## 2 Optimized Hybrid Energy System for High-Speed Rail Integrating Carbon-REC Trading
### Models of System Components  
#### 2.2.1 PV Model and ESS Model  
The solar radiation received by PV modules on the train roof is influenced by the high-speed motion of the train. As the high-speed train travels along the track, solar radiation varies with the position of train, date, and time. Raw data for global horizontal irradiance, diffuse horizontal irradiance, and air temperature were sourced from 13 meteorological stations owned by SOLCAST [36]. In this study, every two adjacent stations shared meteorological data from one weather station. These data were sampled every 10 min and allocated to specific fixed time points based on the train's location and travel time along the route. Consequently, the instantaneous power generation of the PV arrays on the high-speed train could be calculated using date, local time, and ambient temperature data recorded at 10 min intervals. Practical environmental conditions were incorporated to enhance the accuracy of the proposed computational methodology. This study implemented a mathematical model to calculate the power output of PV modules and derived the PV system's output power at each time step \(t\) (\(t\) = 1, 2,..., 608) using Equation (1) [37], which converts solar irradiance into electrical power. \[P_{PV}(t)=\eta_{PV}\times A_{PV}\times I(t) \tag{1}\]  
where \(\eta_{PV}\) represents the instantaneous power generation efficiency of the PV generator, and \(A_{PV}\) denotes the total area (m\({}^{2}\)) of PV modules utilized in the PV power generation system, which is set to 2000 m\({}^{2}\) in this study. \(I(t)\) indicates the total solar irradiance (W/m\({}^{2}\)). The rated power of individual PV panels in this system is 650 W, resulting in a total installed capacity of 1300 kW (2000 \(\times\) 650 W) under the specified total installation area of 2000 m\({}^{2}\). It should be noted that the costs of power conversion equipment, including DC/DC converters, inverters, and control devices, have been included in the investment cost of the system. The grid energy consistently serves as the primary power source for the entire high-speed rail train power system. During train startup under traction mode, the grid supplies the predominant proportion of electrical energy. In other operational modes, the grid compensates for load demands when the combined energy supply from PV and ESS proves insufficient. To address PV generation intermittency and ensure stable power injection in high-speed rail systems, ESSs are deployed to regulate power imbalances, incorporating  
Figure 3: The PV power generations at 13 stations along the high-speed railway route. state of charge (SOC) management for operational stability. This study specifically selects lithium iron phosphate batteries as the energy storage device. Because the output power of the PV is intermittent and the high-speed railway power system requires a smooth input of electricity, a lithium iron phosphate battery is used as the ESS to regulate the insufficient or excess power in the entire system, while also considering the State of Charge (SOC). The work selects LiFePO\({}_{4}\) battery as the ESS. When the total power generation of the high-speed railway power grid and the PV exceeds the load, the ESS is charged; when the high-speed train generates RBE, the ESS is also charged. The energy for the time step \(t\) can be calculated by Equation (2). \[E_{(t)}=E_{(t-1)}+P_{ch}\times\frac{1}{6}\times\eta_{ch} \tag{2}\]  
where \(E_{(t)}\) and \(E_{(t-1)}\) represent the energy content of the ESS at time \(t\) and time \(t-1\), respectively, with the unit of kWh, and 1/6 converts the time from minutes to hours to ensure consistent units in energy calculation; \(\eta_{ch}\) denotes the charging efficiency, which is set at 90% for the work; \(P_{ch}\) indicates the charging power of the ESS, which is a positive value with the unit of kW. On the other hand, when the load demand exceeds the generated energy, the ESS discharges; similarly, during the traction operation at startup, the ESS also discharges.