three-dimensional lithium-ion battery model (presentation)
TRANSCRIPT
Three-Dimensional Lithium-Ion Battery ModelUnderstanding Spatial Variations in Battery Physics to Improve Cell
Design, Operational Strategy, and Management
Gi-Heon Kim and Kandler Smith
4th International Symposium on Large Lithium Ion Battery Technology and ApplicationTampa, Florida
May 12–14, 2008
[email protected], [email protected]
NREL/PR-540-43166
Multi-Scale Physics in Li-ion Battery
Li+
e
Li+
LixC6
Li+
e
Li+
LixC6
Li+
e
Li+
Liy-MetalOxide
Li+
e
Li+
Liy-MetalOxide
Solid-Phase Lithium TransportLithium Transport in Electrolyte
Electrochemical Kinetics
( ) Ues −−= φφη
Charge Conservation/Transport(Thermal) Energy Conservation
• Kinetics• Phase transition• Ion transport• Energy dissipation• Heat transfer
Basic battery physics occurs in a wide range of length & time scales
Requirements & Resolutions
[m]10-10
10-8
10-6
10-4
10-2
100
“Requirements” are usually defined in a macroscale domain and terms.
PerformanceLifeCostSafety
Design of Materials
VoltageCapacityLattice stabilityKinetic barrierTransport property
Design of Electrode ArchitectureLi transport path (local)Electrode surface areaDeformation & fatigueStructural stabilityInterface physics
Design of Electrodes Pairing and Lithium TransportElectrodes selectionLi transportPorosity, tortuosityLayer thicknesses Load conditions
Design of Electronic Current & Heat Transport
Electric & thermal connectionsDimensions, form factorComponent shapes
050
100150
200
0
50
100
1503.08
3.09
3.1
3.11
3.12
3.13
X(mm)
Voltage [V]
Y(mm)
10-10
10-8
10-6
10-4
10-2
100
10-10
10-8
10-6
10-4
10-2
100
Li+
NREL’s Li-ion Battery Model Activitiesfocusing on different length scale physics
a) Quantum mechanical and molecular dynamic modelingb) Numerical modeling resolving architecture of electrode materialsc) Electrode-scale performance model d) Cell-dimension 3D performance model
[m]
a) b) c) d)
Why use a 3D model?
Enhanced understanding provides an opportunity for improving cell …• Design• Operation Strategy• Management• Safety
Spatially Nonuniform Battery Physics
Dimension (Size effect, A/V )
Chemical Kinetics
Heat & Mass Transport
Charge Conservation
Spatial Distribution of …
• Electrical Potentials• Temperatures
Design of current and heat flow paths
Flux (gradient) Barrier (distance)
Spatial Difference(gradient x distance)
Electrode-Scale Model
Chemical Kinetics
( ) qTktTcp ′′′+∇⋅∇=∂∂ρ
Heat & Mass Transport
Charge Conservation
This model captures relevant solid-state and electrolyte diffusion dynamics and predicts the current/voltage response of a battery.
Composite electrodes are modeled using porous electrode theory, meaning that the solid and electrolyte phases are treated as superimposed continua without regard to microstructure.
Li+
r
NREL’s Model• Finite-Volume Method• Matlab Environment
(Doyle, Fuller, and Newman, 1993)
Addressing the effects of:
Nonuniform distributions Thermal/electrical path design inside cells/batteries Localized phenomena Geometries; shape and dimensions of cell component
3D Battery Dimension Model
Current Density
Temperature
Current DensityCurrent Density
TemperatureTemperature
Approach in the Present Study:Multi-Scale Multi-Dimensional (MSMD) Modeling
Cur
rent
Col
lect
or (C
u)
Cur
rent
Col
lect
or (A
l)
p
Neg
ativ
eE
lect
rode
Sep
arat
or
Pos
itive
Ele
ctro
de
Image source: www.dimec.unisa.it
SimulationDomain
X
R
x
=
• Multi-scale physics from sub-micro-scale to battery-dimension-scales• Difficulties in resolving microlayer structures in a computational grid
Macro Grid Micro Grid(Grid for Sub-grid-scale Model)
+
To Address …
),,( tRXT ),,,( txRXsφ),,,( txRXeφ
),,,,( trxRXcs
),,,( txRXce
Cur
rent
Col
lect
or (C
u)
Cur
rent
Col
lect
or (A
l)
p
Neg
ativ
eE
lect
rode
Sep
arat
or
Pos
itive
Ele
ctro
de
Image source: www.dimec.unisa.it
Detailed Structure
X
R
x
≈ Cell Dimension Transport Model
Electrode Scale Submodel (1D)+
),,( tRXV
),,,( txRXQi
),,,( txRXjLi),,( tRXSOC
),,( tRXi
VAdxQtRXQ
xi∫=),,(
NOTE:Selection of the “sub-grid electrochemical model” is independent of the “macro-grid model” selection.
