Order Reduction for a Control-Oriented Model of the Water Dynamics in Fuel Cells

Predicting the water dynamics and estimating humidity and flooding conditions in a low-temperature fuel cell are critical for robust operation and long life. Previous work by McKay et al [1] shows that the fuel cell anode, cathode, and membrane water dynamics and gaseous species concentrations can be accurately modeled by discretizing the partial differential equations that describe mass transport into three segments. Avoiding sensitivities associated with over-parameterization, and allowing for the real-time computations necessary for embedded controllers, requires in-depth investigation of the model order. In this paper the model from [1] is formulated into a bond graph representation. The objective is to establish the necessary model order for the fuel cell model using the Model Order Reduction Algorithm (MORA) [2], where an energy-based metric termed the Activity is used to quantify the contribution of each element of the model. Activity is a scalar quantity that is determined from the generalized effort and flow through each element of the model. We show the degree of model order reduction and provide a guideline for appropriate discretization.