## 2 Materials and Methods
### Digital Vehicle Model
Among the empirical formulas created for the fuel cell, Equation (11) expresses the voltage value created per cell, Equation (12) expresses the fundamental voltage value in the system excluding losses, Equation (13) expresses the voltage drop due to activation loss, Equation (14) expresses the ohmic voltage loss, and Equation (16) declares the concentration voltage loss. Equation (17) is the total voltage produced in the fuel cell stack, Equations (18) and (19) are the flow equations of the anode and cathode, and Equation (20) is the cathode water flow equation. Equation (11) is the voltage per cell in the fuel cell stack. \[\mathrm{V}_{\mathrm{cell}}=\mathrm{V}_{\mathrm{nerst}}-\mathrm{V}_{\mathrm{ act}}-\mathrm{V}_{\mathrm{ohm}}-\mathrm{V}_{\mathrm{con}} \tag{11}\]  
Equation (12) is the Nernst voltage that includes T as the cell temperature, F as the Faraday constant, R as the gas constant, and \(\mathrm{P}_{\mathrm{H}_{2}}\), \(\mathrm{P}_{\mathrm{O}_{2}}\), and \(\mathrm{P}_{\mathrm{H}_{2}O}\) are hydrogen, oxygen, and vapor pressures, respectively. \[\mathrm{V}_{\mathrm{nerst}}=1.229-0.85*10^{-3}*(\mathrm{T}-298.15)+\frac{ \mathrm{R}*\mathrm{T}}{2*\mathrm{F}}*\mathrm{ln}\left(\frac{\mathrm{P}_{ \mathrm{H}_{2}}*\mathrm{P}_{\mathrm{O}_{2}}^{0.5}}{\mathrm{P}_{\mathrm{H}_{2}O }}\right) \tag{12}\]  
Equation (13) is the activation loss voltage, also expressed by the Tafel equation [50], occurring in low current regions. In related parameters, \(\mathrm{n}\) is the cell number and \(\alpha\) is the  
Figure 3: Drive resistance forces on a vehicle. charge coefficient. The rest of the parameters can be extracted from the Tafel equation in the related reference. Figure 2:0  
Equation (14) is the ohmic loss occurring in the continuous operating region. In the ohmic loss, I is the instant current and \(\mathrm{R_{mem}}\) is the membrane resistance. Figure 2:1  
Equation (15) is the membrane resistance expression used in the ohmic loss calculation. \(\mathrm{Tm}\) is the membrane thickness, and \(\mathrm{\sigma}\) is the conductivity value of the membrane. Figure 2:2  
Equation (16) is the concentration loss in high current regions. Figure 2:3  
Equation (17) is the total voltage produced from cells connected in series in the fuel cell stack. \(\mathrm{V_{cell}}\) is the produced voltage in a cell. Figure 2:4  
Equation (18) includes the expressions for anode flow. \(\mathrm{V_{a}}\) is the anode volume, \(\mathrm{m_{H_{2}}}\) is the hydrogen flow rate, and \(\mathrm{k_{a}}\) is the flow constant for the anode. \[ \begin{array}{rl}\frac{\mathrm{V_{a}}}{\mathrm{R*T}}\frac{\mathrm{d}\mathrm{ P}_{\mathrm{H_{2}}}}{\mathrm{dt}}&=\mathrm{m_{H_{2}-i}}-\mathrm{m_{H_{2}-o}}- \frac{1}{4*\mathrm{F}}\\ \frac{\mathrm{m_{H_{2}}}}{\mathrm{m_{H_{2}}}}&=\mathrm{k_{a}}*\left(\mathrm{P _{H_{2}}}-\mathrm{P_{amb}}\right)\end{array}  \tag{18}\]  
Equation (19) has the fundamental explanations for cathode flow. \(\mathrm{V_{c}}\) is the cathode volume, \(\mathrm{m_{O_{2}}}\) is the oxygen flow rate, and \(\mathrm{k_{c}}\) is the flow constant for the cathode. \[ \begin{array}{rl}\frac{\mathrm{V_{c}}}{\mathrm{R*T}}\frac{\mathrm{d}\mathrm{ P}_{\mathrm{O_{2}}}}{\mathrm{dt}}&=\mathrm{m_{O_{2}-i}}-\mathrm{m_{O_{2}-o}}- \frac{1}{4*\mathrm{F}}\\ \mathrm{m_{O_{2}}}&=\mathrm{k_{c}}*\left(\mathrm{P_{O_{2}}}-\mathrm{P_{amb}} \right)\end{array}  \tag{19}\]  
Equation (20) is the expression of the cathode water. \[\frac{\mathrm{V_{c}}}{\mathrm{R*T}}\frac{\mathrm{d}\mathrm{P}_{\mathrm{H_{2}O -C}}}{\mathrm{dt}}=\mathrm{m_{H_{2}O-ic}}-\mathrm{m_{H_{2}O-oc}}-\frac{1}{2* \mathrm{F}} \tag{20}\]  
The polarization curve in Figure 4 expresses the main loss behavior during the working stage of a fuel cell [51]. At low currents, the activation loss due to the barrier that must be overcome for the reaction to begin is dominant. Ohmic loss, which occurs due to the resistance encountered by ions moving in the electrolyte and electrons moving in the external circuit, is constantly effective.