Stéphan Astier, 11/2008 Fuel Cells Energy Modelling Bond...

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Stéphan Astier, 11/2008

Fuel Cells

Energy Modelling

Bond Graph


Fuel cells

SOFC Stack

Stack PEMFC(1)

Works at 80°C

SOFC Stack

at hightempérature

> 700 °C

1 cell delivers very low voltage (0.7V)

serie connexion of mise en série de Ns cells (Ns 100) STACK

membraneBipolar plate

2


AFC

PEMFCPAFC

MCFC

SOFC

70-100°C

70-100°C

150-210°C

600-800°C

850-1100°C

basses T°

> 550°C

OH-

CO32-

O22-

H+

alcalin

polymère

acidephosphorique

carbonate fondu

oxyde solide

< 200°C

hautesT°

H2

H2

H2

H2

H2O

H2O

H2OCO2

O2

O2

O2

O2

H2O

CO2

H2, H2O, CO2

Fuel : H2, (+C02 si MCFC)

O2, N2, H2O,CO2

OXYDANT: O2, (+N2 si air) (+C02 si MCFC)

e-

FC name

Electrolyte Charges nature

Different typesof fuel cells

Température

+ Cogeneration


PEM Fuel CELL

Electricityheat

H2 + 1/2 02 H20

inverse electrolysis

water

Efficiency > 50 %

Show video

+

3


Diffusion losses

Activation losses

Conduction losses

Electricenergy

Electrochemical conversionChemicalenergy

Electricgenerator

or receptor

External environment = chemical and thermal energy stored

Externalstorings

Air,oxygen

Thermaluse

Internalstorings

Flux of matter(oxider, reductor, electrolyte)

Entropy fluxes

Thermal flux

2 internal storageElectric double layer

flux electric charges

Electrochemicalcomponent

Internal thermal storage

Energy modelling of electrochemical device


Energy approachEnergy approach

Bond Graph principlesBond Graph principles

Energy exchanges within a system are described by bonds which reEnergy exchanges within a system are described by bonds which represent power exchanges.present power exchanges.

eeenergy object11

energy object22ff

eeenergy object11

energy object22ff

EffortEffort ee and flowand flow ff have different interpretations in the different fields of physihave different interpretations in the different fields of physics.cs.

ds/dt: Entropy flow (J.K-1.s-1)T: Temperature (K)Thermal

dq/dt: Volume flow (m3.s-1)P: Pressure (Pa)Hydraulic

dn/dt: Molar flow (mol.s-1): Chemical potential (J.mol-1)Chemical

V: Velocity (m.s-1)F: Force (N)Mechanical

i: Current (A)v: Voltage (V)Electrical

f: flow (unit)e: Effort (unit)System

The causal bar indicates the effort direction.The causal bar indicates the effort direction.

p = e . f power

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Bond Graph elementsBond Graph elements

Only a limited number of elements are necessary to describe theOnly a limited number of elements are necessary to describe the majority of systems:majority of systems:

An elementAn element RSRS (entropy production) can be used for coupling to a thermal part of the model.can be used for coupling to a thermal part of the model.

EnvironmentFlow source

SSff

EnvironmentEffort source

SSee

Potential storageCapacitance

CC: c

Inertial storageInductance

II: i

DissipationFriction

Resistance

RR: r

Equation without causalityRepresentsElement

0rfe

0dtdfie

0dtdecf

cste

cstf



Bond Graph junctionsBond Graph junctions

The exchanges between several elements or different fields of phThe exchanges between several elements or different fields of physicsysicsare implemented through junctions:are implemented through junctions:

GyratorGY

TransformerTF

Equality of efforts0

Equality of flows1

EquationRepresentsJunction

iie 0

iif 0

1221 , rffree

1221 , rferfe

Causal rules:Causal rules:

•• only one element can fix the flow through a 1only one element can fix the flow through a 1--junction ;junction ;•• only one element can fix the effort through a 0only one element can fix the effort through a 0--junction.junction.