Solution Variables
T∞=35oCh= 25W/m2K 163mm
3mm
27mmkX= 29W/mKkR= 0.8W/mK
X
R
time step size: 0.5 sec, time step #: 360
Computation time: 98 minutes (Windows/PC)Simulation time: 3 minutes
Axisymmetric FVM Model for Macro-Domain Model + 1D FVM Model for Electrochemistry Submodel
Model Combination
150A Constant Current Discharge
X R x rGrid# 12 8 14 4
0 0.5 1 1.5 2 2.52.5
3
3.5
4
Time(min)
Vol
tage
(V)
Vo
Vocv
0 0.5 1 1.5 2 2.52.5
3
3.5
4
Time(min)
Vol
tage
(V)
Vo
Vocv
Simulation ResultsSnapshot 2 minutes after start of discharge
X(mm)R
(mm
)
Normalized ANODE SURFACE CONCENTRATION
0 20 40 60 80 100 120 140 1605
10
15
20
25
0.99
0.995
1
1.005
1.01
X(mm)
R(m
m)
Normalized CHATHODE SURFACE CONCENTRATION
0 20 40 60 80 100 120 140 1605
10
15
20
25
0.99
0.995
1
1.005
1.01
X(mm)
R(m
m)
TEMPERATURE [oC]
0 20 40 60 80 100 120 140 1605
10
15
20
25
48
49
50
X(mm)
R(m
m)
CURRENT PRODUCTION [A/m2]
0 20 40 60 80 100 120 140 1605
10
15
20
25
162
164
166
168
X
R
For details about the State Variable Model:See the Poster Presentation by Kandler Smith (NREL) titled,
“Fast Running Electrochemistry-Based Models for Battery Design, Integration, and Control”
SVM is preferred because of its fast executionSVM, developed by Kandler Smith (NREL), quickly solves “Newman type”
governing equations using numerical schemes for calculating load reduction.Dropping very fast battery responses (approx. 60 Hz or more) is one of the main
calculation order reduction methods used in the model.SVM is promising for use in on-board BMS reference model because of its
fast execution and capability to provide nonmeasurable electrochemical parameters and current and voltage responses with potentially better accuracy.
MSMD model incorporating SVM Submodel runs ~1.75 faster than real time.
Axisymmetric FVM Model for Macro-Domain Model + State Variable Model (SVM) for Submodel
Another Combination Choice
Analysis
Temperature Variation in a Cylindrical CellUniform Potential AssumptionImpact of Aspect RatioImpact of Cell Size
Temperature & Potential Variation in a Prismatic CellImpact of Tab Location and Size
Analysis
Temperature Variation in a Cylindrical CellUniform Potential AssumptionImpact of Aspect RatioImpact of Cell Size
Temperature & Potential Variation in a Prismatic CellImpact of Tab Location and Size
Considerations for Addressing Thermal Issues in PHEV-type Cells
High energy and high power requirements
Large format may be preferred to small cellsFewer number of components Fewer interconnectsLess monitoring & balancing circuitryLess expensiveLess weight
Significant heating may be possible, depending on power profile
Internal temperature imbalance can lead to unexpected performance and life degradation
For a fixed capacity (electrode volume), surface area for heat rejection can be increased via:
• Reducing D/H ratio• Increasing number of cells in parallel (#P) 1P
2P
3P
40Ah
D
H
*Surface area includes side, top & bottom of can. All cells assumed to have inactive inner mandrel with 8mm diameter.
