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Multi-Scale Multi-Dimensional Li-ion Battery 

Model for Better Design and Management

PRiME 2008, 214th Electrochemical Society Pacific Rim Meeting

Honolulu, HI • October 12–17, 2008

Sponsored by Electrochemical Society

Gi-Heon Kim* and Kandler Smith

National Renewable Energy Laboratory

*gi_heon_kim@nrel.gov • NREL/PR-540-44350

Sustainable Energy Future 
National Renewable Energy Laboratory 2 Innovation for Our Energy Future

10 [m] -10 10-8 10-6 10-4 10-2 100

“Requirements” are usually defined 

in a macroscale domain and terms.

Performance

Life

Cost

Safety

Design of Materials

Voltage

Capacity

Lattice stability

Kinetic barrier

Transport property

Design of Electrode 

Architecture

Li transport path (local)

Electrode surface area

Deformation & fatigue

Structural stability

Surface physics

Design of Electrodes 

Pairing and Lithium 

Transport

Electrodes selection

Li transport

Porosity, tortuosity

Layer thicknesses 

Load conditions

Design of Electron 

Current & Heat 

Transport

Electric & thermal 

connections

Dimensions, form factor

Component shapes

Requirements & Resolutions 

Multi-Scale Physics in Li-Ion Battery
National Renewable Energy Laboratory 3 Innovation for Our Energy Future

0

50

100

150

200

0

50

100

150

3.08

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+

a) Quantum mechanical and molecular dynamic modeling

b) Numerical modeling for addressing the impacts of the architecture of 

electrode materials

c) 1D performance model capturing solid-state and electrolyte diffusion 

dynamics

d) Cell-dimension 3D model for evaluating macroscopic design factors

[m]

a) b) c) d)

The Need for a Multi-Scale Model

Numerical approaches focusing on different length scale physics
National Renewable Energy Laboratory 4 Innovation for Our Energy Future

Why Macro-scale Transport Becomes Critical

Sub-electrode scale physics

Kinetics

Li diffusion

Ion transport

Heat dissipation

Spatial variation of ...

• Electric potentials

• Temperatures

Design of current and 

heat flow paths

Size Effect

Dimension

Surface Area / Volume

Spatial Difference

(gradient x distance)

Flux (gradient) 

Barrier (distance)

Dimension Increase

Spatial Imbalance

Increase
National Renewable Energy Laboratory 5 Innovation for Our Energy Future Current Collector (Cu) Current Collector (Al)

p

Negative

Electrode

Separator

Positive

Electrode

Image source: www.dimec.unisa.it

Simulation

Domain

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 Model)

+

To address ...

Multi-Scale Multi-Dimensional (MSMD) Modeling

Approach in the Present Study
National Renewable Energy Laboratory 6 Innovation for Our Energy Future

tRXT ),,( txRX ),,,( φs

txRX ),,,( φe

trxRXc ),,,,(s

txRXc ),,,(e

tRXV ),,(

txRXQ ),,,(i

txRXj ),,,( Li

SOC tRX ),,(

tRXi ),,(

V

Adx QtRXQ

x

= ∫ i ),,(

NOTE:

Selection of solution scheme 

for either grid system is 

independent of the other.

Current Collector (Cu)

Current Collector (Al)

p

Negative

Electrode

Separator

Positive

Electrode

Image source: www.dimec.unisa.it

Detailed 

Structure

X

R

x

≈ Cell Dimension 

Transport Model

Electrode Scale 

Submodel (1D) +

Solution Variables
National Renewable Energy Laboratory 7 Innovation for Our Energy Future

Previous Studies

AABC 08, Tampa, May 2008
National Renewable Energy Laboratory 8 Innovation for Our Energy Future

Previous Studies

AABC 08, Tampa, May 2008
National Renewable Energy Laboratory 9 Innovation for Our Energy Future

Previous Studies

AABC 08, Tampa, May 2008

“Poorly designed electron 

and heat transport paths can 

cause excessive nonuniform use of materials, 

and then deteriorate the performance and 

shorten the life of the battery.” 

Findings:
National Renewable Energy Laboratory 10 Innovation for Our Energy Future

Previous Studies

AABC 08, Tampa, May 2008

“Poorly designed electron 

and heat transport paths can 

cause excessive nonuniform use of materials, 

and then deteriorate the performance and 

shorten the life of the battery.” 

Findings:
National Renewable Energy Laboratory 11 Innovation for Our Energy Future

Previous Studies

Int’l Conf. on Advanced Li Batteries for Automotive App., ANL, Sept. 2008

Model Validation Study against Thermal Imaging Test Data 

“Heat and electron transport interacts 

with micro-scale electrochemical 

processes and determines the distribution 

of temperature and electric potential.” 

