PEM_Fuel_Cell_Electric_Circuit_Model

8/7/2019 PEM_Fuel_Cell_Electric_Circuit_Model

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PEM Fuel Cell Electric Circuit Model

Power Electronics for Fuel CellsWorkshop

National Fuel Cell Research Center

University of California, Irvine

August 8-9, 2002

Randall GemmenNational Energy Technology Lab

Parviz FamouriElectroMechanical Systems Lab

West Virginia University


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Goals for Modeling

Model the dynamic behavior of the fuel cell

Must be electrical circuit model

A Black box type model easy to use for power

electronics engineers

Use of standard circuit analysis packages such as

P-Spice


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Page 1

PEM Fuel Cell System

FuelSupplyAirSupply

Humidifier Humidifier

Anode

ExhaustCathode

Exhaust

+

_

Stack

Voltage


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Page 1

Proposed Fuel Cell Model

l Uniform & Constant Temperature: T=80 deg. C.

l Uniform & Constant Pressure: P=101000 Pa.Panode=PH2 + PH2O Pcathode=PO2 + PH2O+ PN2

l Stack voltage:Vstack= N [Eo + RT/nF ln(PH2 PO2

1/2 / PH2O) -Z*I -e -D]

where, N = number of cells,e = electrochemical overpotential,

D= diffusionoverpotential, Z = cell impedance.

l Cell impedance model accounts for cell electrical capacitance.

l Flow is laminar.

l Saturated inlet gas.

l Ignore condensation in channels.


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Page 1

Conservation Equations

l Anode Mole Conservation:

l Cathode Mole Conservation:

where, P=partial pressure, V=FC volume, m=mole flow, =mole density,

U=velocity, A=channel flow area, I=current, R=univ. gas constant,T=temperature.

F

IUAm

dt

dP

RT

VoutOinO

Oc

4)()( 2_2

2 = &

F

IUAm

dt

dP

RT

VoutHinH

Ha

2)()( 2_2

2 = &


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Page 1

Conservation Equations

l Flow:

where, K=flow constant,P=pressure drop across cell=Po-Ph, U=velocity,A=flowarea.

l Humidifier Pressure:

UAPKmin ==&

( )ohihh

hh mmV

RT

dt

dP&& =


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Page 1

Applied Circuit Analogy for P-Spice

l Voltage-Current Integration

Pressure=Voltage

Mole Flow=Current

Volume/RT=Capacitance

C

i

dt

dV=


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f1(I)

I- +

+

-

+

V

-

f2(I)

- +

f3(I)

- +

R1 R

2

C

where:

RT

2F

PH2

1.2

PO2

PH2O

f

1(I) = ln

-RT

F

I

IO

f2(I) = ln

RT

2F

I

Imax

f

3(I) = ln 1 -

Main Circuit

Electrochemical over potential

Concentration over potential

Nernst factor


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Humidifier Circuits

2iOm& V

O2/(RT

O2)

2oOm&R

O2

EO2

+P

hO2

-

2iH

m&

VH2/(RTH2)

2oHm&

RH2

EH2

+P

hH2

-

Air supply

Fuel Supply

( )22222

oHiHH

HhH

mmV

RT

dt

dP&&

=

( )222

22oOiO

O

OhO mm

V

RT

dt

dP&& =


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Conservation Circuits

inHm _2& I/2F

+

PH2

-

Va/(RT)

H2

UA

H2O

O2

H2

F

IUAm

dt

dP

RT

VoutHinH

Ha

2)()(

2_22 = &

F

IUAm

dt

dP

RT

VoutOinO

Oc

4)()( 2_2

2 = &inOm _2& I/4F

+

PO2

-

Vc/(RT)

O2

UA

inOHm _2&

I/2F

+

PH2O

-

Vc/(RT)

H2OUAF

IUAm

dt

dP

RT

VoutOHinOH

OHc

2)()( 2_2

2 += &


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Output Voltage

Stacks voltage at 100% flow rate at 1.4 kW


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V-I for Different Fuel Flow Rates

PEM Output Voltage vs. Current for Different Fuel

Flow Rates

0

10

20

30

40

50

60

70

0.0 10.0 20.0 30.0 40.0 50.0

Output Current (A)

Ou

tputVoltage(V)

100% Flow

75% Flow

50% Flow

25% Flow


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Conclusion

An electric circuit model for a PEM fuel cell isdeveloped based on

Cathode and anode humidifier circuit models

Cathode and anode mole conservation circuit models Model simulation behaves similar to PEM fuel cell

Experimental verification is planned

Development of SOF circuit model is next

Documents

PEM_Fuel_Cell_Electric_Circuit_Model