Analysis Parameters
20Ah
13.3
Ah
The two cases explored in this presentation:
2
Tamb= 35˚CSOC = 50%
• Steady-State, Charge Sustaining• Liquid Cooling (150 W/m2K)
200A Geometric Cycle2
Tamb= 35˚CSOC = 50%Tamb= 35˚CSOC = 50%
• Steady-State, Charge Sustaining• Liquid Cooling (150 W/m2K)
200A Geometric Cycle
Moderate Thermal Condition Severe Thermal Condition
Two Usage Profiles
1• Transient, Charge Depleting• Natural Convection (15 W/m2K)
Tinit = 35˚CTamb= 35˚CSOCinit = 100%
150A Max. Cont. Discharge1• Transient, Charge Depleting• Natural Convection (15 W/m2K)
Tinit = 35˚CTamb= 35˚CSOCinit = 100%
Tinit = 35˚CTamb= 35˚CSOCinit = 100%
150A Max. Cont. Discharge
Air
1• Transient, Charge Depleting• Natural Convection (15 W/m2K)
Tinit = 35˚CTamb= 35˚CSOCinit = 100%
150A Max. Cont. Discharge1• Transient, Charge Depleting• Natural Convection (15 W/m2K)
Tinit = 35˚CTamb= 35˚CSOCinit = 100%
Tinit = 35˚CTamb= 35˚CSOCinit = 100%
150A Max. Cont. Discharge
Air
T
Q
i
D/H = ¼h = 15 W/m2KTamb = 35°C
Transient Results
Results:150 A Continuous Discharge
After 500 seconds of discharge:• Cell center is slightly warmer
than exterior• Preferential reaction current at
cell center
Near the end of discharge:• Cell center depleted/saturated• Preferential reaction current at
cell exterior
D/H = ¼h = 15 W/m2KTamb = 35 C
1P
2P
3P
Moderate usage + air convection = small internal gradients
2.7˚C
150 A Single Discharge (at End)
40Ah
D
H
20Ah
13.3
Ah
200 A Geometric Cycling
∆T= ~17 oC
~16% difference inlocal current production
At Steady State
( )AI
i
avgTT −D/H = ¼h = 150 W/m2KTamb = 35°C1P size cell (40 Ah)
1P
D/H = ¼h = 150 W/m2KTamb = 35 C
2P
3P
Severe usage + liquid cooling = large internal gradients
18˚C
200 A Geometric Cycle (Steady-State)
40Ah
D
H
20Ah
13.3
Ah
h = 150 W/m2KTamb = 35°C
• Under severe usage, low D/H and/or >1P designs significantly reduce thermal stress
• Larger diameter leads to higher internal gradient
• Multidimensional electrochemical cell model quantified the impacts of D/H aspect ratio and cell size on the internal temperature difference.
