Stéphan Astier, 11/2008
Fuel Cells
Energy Modelling
Bond Graph
Stéphan Astier, 11/2008
Fuel cells
Bipolar plate
membrane
SOFC Stack
SOFC Stack
Stack PEMFC(1)
at high
température
> 700 °C
Works at 80°C
1 cell delivers very low voltage (0.7V)
serie connexion of mise en série de Ns cells (Ns 100)
STACK
1
Stéphan Astier, 11/2008
Different types
of fuel cells
Electrolyte
FC name
Charges nature
Température
eO2, N2, H 2O,
CO2
H2, H2O, CO 2
AFC
PEMFC
PAFC
MCFC
SOFC
alcalin
OH-
H2
H2O
H2
H2
H2O
CO2
H2
H2O
H+
O2
70-100°C
polymère
O2
70-100°C
acide
phosphorique
H2O
150-210°C
carbonate fondu
CO32-
O2
CO2
oxyde solide
O22-
O2
basses T°
< 200°C
hautes
T°
> 550°C
600-800°C
850-1100°C
+ Cogeneration
Fuel : H 2, (+C02 si MCFC)
OXYDANT: O2, (+N 2 si air) (+C02 si MCFC)
Stéphan Astier, 11/2008
PEM Fuel CELL
Show video
water
H2 + 1/2 02
H20 +
inverse electrolysis
Electricity
heat
Efficiency > 50 %
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Stéphan Astier, 11/2008
Energy modelling of electrochemical device
External environment = chemical and thermal energy stored
Air,
oxygen
Internal
storings
Electrochemical
component
2 internal storage
Electric double layer
Internal thermal storage
Entropy fluxes
Chemical
energy
Electric
energy
Electrochemical conversion
Diffusion losses
Conduction losses
Activation losses
External
storings
Electric
generator
or receptor
Thermal
use
Flux of matter
(oxider, reductor, electrolyte)
Thermal flux
flux electric charges
Stéphan Astier, 11/2008
Energy approach
Bond Graph principles
p=e.f
power
Energy exchanges within a system are described by bonds which represent
represent power exchanges.
energy object
1
e
f
energy object
2
Effort e and flow f have different interpretations in the different fields of physics.
physics.
System
Electrical
Mechanical
Chemical
Hydraulic
Thermal
e: Effort (unit)
v: Voltage (V)
F: Force (N)
: Chemical potential (J.mol-1)
f: flow (unit)
i: Current (A)
V: Velocity (m.s-1)
dn/dt: Molar flow (mol.s-1)
P: Pressure (Pa)
dq/dt: Volume flow (m3.s-1)
T: Temperature (K)
ds/dt: Entropy flow (J.K-1.s-1)
The causal bar indicates the effort direction.
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Stéphan Astier, 11/2008
Energy approach
Bond Graph elements
Only a limited number of elements are necessary to describe the majority of systems:
Element
Represents
R: r
Dissipation
Friction
Resistance
Equation without causality
e rf
0
df
0
dt
de
c
0
dt
I: i
Inertial storage
Inductance
C: c
Potential storage
Capacitance
Se
Environment
Effort source
e
cst
Sf
Environment
Flow source
f
cst
e i
f
An element RS (entropy production) can be used for coupling to a thermal part of the model.
Stéphan Astier, 11/2008
Energy approach
Bond Graph junctions
The exchanges between several elements or different fields of physics
physics
are implemented through junctions:
Junction
Represents
1
Equality of flows
Equation
ei
0
fi
0
i
0
Equality of efforts
i
TF
Transformer
e1
re2 , f 2
rf1
GY
Gyrator
e1
rf 2 , e2
rf1
Causal rules:
• only one element can fix the flow through a 11-junction ;
• only one element can fix the effort through a 00-junction.
