# A Sea Horse Optimization-Based Approach for PEM Fuel Cell Model Parameter Estimation
## 2 Mathematical Modeling of PEMFC  
Fuel cells are specialized electrochemical devices that convert chemical energy directly into electrical energy. These systems include a semi-permeable membrane that allows for the passage of protons while blocking electrons. Proton exchange membrane fuel cells (PEMFCs) feature a multilayered structure comprising a polymer-based membrane, anode and cathode electrodes, catalyst layers, gas diffusion layers, bipolar plates, and sealing components. The polarization curve represents a key performance characteristic of PEMFCs, providing insight into their voltage-current behavior under various load conditions [27]. The rapid voltage drop observed at the beginning of the curve in Figure 1 is defined as the activation loss. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Ref.**} & \multirow{2}{*}{**Optimization Methods**} & \multicolumn{6}{c}{**Description of the Adopted Model**} \\ \cline{3-8}  & & **Ballard** & \multirow{2}{*}{**BCS**} & \multicolumn{2}{c}{**Nedstack**} & \multirow{2}{*}{**Temasek**} & \multirow{2}{*}{**WNs**} & \multirow{2}{*}{**SR-12**} \\  & & **Mark V** & & & & **PS6** & \\ \hline
[15] & Flower Pollination Algorithm & Yes & Yes & Yes & Yes & Yes & Yes \\
[16] & Whale Optimization Algorithm & Yes & - & - & - & - & - \\
[10] & Bee Colony Algorithm & - & - & - & - & Yes & - \\
[17] & Cuckoo Search Algorithm & Yes & Yes & - & - & Yes & Yes \\
[18] & Monarch Butterfly Optimization Algorithm & - & - & Yes & - & - & - \\
[13] & Grey Wolf Optimization Algorithm & Yes & Yes & - & Yes & Yes & Yes \\
[19] & Salp Swarm Optimization Algorithm & - & Yes & Yes & - & - & - \\
[20] & Sunflower Optimization Algorithm & - & - & Yes & - & - & - \\
[21] & Grasshopper Optimization Algorithm & Yes & - & - & - & Yes & Yes \\
[22] & Slime Mould Algorithm & Yes & - & - & - & - & Yes \\
[6] & Spotted Hypera Optimization Algorithm & Yes & Yes & Yes & Yes & Yes & - \\
[23] & Neural Network Algorithm & Yes & Yes & Yes & - & - & - \\
[24] & Chaos Game Optimization Technique & Yes & - & Yes & - & - & Yes \\ SHO & Sea Horse Optimization & Yes & - & - & - & - & - \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Optimization methods and descriptions of the adopted models in literature. This phenomenon arises from the energy barrier required to initiate electrochemical reactions on the electrode surfaces. At low current densities, this effect is predominant and represents a major factor limiting cell efficiency. In the intermediate current density region, the voltage exhibits a more linear decline, which corresponds to the ohmic polarization region. This section reflects losses due to ionic and electrical resistances within the cell. Proton conduction through the membrane and the conductivity associated with the electrodes primarily influence the voltage behavior in this region. It is typically regarded as the most efficient operating range for PEMFC systems. Toward the end of the curve, a sharp voltage drop occurs at high current densities, attributed to concentration polarization. This results from insufficient transport of reactant gases (hydrogen and oxygen) to the electrode surfaces. When the gas diffusion limits are approached, the reaction rate is constrained, causing a noticeable decline in cell performance. In conclusion, the polarization curve provides a critical foundation for analyzing PEMFC performance under varying operating conditions and plays an essential role in guiding system design and control strategy development [28]. As shown in the PEMFC structure in Figure 2, hydrogen and oxygen gases undergo an electrochemical reaction, enabling them to produce electricity [29]. Figure 1: Typical polarization curve for PEMFC. Figure 2: Structural components and electrochemical reaction flow of a PEM fuel cell.