Fuel Cell Frequency Response Function Modeling for Control Applications

This paper provides the framework for first-order transfer function modeling of a fuel cell for controls use. It is shown that under specific conditions a fuel cell can be modeled as a first-order system. With a first order model, it is possible to determine how the fuel cell responds dynamically on a systems level before incorporating it into a larger more complex system. Current data sheets for fuel cells provide limited information of the output of the fuel cell, and a polarization curve based on static operation. This is vital information, but gives no insight into how the fuel cell responds under dynamic conditions. Dynamic responses are important when incorporating fuel cells as a power source in larger systems, such as automobiles, as loads and conditions are constantly changing. The modeling technique used in this research is the frequency response function. In this approach an experimental frequency response, or Bode plot, is computed from a frequency rich input signal and corresponding output signal. Here the controlled input is the Hydrogen flow and the output is the fuel cell voltage. During these tests, the fuel cell was connected to a constant resistance load. Using the frequency response function approach, a family of first-order transfer function models was created for a fuel cell at different operating temperatures and reactant relative humidity. These models are validated through comparison to experimental step responses. From this family of models the variations in the first-order model parameters of static gain and time constant are quantified. Static gain varied from 0.675 to 0.961 and the time constant ranged between 4.5 seconds and 10.5 seconds.