Dynamic Modelling and Control of Polybenzimidazole Fuel Cells

A dynamic fuel-cell model for high-temperature PEM fuel cells with PBI membranes has been developed in Simulink. In such models it is common to use the current density as input variable, but this model uses a different approach. The current density is regarded as an unrealistic control variable, since it cannot be controlled directly. Instead, it is possible to simulate the effect of changing the characteristic of the external circuit, a more realistic manipulated variable, with resistances or MOSFET transistors. Experimental runs have been executed to confirm the theoretical development. To measure the parameters needed for the model, impedance tests on the fuel cell are considered an effective way to extract parameters by means of parameter regression: the model has therefore been extended and reimplemented to produce simulated impedance plots, that show good agreement with experimental measurements on fuel cells. INTRODUCTION Research in fuel cells has shown a rapid growth. The relatively minor interest for their dynamics has recently increased as a topic in its own merit and as a prerequisite for control analysis and controller design. However, many models provided in the literature [1, 2, 3, 4, 5] were not intended for control studies, and in that context they are often “flawed” because they consider current density as an input to the system. This is unrealistic from a processcontrol perspective, because in reality the current is determined by the characteristics of the fuel cell and of its external load, and is not set directly by the control system. Currently, most PEM fuel cells are based on electrolytes that rely on liquid water for protonic conduction, binding them to an operating temperature below 100 ◦C (unless pressurized). In polybenzimidazole (PBI)-based fuel cells, water is produced in gaseous form, and since the membrane relies on phosphoric acid to function, the water management issue is removed. Finally, high-temperature PEM fuel cells based on PBI electrolyte exhibit a high tolerance to carbon monoxide [6]. ∗Corresponding author: [email protected] The parameters used in the model need to be measured appropriately. Impedance tests are measurement of the impedance of the fuel cell at various frequencies. By applying the proposed model structure to calculate the impedance of the fuel cell, a plot of clear resemblance to experimental results is obtained. The fundamental theory about impedance spectroscopy can be found in many textbooks, for example in Macdonald [7]. The objective of this paper is to show the development of a model using the external circuit’s characteristic as an input, and how this model is able to explain experimental results observed on a PBI fuel cell. Another objective is making the point that dynamic models for control-design purposes should make use of proper manipulated input variables, instead of using either voltage or current as an input. Furthermore, the usefulness of impedance measurements in determining the model parameters will be demonstrated. EXPERIMENTAL METHODS Experiments were carried out on a PBI fuel cell, previously assembled in the laboratory of the Depart-