## 5 Case Study
### Effect of the Target Times on the Energy Consumption  
It is clear that the arrival timing point has a decisive role in the energy consumed by a train because it determines the running time of the journey. The inverse relationship between the running time and the energy consumption has been widely studied in the literature. Usually, this time is imposed by the timetable so there is no much flexibility to modify it. On the other hand, intermediate target times can be selected with more flexibility. The intermediate timing points are planned to guarantee the correct crossing order of trains and to ensure the operational separation between trains that run on the same track. Therefore, any intermediate target time can be selected given that the previous criteria are met and the train is capable of fulfilling it. The intermediate timing points determine the average speed in the different sections of the track. They have an impact on the way the train can be driven and affect directly to the final energy consumption. For this reason, it is necessary to select these target times bearing in mind the effect on the consumption apart from the operational requirements. The case of one intermediate timing point can be taken to illustrate the effect of the intermediate target time value on the energy consumption. If the intermediate target time is delayed, from the nominal 0:12:03 to 0:14:40, the train will have to perform a different speed profile to meet the new objectives although the arrival target time is maintained. Figure 13 shows the solution obtained by the algorithm with the delayed timing point compared with the solution obtained using the nominal timetable, studied in Sections 5.1 and 5.2. It can be seen how the new target time forces slower driving in the first section of the track before the intermediate timing point compared with the nominal timetable solution. In the second section, the new timing point forces the application of flat-out driving. The optimal distribution of the margin time between the first and the second section depends on the slopes of the lane and the speed limitations. In this case, the energy consumption obtained with the new solution is greater  
Figure 13: Speed profile (**a**) and position evolution with time (**b**) of the solution found by the algorithm for the case of one intermediate delayed timing point. (1.14 MWh) than the energy consumption obtained by the nominal timetable speed profile (0.96 MWh). This difference is 18.7% of energy consumption. Another example can be shown in the case of two intermediate timing points. If the target time of the point located at 278 km is reduced from the nominal timetable 0:16:20 to 0:15:00, the running time available between the two intermediate timing points decreases. As the arrival timing point is not modified, the running time between the second intermediate timing point and the arrival increases. Figure 14 depicts the effect of the modified timing points on the speed profile of the solution obtained by the DE algorithm compared with the nominal solution studied in Section 5.3. The first section of the journey is very similar for both speed profiles because the first intermediate timing point has not changed. However, the modification of the second target time forces the train to run close to the speed limits until it starts a long coast at 270 km position. This long coast period allows the train to meet the increased time difference between the second timing point and the arrival target. On the other hand, the nominal solution applies a lower holding speed without braking command in the second section and starts to coast at 285 km position. The results show that the modified timing point solution presents higher energy consumption (0.99 MWh) than the nominal speed profile (0.96 MWh). This 3.1% of increase is due to the modifications in the timing points. The energy consumption increases mainly because of the section where the train is driven close to the maximum speed limits.