## 2 System Model Description
### Fuel Economy Model  
The energy consumption of an FCHV includes both hydrogen and electric energy. To facilitate assessment, the energy consumption of the battery system is converted into equivalent hydrogen energy. This approach assumes an equal state of charge (SOC) at the beginning and end of the driving cycle, ensuring that the energy exchanged by the battery is accurately represented as hydrogen energy. Thus, fuel economy is defined as the hydrogen consumption of both the fuel cell and the battery during the driving cycle.  
In the driving cycle simulation, the hydrogen consumption of the fuel cell system is treated as a discrete variable, and the hydrogen consumption can be calculated as follows in Equation (5):  
\[C_{fc_{th_{2}}}(t)=\frac{P_{fcnet}(t)\Delta t}{LHV\cdot\eta_{fc}} \tag{5}\]  
where \(LHV\) denotes the lower heating value of hydrogen, which is 120 MJ/kg. The index \(t\) corresponds to the time step within the driving cycle, while \(\Delta t\) represents the time increment for each step in the cycle. The FCS efficiency, \(\eta_{fc}\) is determined as a function of the FCS net power output using a lookup table.  
The hydrogen consumption for the battery in this study is determined using an equivalent hydrogen consumption model.  
\[C_{bat_{th_{2}}}(t)=\left\{\begin{array}{l}\eta_{bat_{dis}}\ \frac{\int P_{bat}dt}{ \eta_{fc,avg}\eta_{fc,calc}LH\
u},P_{bat}(t)<0\\ \frac{\int P_{bat}dt}{\eta_{fc,avg}\eta_{bat_{dis}}\eta_{tf,calc}LH\
u},P_{bat}( t)>0\end{array}\right. \tag{6}\]  
where \(\eta_{bat_{dis}}\), \(\eta_{bat_{dis}}\) is the battery charge/discharge efficiency and \(\eta_{fc,calc}\) is the average efficiency of the fuel cell's DC-DC converter. These efficiency parameters are all treated as constants.  
In the power system of an FCHV, the battery functions as an auxiliary power source. The battery model adopted in this study is the Rint model, which characterizes the relationship between internal resistance, current, and voltage as described by Equation (7).  
\[I_{bat}(t)=\frac{\mathrm{U}_{bat}(t)-\sqrt{\mathrm{U}_{bat}^{2}(t)-4P_{bat}(t)R _{bat}(t)}}{2R_{bat}} \tag{7}\]  
where \(I_{bat}(t)\) and \(R_{bat}(t)\) represent the current and resistance values of the battery at a given time step, respectively.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Symbol** & **Value** & **Unit** \\ \hline Mass & \(m_{v,b}\) & 1848 & kg \\ Coefficient of friction & \(f\) & 0.015 & - \\ Drag coefficient & \(C_{d}\) & 0.3 & - \\ Air density & \(\rho\) & 1.025 & kg/m\({}^{3}\) \\ Frontal area & \(F\) & 2.79 & m\({}^{2}\) \\ Power-to-weight ratio of the fuel cell & \(\gamma_{fc}\) & 0.157 & kW/kg \\ Specific energy of the battery & \(\beta_{bat}\) & 70 & Wh/kg \\ Transmission efficiency & \(\eta_{GB}\) & 0.95 & - \\ Motor efficiency & \(\eta_{mt}\) & 0.95 & - \\ DC–AC converter efficiency & \(\eta_{dac}\) & 0.95 & - \\ Fuel cell DC–DC converter efficiency & \(\eta_{fc,calc}\) & 0.95 & - \\ Brake energy recovery rate & \(\eta_{recovery}\) & 0.6 & - \\ \hline \hline \end{tabular}
\end{table}
Table 1: Parameters of the research FCHV.  
The state of charge (SOC) of the battery is calculated using Equation (8). The SOC decreases during power output and increases during regenerative braking, reflecting the dynamic energy flow within the system.  
\[\text{SOC(t)}=SOC_{int}-\frac{\eta_{bat}}{Q_{bat}}\int_{0}^{t}I_{bat}(t)dt \tag{8}\]  
where \(SOC_{int}\) denotes the initial state of charge and \(\eta_{bat}\) refers to the average efficiency of the battery during charging and discharging.