Modeling and Analysis for Control of Reactant and Water Distributions in Fuel Cells.

Abstract

It is shown that the critical task of controlling the water accumulation within the gas diffusion layers (GDL) and channels of a polymer electrolyte membrane fuel cell (PEMFC) benefits from a partial differential equation (PDE) approach. Starting from first principles, a fuel cell model is represented as a boundary value problem for a set of six coupled, nonlinear, second-order PDEs for mass transport across the gas diffusion layer, from channel-to-channel. The multi-input, multi-output model includes nonlinearities related to both switching and PDEs with polynomial coefficients in the dependent variable. The six PDEs are approximated, with justification founded in linear systems theory and a time-scale decomposition approach, by a semi-analytic solution (SAS) model that, compared to the full numeric solution, requires only one-third the number of states to be numerically integrated. This model simplification plays a critical role in the fundamental goal of the research, which is to provide a control-oriented model that maintains the meanings of the states in order to apply physically intuitive control algorithms. The SAS model consists of a set of numeric transient, analytic transient, and analytic steady-state solutions to the system of PDEs. Model accuracy is verified by comparison to the experimental voltage transient response from a 24-cell stack, and to the predictive capability of the full-order numeric model. The SAS model predicts degradation due to liquid water accumulation and voltage variations due to changes in inputs such as stack current, reactant excess ratio, and overall stack temperature with negligible variation versus the full-order model. The SAS model is created for application to real-time automatic control of spatial and temporal water and reactant distributions within a PEMFC. The semianalytic solution is analyzed for open-loop stability and to gain insight into the physics of the equilibrium water distributions. Candidate distributions for vapor and liquid water are then identified which allow maximum membrane hydration while simultaneously avoiding voltage degradation that results from anode liquid water accumulation (flooding). The desired distributions would be maintained via control of the channel conditions (boundary value control) with the ultimate goal to maximize hydrogen utilization and prolong fuel cell life.