Three order state space modeling of proton exchange membrane fuel cell with energy function definition

The fuel cell is a complex system which is the centre of a lot of multidisciplinary research activities since it involves intricate application of various fields of study. The operation of a fuel cell depends on a wide range of parameters. The effect of one cannot be studied in isolation without disturbing the system which makes it very difficult to comprehend, analyze and predict various phenomena occurring in the fuel cell. In the current work, we present an equivalent electrical circuit of the pneumatics and fluidics in a fuel cell stack. The proposed model is based on the physical phenomena occurring inside fuel cell stack where we define the fluidic-electrical and pneumatic-electrical analogy. The effect of variation in temperature and relative humidity on the cell are considered in this model. The proposed model, according to the considered hypothesis, is a simple three order state space model which is suitable for the control purpose where a desired control structure can be formulated for high-end applications of the fuel cell as a subpart of a larger system, for instance, in hybrid propulsion of vehicles coupled with batteries and supercapacitors. Another key point of our work is the definition of the natural fuel cell stack energy function. The circuit analysis equations are presented and the simulated model is validated using the experimental data obtained using the fuel cell test bench available in Fuel Cell Laboratory, France.