Findings:
National Renewable Energy Laboratory 12 Innovation for Our Energy Future

Previous Studies

Int’l Conf. on Advanced Li Batteries for Automotive App., ANL, Sept. 2008

Model Validation Study against Thermal Imaging Test Data 

“Heat and electron transport interacts 

with micro-scale electrochemical 

processes and determines the distribution 

of temperature and electric potential.” 

Findings:
National Renewable Energy Laboratory 13 Innovation for Our Energy Future

Previous Studies

Int’l Conf. on Advanced Li Batteries for Automotive App., ANL, Sept. 2008

Model Validation Study against Thermal Imaging Test Data 

“Heat and electron transport interacts 

with micro-scale electrochemical 

processes and determines the distribution 

of temperature and electric potential.” 

Findings:
National Renewable Energy Laboratory 14 Innovation for Our Energy Future

Previous Studies

Int’l Conf. on Advanced Li Batteries for Automotive App., ANL, Sept. 2008

Model Validation Study against Thermal Imaging Test Data 

“Heat and electron transport interacts 

with micro-scale electrochemical 

processes and determines the distribution 

of temperature and electric potential.” 

Findings:
National Renewable Energy Laboratory 15 Innovation for Our Energy Future

Current Analysis

Macro-Scale Design Evaluation

Impacts of “Aspect Ratio” of a Cylindrical Cell

“Nominal”

“Large H” “Large D”

Each cell was virtually designed to deliver 20 Ah for PHEV-10 Applications.
National Renewable Energy Laboratory 16 Innovation for Our Energy Future

Assumption for Model Simplification

Extended Foil

Extended Foil Axisymmetric
National Renewable Energy Laboratory 17 Innovation for Our Energy Future

Brief Look at What “H/D Ratio” Means 

2

2

, ~ H i P foilloss δ

ρ ⋅ ′′

H

W

Volume = const

Identical electrodes

Same foil thicknesses

Al: 20 μm, Cu: 15 μm

H

D

H x W = const

i′′: current [A/m2] 

ρ: resistivity

δ: foil thickness

0

0

H

P
National Renewable Energy Laboratory 18 Innovation for Our Energy Future

Brief Look at What “H/D Ratio” Means 

2

2

, ~ H i P foilloss δ

ρ ⋅ ′′

2 ~ H i Vfoil δ

ρ ⋅ ′′

∆

H

W

Volume = const

Identical electrodes

Same foil thicknesses

Al: 20 μm, Cu: 15 μm

H

D

H x W = const

+

-

e- +

- eVoltage at Positive Foil Voltage at Negative Foil

i′′: current [A/m2] 

ρ: resistivity

δ: foil thickness

0

0

H

δ

ρ 2 ⋅i ′′

δ

ρ 2 ⋅i ′′

+

-

P
National Renewable Energy Laboratory 19 Innovation for Our Energy Future

10-s Power Capability Comparison

Large H

Nominal

Large D

• Large H design has almost 10% less power 

capability.

D[mm]: 28

H[mm]: 350

D[mm]: 50

H[mm]: 107

D[mm]: 115

H[mm]: 20

40

110

90

60

50

100

80

70

120

30

27

73

60

40

33

67

53

47

80

20

10 20 30 40 50 60 70 80 90

SOC (%)

Discharge Power (kW)

Charge Power (kW)

HPPC, BSF = 78

Hybrid Pulse Power Characterization (HPPC) 

Battery Size Factor = 78
National Renewable Energy Laboratory 20 Innovation for Our Energy Future

Analysis Macro-Scale Design Evaluation

Constant Discharge Simulation

Standard Vehicle Driving Profile Simulation 

Impacts of “Aspect Ratio” of a Cylindrical Cell
National Renewable Energy Laboratory 21 Innovation for Our Energy Future

0 2 4 6 8 10 12

25

30

35

40

45

t (m)

T (oC)

Tmin

T

avg

Tmin

0 2 4 6 8 10 12

2

2.5

3

3.5

4

t (m)

V (V)

5C Discharge

R (mm)

0

5

10

15

20

25

R (mm)

0

5

10

15

20 A B 25

A

A

B

B

Temperature, T-Tavg

Reaction Current, (i-iavg)/iavg [%]

Working Potential

A

– Nominal Cell + -
National Renewable Energy Laboratory 22 Innovation for Our Energy Future

0 2 4 6 8 10 12

2

2.5

3

3.5

4

t (s)

V (V)

Large D

Nominal

Large H

0 2 4 6 8 10 12

25

30

35

40

45

t (s)

T

avg (° C)

Large D

Nominal

Large H

Snapshot Comparison for H/D ratio

X (mm)

0 20 40 60 80 100

5

10

15

20

25

X (mm)

