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The functioning and the achievable power of a fuel cell are determined by several parameters simultaneously. Part of these cannot be measured directly, therefore the model equations of the cell contain some unknown parameters. In our case these include the effective conductivity of the solution phase, the exchange current density of the cathode and the limiting current of the cathode. Parameter estimation means that the unknown parameters are fitted to measurements.

Setting the parameters could also be done “manually”. This means that the model is run numerically for several different combinations of the parameter values, and we select the set of values for which the numerical solution best fits the measurements. This procedure is unfortunately rather time-consuming, and only allows to try a finite number of combinations from the possible (infinitely many) ones. There exists however a mathematical method by which the optimal parameter set (in case it exists) can be found in a few iteration steps. For the solution of this problem we used the minimization method of Levenberg and Marquardt, which is a clever combination of the well-known Newton and steepest descent methods.

The measurements were done in the following way. We used the instrument of Fuel Cell Technologies, INC., developed specially for university experiments. The device makes the following tests: it measures the cell voltage and cell resistance by constant current. The power of the cell is computed from the current and the voltage. The instrument can be controlled from a computer with the help of a LabVIEW program. All the important quantities: the pressure, the current density, the temperature, the voltage, the material parameters of the gases and the water content can be set through the control panel. During the measurements, the current density was studied as a function of the cell potential. (For historical reasons, the diagrams show the cell potential versus the current density, so we obtain the so-called V-I curves.) The measurements were done on three temperatures (40 °C, 60 °C és 80 °C) and two pressures (1 bar and 2 bar). We studied catalysts with different Nafion contents (14, 30 and 50%).

The results of the fitting with 50 percent Nafion content, on 60°C and 2 bar pressure

The results of the fitting with 50 percent Nafion content, on 80°C and 2 bar pressure