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Stéphan Astier, 11/2008
Electrochemical conversion and energy storage
Electrochemical conversion
E
G
nF
I
nF J
E: battery openopen-circuit voltage
G: free enthalpy variation
I: current in the battery
J: molar flow of lithium ions
n: number of lithium ions moles exchanged for one mole of electrons
electrons (n=1)
F: Faraday constant
nF
- G (J.mol-1)
J
(mol.s-1)
E (V)
TF
Chemical field
I (A)
Electrical field
Stéphan Astier, 11/2008
Reversible eco-fuel / electricity storage systems
Principle of a H2/O2 Regenerative Fuel Cell RFC or URFC (Unitized …)
H2
Fuel Cell
O2
H2O
H2O
H2
Electicale
O2
Power
H2
O2
Electrolyser
Electricity
O2
H2
Heat
HEAT
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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Stéphan Astier, 11/2008
LithiumLithium-ion battery operation principle
Electrochemical process
I
Load
e-
Li ions
LiH'
Insertion
Li
Insertion
material
H'
conductor
material
material
H'
zLi
H
H
ze
zLi
ze
LiH
Stéphan Astier, 11/2008
LithiumLithium-ion battery model
Electrochemical conversion and energy storage
Energy storage
G: free enthalpy variation
G
G
0
G storage
G0: reference free enthalpy variation
Gstorage: available amount of chemical stored energy
- G0 (J.mol-1)
J (mol.s-1)
1
- G (J.mol-1)
J (mol.s-1)
nF
TF
E (V)
I (A)
- Gstorage (J.mol-1)
J (mol.s-1)
- G0
Cstorage
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Stéphan Astier, 11/2008
LithiumLithium-ion battery model
Activation and doubledouble-layer phenomena
Activation phenomenon
DoubleDouble-layer phenomenon
Electrode
Ract
If
Ract: linear activation resistance
act:
voltage drop due to activation phenomenon
If: faradic current
If
act
I
I dl
Electrolyte
e
Li
e
Li
e
Li
e
Li
Electrochemical
double-layer
Reactive process
Double layer capacitor
Propriétés comparées des moyens de stockage
Cdl
Stéphan Astier, 11/2008
7
Propriétés comparées des moyens de stockage
Stéphan Astier, 11/2008
Stéphan Astier, 11/2008
Electricity - hydrogen reversible transformation,
two energy carriers with complementary properties
Fuel Cell
WATER + ELECTRICITY + HEAT
HYDROGEN + OXYGEN
Electrolyser
I (A)
Electrolyser
Electricity
(Solare, …)
Hydrogen
energy
0,5 1
Flux carrier
1,5 2
V (volt)
Stock carrier
Fuel cell
I (A)
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Stéphan Astier, 11/2008
Thierry ALLEAU
Stéphan Astier, 11/2008
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Stéphan Astier, 11/2008
Thierry ALLEAU
Stéphan Astier, 11/2008
Thierry ALLEAU
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Stéphan Astier, 11/2008
Centrale 250 kW PEM
Ballard Power Systems
Electricity
and
Heat
Cogeneration
Stationary
Centrale domestique
7 kW PEM Plug Power
Stéphan Astier, 11/2008
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Stéphan Astier, 11/2008
THE HYDROGENE FUEL
A stock energy carrier
stored in a tank as gazoline
Energies spécifiques des combustibles
Meilleurs accumulateurs
actuels ( Li-ion)
Essence
Uranium
Hydrogène
10 000 Wh/kg 30 000 Wh/kg 116 106 Wh/kg
150 Wh/kg
What sources of hydrogen ?
What storage devices and tanks ?
What specifical energies ?
Stéphan Astier, 11/2008
Specific energies of hydrogen storage devices
Energy by mass
Energby volume
35
30
25
20
15
10
5
S1
Essence
Méthanol
Gaz nat liqu
bars
Gaz nat 200
H2 liquide
bars
H2 gaz 700
bars
H2 gaz 300
0
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Stéphan Astier, 11/2008
Thierry ALLEAU
Stéphan Astier, 11/2008
Thierry ALLEAU
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Stéphan Astier, 11/2008
Photographie NASA – Aerovironment 2002
A training device for a future power chain
« Solar energy, Hydrogen, Electricity »
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