1. 19th March 2004 Advances in FC Modeling for Control System Development1 Advances in Fuel Cell Modeling for Control System Development F. Grasser Prof. A. Rufer EPFL Laboratoire d ’Electronique Industrielle Source: U. Bossel: « The Birth of the Fuel Cell »

2. 19th March 2004 Advances in FC Modeling for Control System Development2 Outline Introduction / Goals Modeling Concept Stack Modeling Goals Examples: Voltage, Gas Composition, Water Transfer Outlook Questions

3. 19th March 2004 Advances in FC Modeling for Control System Development3 Goals Intelligent System Control Controller maximizes power/efficiency by adjusting operating parameters (lambda, pressure, etc.) State estimation Reduce sensor requirements through estimation techniques Estimate non-measureable system parameters

4. 19th March 2004 Advances in FC Modeling for Control System Development4 Modeling Concept State variables inputs (user + system) outputs

5. 19th March 2004 Advances in FC Modeling for Control System Development5 Stack Modeling: Goals Describe overall voltage Model ‘average’ cell Lumped / averaged parameter description of processes in cell Describe membrane water content Average description of water fluxes across cell Describe water uptake dynamics (currently steady state)

6. 19th March 2004 Advances in FC Modeling for Control System Development6 Stack Modeling: Voltage Losses Equilibrium Voltage Nernst equation Activation overpotential Tafel equation Neglect anode side Concentration overpotential Describe one dimensional diffusion in the GDL Ionic overpotential Ohm’s Law for membrane resistance (fit against water content) Ohmic overpotential Ohm’s Law for GDL and BIP Partial reactant pressures at the reaction site  describe gas composition and diffusion Current density Included in “Nernst” potential  describe gas composition and diffusion Membrane water content  describe water transport Current density

7. 19th March 2004 Advances in FC Modeling for Control System Development7 Stack Modeling: Average Gas Composition Mass balance for each species  Average molar flowrate  Average molar fractions (H 2 0, O 2, N 2 ) Problem H2O, GDL needs to be known  Assume α (α = H 2 0,MEM / H 2 O,REACT )

8. 19th March 2004 Advances in FC Modeling for Control System Development8 Stack Modeling: Average Gas Composition

9. 19th March 2004 Advances in FC Modeling for Control System Development9 Stack Modeling: Reactant Transport Transport GC - GDL Sherwood analogy Transport within GDL Diffusion Account for gas composition in diffusivity Assumptions: Constant pressure in the z-direction Constant diffusivity (based on GC gas composition) Transport to catalyst layer Dissolution in ionomer-water mixture Henry’s Law

10. 19th March 2004 Advances in FC Modeling for Control System Development10 Reactant Transport: Averaging Considerations

11. 19th March 2004 Advances in FC Modeling for Control System Development11 Stack Modeling: Water Transport In this figure: “=“ = proportional to Problem: no analytical solution χ = f( H 2 O,mem ) H2O,mem = f(χ )

12. 19th March 2004 Advances in FC Modeling for Control System Development12 Outlook Experimental work parameter identification model verification Further modeling of the stack region Get analytical expression for steady-state water management Extend to describe membrane water uptake dynamics Designing control strategies

13. 19th March 2004 Advances in FC Modeling for Control System Development13 Questions ?