0 10

5

10

15

20

25

30

35

40

45

50

55

0 50 100 150 200 250 300

4

6

8101214

X (mm)

0 10

5

10

15

20

25

30

35

40

45

50

55

X (mm)

0 20 40 60 80 100

5

10

15

20

25

0 50 100 150 200 250 300

4

6

8101214

-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

∆i [%]

X (mm)

0 10

5

10

15

20

25

30

35

40

45

50

55

0 20 40 60 80 100

5

10

15

20

25

0 50 100 150 200 250 300

4

6

8101214

3.318

3.32

3.322

3.324

3.326

3.328

V

V ∆i [%]

∆i [%]

V

T-Tavg

T-Tavg

T-Tavg

5C Discharge
National Renewable Energy Laboratory 23 Innovation for Our Energy Future

Analysis Macro-Scale Design Evaluation

Constant Discharge Simulation

Standard Vehicle Driving Profile Simulation

Impacts of “Aspect Ratio” of a Cylindrical Cell
National Renewable Energy Laboratory 24 Innovation for Our Energy Future

Approach Virtual Design Evaluation

20Ah PHEV10

Vehicle Simulator

-10

0

10

20

30

40

50

60

70

80

90

0 100 200 300 400 500 600

Time (s)

Vehicle Speed

US06 Midsize Sedan

PHEV 10

0 10 20 30 40 50 60

-600

-400

-200

0

200

400

600

800

CD CS

Power Profile

Multi-Scale

Multi-Dimensional 

Li-ion Battery Model

Battery Responses Feedback
National Renewable Energy Laboratory 25 Innovation for Our Energy Future

US06 Charge-Depleting Cycle

0 100 200 300 400 500 600 700 800

25

30

35

40

45

t (s)

T

avg (° C)

Large D

Nominal

Large H

0 100 200 300 400 500 600 700 800

0

1

2

3

t (s)

T

max

 - Tmin (° C)

0 100 200 300 400 500 600 700 800

0

5

10

15

t (s)

Qtot (kJ)

Large H cell has greatest 

temperature rise because 

long electronic current paths 

result in high foil heating.

Large H cell has greatest 

internal temperature imbalance.

0 10 20 30 40 50 60

-600

-400

-200

0

200

400

600

800

Power (W)

Time (min)
National Renewable Energy Laboratory 26 Innovation for Our Energy Future

Temperature

Imbalance

Large Dia. Cell

Tavg = 35.5oC

Nominal Cell

Tavg = 35.9oC

Large Height Cell

Tavg = 37.6oC

US06 CD cycle

Instant Temperature Imbalance

T –Tavg

[

oC]

X (mm)

R (mm)

0 50 100 150 200 250 300

4

6

8101214

X (mm)

R (mm)

0 20 40 60 80 100

5

10

15

20

25

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

X (mm)

R (mm)

0 10

5

10

15

20

25

30

35

40

45

50

55

0 100 200 300 400 500 600 700 800

0

1

2

3

t (s)

T

max

 - Tmin (° C)
National Renewable Energy Laboratory 27 Innovation for Our Energy Future

Amp-hour

Throughput

Imbalance Large Dia. Cell

-0.1% to +0.03%

Nominal Cell

-0.20% to +0.33%

Large Height Cell

-1.3% to +3.2%

US06 CD cycle

Material Usage Imbalance

(Ah/m2 –Ah/m2

avg)/Ah/m2avg

X (mm)

R (mm)

0 10

5

10

15

20

25

30

35

40

45

50

55

X (mm)

R (mm)

0 10 20 30 40 50 60 70 80 90 100

5

10

15

20

25

X (mm)

R (mm)

0 50 100 150 200 250 300

4

6

8101214

-1

-0.5

0

0.5

1

1.5

2

2.5

3 [%]

0 20 40 60 80 100 120

-1000

-500

0

500

1000
National Renewable Energy Laboratory 28 Innovation for Our Energy Future

Summary

Nonuniform battery physics, which is more probable in large-format 

cells, can cause unexpected performance and life degradations in 

lithium-ion batteries. 

A Multi-Scale Multi-Dimensional Model was developed as a tool for 

investigating interactions between micro-scale electrochemical 

processes and macro-scale transports using a multi-scale modeling

scheme. 

The developed model is used to provide a better understanding and 

help answer engineering questions about improving the design, 

operational strategy, management, and safety of cells.

Engineering questions to be addressed in future work 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 nonmeasurable 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 shorts and overcharge? 
National Renewable Energy Laboratory 29 Innovation for Our Energy Future

Acknowledgments

Vehicle Technology Program at DOE

• Dave Howell

• Tien Duong

NREL Energy Storage Task

• Ahmad Pesaran