Novel determination method of charge transfer coefficient of PEM fuel cell using the Lagrange's multiplier method

This paper presents an evaluation of the transfer coefficient of a reversible PEM fuel cell by using the Lagrange's undetermined multiplier technique. In a first step, the technique using the activation polarization was presented. Then we put the stress on the Lagrange's undetermined multiplier technique. The mathematical bases of this method are presented. Subsequently, an experimental determination of the transfer coefficient was carried out by using the two methods. For that purpose, a kit called Hydrocar, combining a solar panel, a reversible PEM fuel cell (which is a combination of fuel cell and electrolyser), hydrogen and oxygen storage containers, and a 3 Volts alkaline battery, was experimented. The experimental study of the solar panel was made. Some parameters of the solar panel were determined, such as the fill factor FF, the efficiency η, the short circuit current I_SC, the open circuit voltage V_OC, the maximum power P_m, and the series resistance R_s.The internal resistance R_i and the optimal resistance R_opt of the fuel cell were determined. Finally, experimental study of the electrolyser and the PEM fuel cell was performed. By using the activation polarization, an evaluation of the transfer coefficient was made. Then an evaluation of the transfer coefficient was made by using the Lagrange's undetermined multiplier technique which takes into account the ohmic polarization, the activation polarization and also the current-power characteristic of the fuel cell.