Internal Temperature DifferenceD/H ratio ~4.5˚C ↕2P ~6.0˚C, 3P ~9.0˚C ↓ Tavg
Tamb
ΔTint
-1
200 A Geometric Cycle (Steady-State)
Analysis
Temperature Variation in a Cylindrical CellUniform Potential AssumptionImpact of Aspect RatioImpact of Cell Size
Temperature & Potential Variation in a Prismatic CellImpact of Tab Location and Size
Impact of Tab Location & Size
200 mm
150 mm
• Thickness: 12 mm• 40 Ah• 2-minute discharge, 200 A• 200A geometric cycle
30 mm
60 mm
200A Discharge for 2 minutes
0 20 40 60 80 100 1200
50
100
150
200
250
300
t (s)
I(t) (
A)
Current Field – 2-min 200 A discharge
X(mm)
Y(m
m)
Current Density in positive foil
0 20 40 60 80 100 120 140 160 180 2000
50
100
150
X(mm)
Y(m
m)
Current Density in negative foil
0 20 40 60 80 100 120 140 160 180 2000
50
100
150
X(mm)
Y(m
m)
Current Density in positive foil
0 20 40 60 80 100 120 140 160 180 2000
50
100
150
X(mm)
Y(m
m)
Current Density in negative foil
0 20 40 60 80 100 120 140 160 180 2000
50
100
150
Voltage across Current Collector Foils – 2-min 200 A discharge
Vmax-Vmin= 0.0364 V Vmax-Vmin = 0.0154 V
050
100150
200
0
50
100
1503.08
3.09
3.1
3.11
3.12
3.13
X(mm)
Voltage [V]
Y(mm) 050
100150
200
0
50
100
1503.08
3.09
3.1
3.11
3.12
3.13
X(mm)
Voltage [V]
Y(mm)
Temperature – 2-min 200 A discharge
050
100150
200
0
50
100
15046
47
48
49
50
51
52
X(mm)
Temperature [°C]
Y(mm) 050
100150
200
0
50
100
15046
47
48
49
50
51
52
X(mm)
Temperature [°C]
Y(mm)
Tmax-Tmin = 5.03oC Tmax-Tmin = 1.35oC
0 20 40 60 80 100 120
35
40
45
50
t (s)
T(t)
(° C)
avarage temperaturemaximum temperatureminimum temperature
0 20 40 60 80 100 120
35
40
45
50
t (s)
T(t)
(° C)
avarage temperaturemaximum temperatureminimum temperature
imax-imin = 4.54 A/m2
050
100150
200
0
50
100
150155
160
165
170
175
X(mm)
Current Production [A/m2]
Y(mm) 050
100150
200
0
50
100
150155
160
165
170
175
X(mm)
Current Production [A/m2]
Y(mm)
imax-imin = 13.2 A/m2
Current Production – 2-min 200 A discharge
SOC – 2-min 200 A discharge
SOCmax-SOCmin = 1.91%
050
100150
200
0
50
100
15059.5
60
60.5
61
61.5
62
X(mm)
soc [%]
Y(mm)050
100150
200
0
50
100
15059.5
60
60.5
61
61.5
62
X(mm)
soc [%]
Y(mm)
SOCmax-SOCmin = 0.76%
200A Geometric Cycling
0 200 400 600 800-300
-200
-100
0
100
200
300
t (s)
I(t) (
A)
Temperature Variation
0 200 400 600 800
35
40
45
50
55
t (s)
T(t)
(° C)
avarage temperaturemaximum temperatureminimum temperature
050
100150
200
0
50
100
150-3
-2
-1
0
1
2
3
X(mm)
T - avg(T)
Y(mm)
050
100150
200
0
50
100
15042.5
42.6
42.7
42.8
42.9
43
X(mm)
soc [%]
Y(mm)
SOC swing
050
100150
200
0
50
100
15056.5
57
57.5
58
X(mm)
[ ]
Y(mm)
SOC [%]
0
100
200
0
50
100
15014
14.5
15
15.5
X(mm)
soc swing [%]
Y(mm)
SummaryNonuniform battery physics, which is more probable in large-format
cells, can cause unexpected performance and life degradations in lithium-ion batteries.
A three-dimensional cell performance model was developed by integrating an electrode-scale submodel using a multiscale modelingscheme.
The developed tool will be used to provide better understanding and help answer engineering questions about improving cell design, cell operational strategy, cell management, and cell safety.
Engineering Questions to be addressed in future works include …What is the optimum form-factor and size of a cell?Where are good locations for tabs or current collectors?How different are measured parameters from their non-measurable internal values? Where is the effective place for cooling? What should the heat-rejection rate be?How does the design of thermal and electrical paths impact under current-related safety events, such as internal/external short and overcharge?
Acknowledgments
DOE and FreedomCAR-Fuel Partnership Support• Tien Duong• Dave Howell
NREL Energy Storage Task• Ahmad Pesaran