On controllability and system constraints of the linear models of proton exchange membrane and solid oxide fuel cells

In this paper we first show that the linear models of proton exchange membrane (polymer electrolyte membrane, PEM) and solid oxide (SO) fuel cells, commonly used in power and energy literature, are not controllable. The source of uncontrollability is the equation for pressure of the water vapor that is only affected by the fuel cell current, which in fact is a disturbance in this system and cannot be controlled by the given model inputs: inlet molar flow rates of hydrogen and oxygen. Being uncontrollable these models are not good candidates for studying control of dynamic processes in PEM and SO fuel cells. However, due to their simplicity, they can be used in hybrid configurations with other energy producing devices such as photovoltaic (solar) cells, wind turbine, micro gas turbine, battery (ultra capacitor) to demonstrate some other phenomena, but not for control purposes unless the hybrid models formed in such hybrid configurations are controllable. Testing controllability of such hybrid models is mandatory. Secondly, we introduce some algebraic constraints that follow from the model dynamics and the Nernst open-loop fuel cell voltage formula. These constraints must be satisfied in simulation of considered fuel cell modes, for example, via MATLAB/Simulink or any other computer software package.