## 2 Optimized Hybrid Energy System for High-Speed Rail Integrating Carbon-REC Trading
### Models of System Components
#### 2.2.3 Carbon Model  
To achieve low-carbon systematic optimization in the high-speed rail power system, this study integrates a carbon model into the hybrid power system, which quantifies system carbon emissions and their economic costs from a LCA perspective. The power system primarily consists of the grid as the main energy source, PV for solar energy absorption, and ESS for renewable energy storage. Therefore, carbon modeling is required for these three components individually. \(Emission_{Total}\) represents the daily carbon emissions of the hybrid power system in the high-speed rail, \(Emission_{Grid}\) denotes the daily carbon emissions from grid electricity consumed during high-speed rail operations, \(Emission_{PV}\) reflects the average daily carbon emissions allocated from the entire LCA of PV systems, and \(Emission_{ESS}\) corresponds to the average daily carbon emissions allocated from the entire LCA of ESS. In this study, carbon emissions are measured in kg. The Equation (7) is presented below. \[Emission_{Total}=Emission_{Grid}+Emission_{PV}+Emission_{ESS} \tag{7}\]  
The carbon emissions from grid electricity consumption are first modeled. Given that the data sampling interval in this study is 10 min (\(\frac{1}{b}\) of an hour), \(E_{\text{Grid},i}\) represents the electricity purchased from the grid during the \(i\)-th time interval (10 min), with units of kWh. The parameter \(k\) denotes the number of 10 min intervals during the high-speed train's daily operational period. The calibration yields \(k\)-values of 74 (outbound) and 78 (return), exhibiting a mean value of 76 in this study. The carbon emission factor for grid electricity, \(\rho_{\text{Grid}}\), is set to 0.5568 kg CO\({}_{2}\)/kWh [40]. The Equation (8) is presented below. Figure 4: Load of a round trip of a high-speed train. \[Emission_{Grid}=\sum_{i=1}^{k}E_{\text{Grid,}i}\times\rho_{\text{Grid}} \tag{8}\]  
Next, the carbon emissions over the entire LCA of PV components are modeled. In this study, the installed PV panels cover an area of \(2000\,\mathrm{m}^{2}\), with a rated power generation capacity of \(650\,\mathrm{W}\) per square meter, resulting in a total rated PV power output of \(1300\,\mathrm{kW}\) (\(P_{\text{PV,rated}}=$1300\,\mathrm{kW}$\)). The lifecycle carbon emission factor for PV, \(\rho_{\text{PV}}\), is set to \(200\,\mathrm{kG}\,\mathrm{CO}_{2}/\mathrm{kW}\)[41], which encompasses silicon production, module manufacturing, installation, and recycling processes. \(L_{\text{PV}}\) denotes the total lifespan of the PV system in days. This approach calculates the daily carbon emissions allocated from the entire LCA of the PV system. The Equations (9) and (10) are presented below. \[Emission_{PV}=P_{\text{PV,rated}}\times\rho_{\text{PV}}\times\frac{1}{L_{\text{ PV}}} \tag{9}\]  
\[L_{\text{PV}}=365\times 20 \tag{10}\]  
Next, the carbon emissions over the entire LCA of the ESS are modeled. In this study, the installed ESS capacity, denoted as \(Eb\), is a variable to be optimized, with units of kWh. The lifecycle carbon emission factor for ESS, \(\rho_{\text{ESS}}\), is set to \(130\,\mathrm{kg}\,\mathrm{CO}_{2}/\mathrm{kWh}\)[42], which encompasses material extraction, manufacturing, transportation, and recycling processes. \(L_{\text{ESS}}\) represents the total lifespan of the ESS in days. The Equations (11) and (12) are presented below. \[Emission_{ESS}=Eb\times\rho_{\text{ESS}}\times\frac{1}{L_{ESS}} \tag{11}\]  
\[L_{\text{ESS}}=365\times 5 \tag{12}\]  
In summary, the accounting boundary of the carbon accounting framework proposed in this study encompasses both direct and indirect emissions. Direct emissions originate from the carbon emissions associated with direct electricity consumption from the power grid, while indirect emissions include the lifecycle carbon emissions of equipment.