19th March 2004 Advances in FC Modeling for Control System Development

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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 »

19th March 2004 Advances in FC Modeling for Control System Development

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Outline

• Introduction / Goals

• Modeling Concept

• Stack Modeling

• Goals

• Examples: Voltage, Gas Composition, Water

Transfer

• Outlook

• Questions

19th March 2004 Advances in FC Modeling for Control System Development

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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

Fuel Cell System MeasurementsController

Estimation

User

19th March 2004 Advances in FC Modeling for Control System Development

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Mair outlet

cooling pump

air compressor

pres

sure

con

trol

val

ve

hydrogen recirculation pump

Fuel Cell

H2

M

air

hydrogen

backpressureregulator

heatexchanger

M

M

H

H

Modeling Concept

State variablesinputs (user + system)outputs

19th March 2004 Advances in FC Modeling for Control System Development

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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)

19th March 2004 Advances in FC Modeling for Control System Development

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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

19th March 2004 Advances in FC Modeling for Control System Development

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Stack Modeling: Average Gas Composition

y

zx

IN

OUTGDL

Cathode Gas Channel

O2, in

H2O, in

N2, in

O2, out

H2O, out

N2, out

O2, GDLH2O, GDL

Mass balance for each speciesAverage molar flowrateAverage molar fractions (H20, O2, N2)

Problem H2O, GDL needs to be known

Assume α (α = H20,MEM / H2O,REACT)

19th March 2004 Advances in FC Modeling for Control System Development

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Stack Modeling: Average Gas Composition

19th March 2004 Advances in FC Modeling for Control System Development

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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• Henry’s Law

cathode GDLcatalyst layer GC

cO21 cO2

GCcO22cO2

3

19th March 2004 Advances in FC Modeling for Control System Development

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Reactant Transport:Averaging Considerations

19th March 2004 Advances in FC Modeling for Control System Development

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Stack Modeling: Water Transport

In this figure: “=“ = proportional to

Problem: no analytical solution χ = f(H2O,mem)

H2O,mem = f(χ )

H2O, dif = Δξ

H2O, drag = I

H2O, conv = Δp

H2O, GDL = ΔξH2O, GDL = ΔξχH2O = ξa*

pa

χH2O = ξc*

pc

ξa ξc

anode GDL cathode GDLmembrane

H2O, react = I

19th March 2004 Advances in FC Modeling for Control System Development

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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

19th March 2004 Advances in FC Modeling for Control System Development

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Questions ?