Advances in Fuel Cell Modeling for Control System Development

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Advances in Fuel Cell Modeling for Control System
Development
EPFL Laboratoire d Electronique Industrielle
F. Grasser Prof. A. Rufer
Source U. Bossel  The Birth of the Fuel Cell 
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Outline

• Introduction / Goals
• Modeling Concept
• Stack Modeling
• Goals
• Examples Voltage, Gas Composition, Water
  Transfer
• Outlook
• Questions

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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

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Modeling Concept
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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)

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Stack Modeling Voltage Losses

• Equilibrium Voltage
• Nernst equation
• Activation overpotential
• Tafel equation
• Neglect anode side
• Concentration overpotential
• Describe one dimensionaldiffusion in the GDL
• Ionic overpotential
• Ohms Law for membrane resistance (fit against
  water content)
• Ohmic overpotential
• Ohms 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
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Stack Modeling Average Gas Composition

• Mass balance for each species
• Average molar flowrate
• Average molar fractions (H20, O2, N2)
• Problem H2O, GDL needs to be known
• Assume a (a H20,MEM / H2O,REACT)

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Stack Modeling Average Gas Composition
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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
• Henrys Law

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Reactant TransportAveraging Considerations
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Stack Modeling Water Transport
In this figure proportional to
Problem no analytical solution
? f(H2O,mem)
H2O,mem f(? )
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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

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Questions ?