## 2 Optimized Hybrid Energy System for High-Speed Rail Integrating Carbon-REC Trading
### Models of System Components
#### 2.2.2 Load Model  
This study classifies the operational modes of high-speed rail trains into four distinct categories: traction, cruising, coasting, and braking. The investigated train departs from Hongqiao Station during the outbound journey, traversing 23 intermediate stations before reaching Xining Station, while the return journey originates from Xining Station and passes through 26 intermediate stations before returning to Hongqiao Station, involving multiple mode transitions. The traction mode is defined as the acceleration phase from standstill until reaching the target speed of 350 km/h. In scenarios where adjacent stations are geographically proximate, preventing the train from attaining 350 km/h, the system transitions to subsequent operational modes upon reaching a lower stabilized speed. The cruising mode corresponds to steady-state operation at either 350 km/h or a predetermined constant speed. During coasting mode, the propulsion system is deactivated, leaving the train subject solely to resistance forces that gradually reduce its velocity, with zero load demand in this phase. For braking operations prior to station arrival, the CR400 BF trainset employs a throughput electro-pneumatic braking system integrated with regenerative braking devices. During deceleration, the instantaneous kinetic energy conversion generates substantial electri \begin{table}
\begin{tabular}{l l l l} \hline PV lifetime & efficiency & cost of investment & cost of replacement \\
20 years & 0.25 & USD 876/kW & USD 676/kW \\ \hline Battery lifetime & ch/dis efficiency & cost of investment & cost of replacement \\
5 years & 0.9/1.0 & USD 600/kWh & USD 600/kWh \\ \hline \end{tabular}
\end{table} 
Table 1: The data information of the PV equipment used in this experiment and lists the relevant parameters of LiFePO\({}_{4}\) battery. cal power, which is preferentially utilized for charging the ESS. Any surplus energy beyond ESS capacity is dissipated into the power grid. The traction power of a high-speed train refers to the power required for the train to travel at its designed maximum speed on a straight railway. The traction power is influenced by various factors, including its maximum operating speed, total vehicle mass, resistance at maximum speed, residual acceleration, the transmission efficiency of various components, and the efficiency of the electric motor. The traction power Pk (kW) is derived from the calculation Equation (4) [38]. \[P_{k}=\frac{\left(M\omega_{0}+1.06\times 10^{3}M\triangle a\right)\left(V_{max} +\triangle v\right)\times 10^{-3}}{3.6\eta_{Gen}\eta_{MM}} \tag{4}\]  
where \(M\) represents the weight of the high-speed train, with the unit of t, and it is taken as 505 t; \(\omega_{0}\) represents the basic running resistance per unit weight of the train, with the unit of N/t; \(\triangle a\) represents the residual acceleration, taken as 0.05 m/s\({}^{2}\); \(\triangle v\) represents the headwind speed, taken as 15 km/h; \(V_{max}\) represents the maximum operating speed of the high-speed train, taken as 350 km/h in the work; \(\eta_{Gen}\) represents the gear transmission efficiency, taken as 0.98; \(\eta_{MM}\) represents the electric motor operating efficiency, taken as 0.94; the factor of 1.06 in the equation represents the inertia coefficient. The numerical coefficient 3.6 serves exclusively as the unit conversion factor for transforming velocity measurements from km/h to the fundamental mechanical units of m/s. When the high-speed train reaches a speed of 350 km/h or a certain speed, it begins to operate at a constant velocity; at this point, the net force acting on the train is 0, and the traction force is equal in magnitude to the resistance force.