## 2 The Formation of Energy-Saving Problem of High-Speed Trains  
To address the energy-saving control problem of high-speed trains, we aim to reduce energy consumption, improve traction efficiency, and reduce operating costs during train operation. The multiple aspects covered by this question are shown in Table 1. This paper applies advanced traction control and braking strategies to model the traction process, accurately and dynamically adjusting the strategy to adapt to different operating conditions. The force analysis of the train operation is shown in Figure 1. The train is regarded as a single-particle model, and it is subjected to five forces during its operation: train gravity G, support force N, traction force F, running resistance W, and braking force B. Because the traction and braking force are two different working conditions of a train power system, traction F and braking force B cannot exist simultaneously. The high-speed train adopts a composite braking system with electric braking as the main method and air braking as the auxiliary method. The most commonly used braking method prioritizes non-wearing electric braking. In contrast, air braking or composite braking is used in emergency braking situations and is difficult to describe in specific application scenarios. The basic braking control modes include regular, emergency, anti-skid, and parking braking [17]. Compared with pure mechanical braking, the driving strategy combining regenerative and mechanical braking saves more energy [18]. The brake handling level contains different braking modes, which can meet the requirements of high-speed trains under different operating conditions. These include common brake levels (1A, 1B, 2, 3, 4, 5, 6, 7, 8), OC, REL, and EB. In the same operating environment, different braking operations consume varying amounts of traction electrical energy [19]. Without considering the influence of other conditions, the average increase in traction energy consumption per second for each brake lever position is shown in Table 2. REL corresponds to the traction position, and its traction energy consumption is greater than that of other operations. In the event of an emergency, the brake lever needs to be placed in the \"EB\" position. However, if the train is stopped on a track segment where evacuation is not feasible, the driver can place the brake lever in the \"OC\" position to cancel the excessive braking force. Therefore, compared to common braking positions, it results in higher energy consumption, which is consistent with the statistical results in Table 2.  
By improving the operation mode of high-speed trains, such as by optimizing the acceleration and deceleration strategies of vehicles, improving the speed control of trains \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Challenge** & \multicolumn{4}{c}{**Description**} \\ \hline Braking strategy & \multicolumn{4}{c}{Minimize energy consumption during deceleration and parking} \\ Traction control & \multicolumn{4}{c}{Through intelligent traction control, the train can use energy more efficiently} \\ Energy recovery & \multicolumn{4}{c}{The energy released by the train braking is re-injected into the power supply system} \\ Power system & \multicolumn{4}{c}{Optimize the power system of the train and improve the efficiency of energy utilization} \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Classification of energy-saving strategies for high-speed trains. Figure 1: Force analysis of straight line. (**a**) Acceleration or constant speed; (**b**) Braking. on different road sections, and optimizing the parking strategies of trains, the traction energy consumption during train operation can be effectively reduced [20; 21]. The optimal traction control is studied to determine the application time of the brakes and the type of operating brake handling. The braking problem can be transformed into the following equivalent decision problem.