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EE: battery open: battery open--circuit voltagecircuit voltage

Electrochemical conversion and energy storageElectrochemical conversion and energy storage

Electrochemical conversionElectrochemical conversion

-- G (J.molG (J.mol--11))

J (mol.sJ (mol.s--11))

E (V)E (V)

I (A)I (A)TFTF

Chemical fieldChemical field Electrical fieldElectrical field

GG: free enthalpy variation: free enthalpy variation

II: current in the battery: current in the battery

JJ: molar flow of lithium ions: molar flow of lithium ions

nn: number of lithium ions moles exchanged for one mole of electro: number of lithium ions moles exchanged for one mole of electrons (n=1)ns (n=1)

FF: Faraday constant: Faraday constant

nFG

E

JnFI

nF


ElectricityFuel Cell

ElectrolyserH2

H2

H2O2

O2

O2

H2O Electicale

Power

Heat

Fuel Cell

ElectrolyserH2

H2

H2O2

O2

O2

H2O Electicale

Power

Heat

H2 O2H2O

HEAT

Principle of a H2/O2 Regenerative Fuel Cell RFC or URFC (Unitized …)

Reversible eco-fuel / electricity storage systems

System equivalent to a battery but decoupling ENERGY and POWER

H2 / O2 but also many other redox couples

(redox flow batteries, metal air fuel cells)

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LithiumLithium--ion battery operation principleion battery operation principle

Electrochemical processElectrochemical process

ionsLi ee--

LoadLoadII

zezLiH'LiH' LiHzezLiH

H'materialInsertion

HmaterialInsertion

materialconductor

Li

ionsLi ee--

LoadLoadIIII

zezLiH'LiH' LiHzezLiH

H'materialInsertion

HmaterialInsertion

materialconductor

Li


LithiumLithium--ion battery modelion battery model

Electrochemical conversion and energy storageElectrochemical conversion and energy storage

Energy storageEnergy storage

GG: free enthalpy variation: free enthalpy variation

GG00: reference free enthalpy variation: reference free enthalpy variation

GGstoragestorage: available amount of chemical stored energy: available amount of chemical stored energy

-- G (J.molG (J.mol--11))J (mol.sJ (mol.s--11))

E (V)E (V)I (A)I (A)TFTF11-- GG00 (J.mol(J.mol--11))

J (mol.sJ (mol.s--11))

J (m

ol.s

J (m

ol.s

-- 11))

--GG

stor

age

stor

age

(J.m

ol(J

.mol

-- 11))

CCstoragestorage

-- GG00nF

storage0 GGG

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LithiumLithium--ion battery modelion battery model

Activation and doubleActivation and double--layer phenomenalayer phenomena

Activation phenomenonActivation phenomenon

f

actact I

R

RRactact: linear activation resistance: linear activation resistance

actact: voltage drop due to activation phenomenon: voltage drop due to activation phenomenon

IIff: faradic current: faradic current

Li

Li

Li

Li

e

e

e

e

I

fI

dlI

Electrochemicaldouble-layer

Reactive process

Double layer capacitor

ElectrolyteElectrode

DoubleDouble--layer phenomenonlayer phenomenon

CCdldl

Stéphan Astier, 11/2008Propriétés comparées des moyens de stockage

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Stéphan Astier, 11/2008Propriétés comparées des moyens de stockage


Electricity - hydrogen reversible transformation,two energy carriers with complementary properties

Electricity(Solare, …)

Flux carrier

Hydrogenenergy

Stock carrier

Electrolyser

I (A)

V (volt)210,5 1,5

I (A)

Fuel cell

HYDROGEN + OXYGEN

Electrolyser

Fuel CellWATER + ELECTRICITY + HEAT HYDROGEN + OXYGEN

Electrolyser

Fuel CellWATER + ELECTRICITY + HEAT HYDROGEN + OXYGEN

Electrolyser

Fuel CellWATER + ELECTRICITY + HEAT

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Thierry ALLEAU


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Thierry ALLEAU


Thierry ALLEAU

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Centrale 250 kW PEMBallard Power Systems

Centrale domestique

7 kW PEM Plug Power

Stationary

ElectricityandHeat

Cogeneration


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THE HYDROGENE FUEL

What sources of hydrogen ?

What storage devices and tanks ?

What specifical energies ?

A stock energy carrierstored in a tank as gazoline

Energies spécifiques des combustiblesMeilleurs accumulateurs

actuels ( Li-ion)150 Wh/kg

Essence

10 000 Wh/kg

Hydrogène

30 000 Wh/kg

Uranium

116 106 Wh/kg


H2

gaz

300

bars

H2

gaz

700

bars

H2

liqui

de

Gaz

nat

200

bars

Gaz

nat

liqu

Mét

hano

l

Esse

nce

S 1

05

1 01 52 02 53 03 5

Specific energies of hydrogen storage devices

Energby volume

Energy by mass

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Thierry ALLEAU


Thierry ALLEAU

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A training device for a future power chain« Solar energy, Hydrogen, Electricity »

Photographie NASA – Aerovironment 2002

Stéphan Astier, 11/2008 Fuel Cells Energy Modelling Bond...

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