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Topic: Analytical Modeling of the Polarization Curves of a 40-W Fuel Cell Stack 


Author: Shaker Haji 

Institution: Department of Chemical Engineering, College of Engineering, University of Bahrain 

Location: Manama, Kingdome of Bahrain 



In this study, the performance of a bench scale fuel cell stack, run on hydrogen/air, is measured experimentally. The experimental data, obtained from the 40-watt proton exchange membrane fuel cell (PEMFC), are used in estimating the parameters of a completely analytical model that describes the polarization curve. The analytical model consists of the three fundamental losses experienced by a fuel cell, namely: activation, ohmic, and concentration losses. The current loss is also considered in the model. While the Tafel constants, ohmic resistance, and the concentration loss constant are estimated through multiple linear regression analysis, the limiting current density and the current loss are obtained through measurements. The model and its estimated parameters are used to demonstrate the proportions of the three fundamental losses and to predict the fuel cell delivered power density as a function of the current density. The theoretical equations derived in the literature, which model fuel cell performance, are found to reasonably fit the obtained experimental data. 



In this paper, the i-V data obtained from a 40-watt fuel cell stack operated at 40oC with pure hydrogen and air are fitted to an analytical model, where the voltage output is a function of the thermodynamic voltage and activation, ohmic, and concentration losses. Although nonlinear regression analysis could provide mathematically acceptable fitted parameters, the obtained parameters’ values are not reasonable in fuel cell operating terms. In contrast, linear regression results in better fit in terms of the reasonability of the fitted parameters; however, iL has to be estimated first, which introduces a limitation to this approach. Therefore, it’s very important to refer to the typical values of the polarization curve parameters when performing regression. The thermodynamic voltage in the model is calculated based on Nernst equation. The Tafel intercept (ac) and slope (bc ), the exchange current density (i0,c ), the cell resistance (Rohmic ), and the concentration loss constant (cc) are found by multiple linear regression analysis and are estimated to be around 0.5 V, 40 mV, 3x10-6 A/cm2, 0.4 Ω.cm2, and 40 mV, respectively. The transfer coefficient of the oxygen reduction reaction, αc , is found to be very small − around 0.16. Using the fitted parameters of the model, the proportions of the three fundamental types of losses are illustrated where it is shown that the activation losses are by far the largest losses experienced by the fuel cell at any current density. When operated at 40±1.5oC with an air flow rate of 2.87 slm, the maximum fuel cell efficiency and power density are measured to be 50% at 0.038 A/cm2 and 0.17 W/cm2 at 0.325 A/cm2, respectively.
In conclusion, it is demonstrated in this study that a theoretically derived equation can reasonably model the polarization curve of a PEM fuel cell operating under steady-state.

Keywords: PEMFC, Performance Modeling, Polarization Curve, i-V curve, Fuel Cell Losses. 


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