Parameterization of Fuel Cell Stack Voltage: Issues on Sensitivity, Cell-to Cell Variation, and Transient Response

We present here a calibrated and experimentally validated lumped parameter model of fuel cell polarization for a hydrogen fed multi-cell, low-pressure, proton exchange membrane (PEM) fuel cell stack. The experimental methodology devised for calibrating the model was completed on a 24 cell, 300 cm² stack with GORE™ PRIMERA^® Series 5620 membranes. The predicted cell voltage is a static function of current density, stack temperature, reactant partial pressures, and membrane water content. The maximum prediction error associated with the sensor resolutions used for the calibration is determined along with a discussion of the model sensitivity to physical variables. The expected standard deviation due to the cell-to-cell voltage variation is also modelled. In contrast to other voltage models that match the observed dynamic voltage behavior by adding unreasonably large double layer capacitor effects or by artificially adding dynamics to the voltage equation, we show that a static model can be used when combined with dynamically resolved variables. The developed static voltage model is then connected with a dynamic fuel cell system model that includes gas filling dynamics, diffusion and water dynamics and we demonstrate the ability of the static voltage equation to predict important transients such as reactant depletion and electrode flooding. It is shown that the model can qualitatively predict the observed stack voltage under various operating conditions including step changes in current, temperature variations, and anode purging.