Comparing the Precision of Empirical, Semi-empirical and Analytical Equations for Polarization Curve Fitting of Proton Exchange Membrane Fuel Cell

The performance of a proton exchange membrane fuel cell is expressed mainly by the polarization curve. Polarization curve is determined by calculating the thermodynamic potential and activation, ohmic, and concentration losses. Applying the curve fitting equations of the polarization curve, the cell output voltage can be calculated for a specific current density and for the specific operating conditions. Therefore numerous equations have been presented to predict or fit the polarization curve, due to the nonlinearity of the curve; their precision is the main challenge. Nevertheless, the comparison of these equations has been accomplished neither wholly nor in the entire range of the polarization curve. In this study, first of all, equations are categorized into analytical, semi-empirical, and empirical equations, and then their precision were compared as quantitative and qualitative by polarization curve and tools such as sum of squares due to error, coefficient of determination (r2), iterations and values of corresponding parameters, with the aid of Matlab software. The results show that among the investigated empirical equations, our equation is more precise. Akimoto’s equation and Haji’s equation were found as the best semi-empirical and analytical equation, respectively. Finally, the best equations were compared together with two sets of experimental data, our equation and Haji’s equation totally had the highest precision (r2> 0.999); therefore they were introduced as the best investigated equations.