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

gi_heon_kim@nrel.gov, kander_smith@nrel.gov

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