## 2 Modeling
### PEMFC Description  
Since the flow rate of unreacted hydrogen in the AOG is inversely proportional to the fuel utilization efficiency of the PEMFC, the proper prediction of fuel utilization efficiency is important to calculate the hydrogen consumption rate in the PEMFC. Power by the PEMFC stack (\(P_{stack}\)) can be calculated as the product of the number of the unit cell (\(n_{cell}\)), unit cell voltage (\(V_{cell}\)), unit cell current (\(i\)), and MEA area (\(A_{MEA}\)), as shown in Equation (11). \[P_{stack}=n_{cell}V_{cell}\cdot i\cdot A_{MEA} \tag{11}\]  
The unit cell voltage in Equation (11) can be calculated from Equation (12) and considering the thermodynamic equilibrium potential (\(V_{o}\)) and the irreversibility of the PEMFC, such as the activation loss (\(\eta_{act}\)), ohmic loss (\(\eta_{ohm}\)), and concentration loss (\(\eta_{lon}\)) [35]. \[V_{cell}=V_{o}-\eta_{act}-\eta_{ohm}-\eta_{con} \tag{12}\]  
The thermodynamic equilibrium potential, activation loss, ohmic loss, and concentration loss are calculated by Equations (13)-(17). Equation (13) can calculate the thermodynamic equilibrium potential in the HT-PEMFC. Equation (13) is a function of cell temperature (\(T_{cell}\)) and 1.1549 V was calculated using a cell temperature of 150 \({}^{\circ}\)C [36]. \[V_{o}=1.1669-0.00024(T_{cell}-373.15) \tag{13}\]  
Activation loss can be calculated by the Butler-Volmer equation that expresses electrochemical kinetics [35]. Since the hydrogen oxidation reaction and oxygen reduction reaction occur in the anode and cathode in fuel cells, the Butler-Volmer equation uses the two half-reactions of Equations (14) and (15) to calculate the activation loss [35; 36; 37; 38; 39]. \[\eta_{act,a}=\frac{i}{i^{ref}_{0,a}}\frac{RT_{cell}}{(\alpha_{a}+\alpha_{c}F)} \bigg{(}\frac{C_{H_{2},ref}}{C_{H_{2}}}\bigg{)}^{0.5} \tag{14}\]  
\[|\eta_{act,c}|=\frac{RT_{cell}}{\alpha_{c}F}\text{ln}\left[\bigg{(}\frac{C_{ O_{2},ref}}{C_{O_{2}}}\bigg{)}^{0.75}\frac{i}{i^{ref}_{0,c}}\right] \tag{15}\]  
Resistance loss and concentration loss occur according to the structural characteristics of the fuel cell (thickness, electronic conductivity, porosity, etc.) and represent losses by hindering the movement of hydrogen protons and electrons. To express \(\eta_{ohm}\) and \(\eta_{con}\), [PERSON] and his colleague suggest Equations (16) and (17) [37]. Because the resistance of the electron flow (R\({}_{\text{elec}}\)) is small compared to the resistance of the proton flow in Equation (16), it is considered an insignificant term, as in other research [25]. \[\eta_{ohm}=i(\frac{\delta_{mem}}{\kappa}+\frac{0.5\delta_{aCL}}{v^{1.5}_{aCL} }+\frac{0.5\delta_{CCL}}{v^{1.5}_{cCL}\kappa}+R_{elec}) \tag{16}\]  
\[\eta_{con}=\frac{RT}{4F}\text{ln}\left(\frac{v^{1.5}_{GDL}D_{O_{2}}C_{O_{2}}}{ v^{1.5}_{GDL}D_{O_{2}}C_{O_{2}}-\delta_{GDL}}\right) \tag{17}\]  
The parameters in Equations (14)-(17) are shown in Table 3.  
The current density of a stack (\(i\)) is a function of the H\({}_{2}\) molar flow rate (\(n_{H2}\)) entering the stack, the fuel utilization efficiency (\(U_{f}\)), the MEA area (\(A_{MEA}\)), and the number of cells (\(n_{cell}\)), as shown in Equation (18). \[i=n_{H_{2}}\times U_{f}\times\frac{2F}{A_{MEA}n_{cell}} \tag{18}\]The fuel utilization efficiency is shown by Equation (19) and is defined by the ratio of the fuel used by the HT-PEMFC to generate power to the total fuel supplied to the HT-PEMFC [35].