## 2 Materials and Methods
### Digital Vehicle Model  
To provide time and cost advantages in the optimization study, a digital model of the real fuel cell electric vehicle was structured in Matlab/Simulink. The digital vehicle model was examined in two areas: the vehicle and fuel cell. While on the vehicle side, there are concepts such as speed, acceleration, torque, power, and energy consumption, on the fuel cell side there are variables such as SoC, current demand, temperature, voltage, and power. Operations between the inputs given in the digital vehicle model and the desired outputs can be carried out with some basic equations. Equations (1)-(10) describe the basic calculations performed in the digital vehicle model. Equations (1)-(5) show the basic resistance forces acting on a vehicle, which are also shown in Figure 3, while Equations (6)-(8) reveal the required motor power calculations. Equations (9)-(10) show the data obtained in the required motor power calculation and the required energy and charge rate calculations. Among the parameters in Equations (1)-(5), \(p\) is the air density, A is the vehicle front surface area, \(\rm V_{v}\) is the vehicle speed, \(\rm C_{d}\) is the drag coefficient, m is the vehicle mass, g is the gravitational acceleration, \(\rm C_{rr}\) is the wheel rolling resistance coefficient, \(\rm\propto\) is the road slope angle, and \(\rm F_{resistance}\) is the total force that the vehicle faces while driving. \[\rm F_{zero}=\frac{1}{2}\rho\rm AV_{v}^{2}C_{d} \tag{1}\]  
\[\rm F_{rr}=mgC_{rr}\cos(\infty) \tag{2}\]  
\[\rm F_{gr}=mg\sin(\infty) \tag{3}\] \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Specification** \\ \hline Gross vehicle weight & 18,000–20,000 kg \\ Vehicle length & 10–14 m \\ Vehicle front area & 7–8 m\({}^{2}\) \\ Drag coefficient & 0.6–0.8 \\ Tire radius & 0.4–0.5 m \\ Transmission ratio & 20–23 \\ Maximum motor power & 200–300 kW \\ Maximum motor torque & 800–1000 Nm \\ Motor type & In-wheel hub PMSM \\ Battery capacity & 25–30 kWh \\ Fuel cell type & Proton Exchange Membrane \\ Fuel cell maximum power & 70 kW \\ Hydrogen tank capacity & 1500–1700 L \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Technical specifications of fuel cell electric vehicle. Figure 2: Fuel cell SoC-power supply behavior. Among the parameters in Equations (6)-(10), \(\mathrm{M}_{w}\) represents the wheel torque, \(\mathrm{i}_{tr}\) is the total transmission ratio, \(\mathrm{i}_{tr}\) is the power transmission efficiency, \(\mathrm{w}_{m}\) is the motor angular speed, and \(\mathrm{P}_{m}\) is the motor power. \(\mathrm{E}_{battery}\) is the total energy in the battery, \(\mathrm{E}_{\mathrm{cons}}\) is drawn energy from the battery, and \(\mathrm{V}_{\mathrm{nominal}}\) is the nominal voltage in the battery. \[\mathrm{M}_{w}=\mathrm{F}_{\mathrm{resistance}}*\mathrm{F}_{w} \tag{6}\]  
\[\mathrm{M}_{m}=\frac{\mathrm{M}_{w}}{\mathrm{i}_{tr}}*\mathrm{i}_{tr} \tag{7}\]  
\[\mathrm{P}_{m}=\mathrm{M}_{m}*\mathrm{w}_{m} \tag{8}\]  
\[\mathrm{E}_{\mathrm{cons}}=\left(\int_{0}^{t}\mathrm{P}_{m}\mathrm{d}t\right) \frac{1}{3600} \tag{9}\]  
\[\mathrm{SoC}=\left(\frac{\mathrm{E}_{\mathrm{battery}}-\mathrm{E}_{\mathrm{ cons}}}{\mathrm{V}_{\mathrm{nominal}}}\right)\frac{1}{3600\mathrm{E}_{\mathrm{battery}}}100 \tag{10}\]  
There are basic empirical formulas expressing the operation of the fuel cell in the literature [43; 44; 45; 46; 47; 48; 49]. The operating principle of the system is similar to the vehicle's basic equations. The net voltage output of the fuel cell is obtained after subtracting the loss voltages from the reference voltage value. In this study, the calculations for the fuel cell used in the digital vehicle model are given in Equations (11)-(20).