Madrid–Sevilla high-speed line, which is fed by a 1 × 25 kV

power supply system. The influence of the regenerated energy losses at the catenary—which depend on its linear resistance, and the engine traction and braking efficiency, which are considered constant and equal—on the energy consumption of the speed profiles generated for both driving strategies has been studied. To generate the driving commands, a nature-inspired algorithm called MOPSO has been used for both driving strategies. Speed profiles have been obtained by simulating driving commands. For each driving strategy and for some values of the linear resistance and engine efficiency, the Pareto curves consisting of the non-dominated speed profiles in terms of energy consumption and running time have been computed. The difference in energy consumption between the considered driving strategies has been calculated for different values of the catenary resistance, engine efficiency and running time, with a special focus on the commercial time. For the commercial running time, the eco-driving strategy produces energy savings with respect to the standard driving strategy between 2.48% and 4.69% at the pantograph for the first case study and between 9.7% and 12.55% for the second.

For a specific running time, the holding speed without braking and final coasting eco-driving strategy produces solutions that consume less energy than the holding speed with braking standard driving strategy. The difference in energy consumption between the considered driving strategies is larger when the losses at the catenary are more significant and when the engine is less efficient.

It was found that the holding speed without braking and final coasting driving strategy produces speed profiles more energy-efficient than the standard driving strategy, mostly due to the final coast phase. For slower speed profiles, the energy consumption is much lower, as the cruise speed is lower; the final coast phase takes place more close to the brake curve at the end of the section; and then the difference in energy consumption between the considered driving strategies is smaller.

Finally, it can be concluded that, although the power supply network presents a high receptivity to braking energy, the eco-driving design can produce significant energy savings.

**Author Contributions:** A.C.: investigation, writing—original draft preparation. A.F.-R.: investigation, software, writing—original draft preparation. A.P.C.: conceptualization, methodology, investigation, writing—review and editing. A.F.-C.: conceptualization, methodology, investigation, writing—review and editing. M.C.F.: writing—review and editing. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Conflicts of Interest:** The authors declare no conflict of interest.
