NREL is a national laboratory of the U.S. Department of Energy, Office of Energy Efficiency and Renewable Energy, operated by the Alliance for Sustainable Energy, LLC.

Evaluation Study for Large Prismatic 

Lithium-Ion Cell Designs Using 

Multi-Scale Multi-Dimensional Battery Model 

Gi-Heon Kim and Kandler Smith

National Renewable Energy Laboratory

Golden, Colorado

NREL/PR-540-46076

This research activity is funded by the U.S. Department of Energy 
Batteries for Electrified Vehicles

National Renewable Energy Laboratory 2 Innovation for Our Energy Future

Electrified drive-train vehicles such as PHEVs and EVs with rangeextenders are believed to be near-term technologies that are 

• displacing significant petroleum use in the transportation sector

• diversifying energy sources for mobility 

Advances in batteries are critical to realize green mobility technologies

DOE’s Energy Storage System Performance Targets for PHEVs
Batteries for Electrified Vehicles

National Renewable Energy Laboratory 3 Innovation for Our Energy Future

Electrified drive-train vehicles such as PHEVs and EVs with rangeextenders are believed to be near-term technologies that are 

• displacing significant petroleum use in the transportation sector

• diversifying energy sources for mobility 

Advances in batteries are critical to realize green mobility technologies

DOE’s Energy Storage System Performance Targets for PHEVs

Performance

Life

Cost

Safety
“Requirements” are usually defined 

in a macroscale domain and terms

Performance

Life

Cost

Safety

Requirements & Resolutions 

Multi-Scale Physics in Li-Ion Battery

• Wide range of length and time scale physics 

• Design improvements required at different scales

• Need for better understanding of interaction among different scale physics

National Renewable Energy Laboratory 4 Innovation for Our Energy Future
Multi-Physics Interaction

National Renewable Energy Laboratory 5 Innovation for Our Energy Future

Comparison of two 40 Ah 

flat cell designs

2 min 5C discharge

working potential working potential

electrochemical

current production

temperature temperature

electrochemical

current production
Multi-Physics Interaction

National Renewable Energy Laboratory 6 Innovation for Our Energy Future

Comparison of two 40 Ah 

flat cell designs

2 min 5C discharge

working potential working potential

electrochemical

current production

temperature temperature

electrochemical

current production

High temperature 

promotes faster 

electrochemical reaction

Higher localized reaction 

causes more heat 

generation

Larger over-potential 

promotes faster discharge 

reaction

Converging current 

causes higher potential 

drop along the collectors
Multi-Physics Interaction

National Renewable Energy Laboratory 7 Innovation for Our Energy Future

Comparison of two 40 Ah 

flat cell designs

This cell is cycled 

more uniformly, can 

therefore use less 

active material ($) 

and has longer life.

2 min 5C discharge

working potential working potential

electrochemical

current production

temperature temperature

soc soc

electrochemical

current production

High temperature 

promotes faster 

electrochemical reaction

Higher localized reaction 

causes more heat 

generation

Larger over-potential 

promotes faster discharge 

reaction

Converging current 

causes higher potential 

drop along the collectors
Charge Conservation

r

η = (φs −φe )−U

Electrode-Scale Performance Model

(k T ) q

t

T

c p = ∇⋅ ∇ + ′′′ ∂

∂

ρ

• Pioneered by Newman group (Doyle, Fuller, 

and Newman 1993)

• Captures lithium diffusion dynamics and charge 

transfer kinetics 

• Predicts current/voltage response of a battery

• Provides design guide for thermodynamics, 

kinetics, and transport across electrodes

e e

eff

e e D

eff

s s

eff

s e

Li c

T

U

q j φ φ U T  +σ ∇φ ⋅∇φ +κ ∇φ ⋅∇φ +κ ∇ ⋅∇φ 

 





∂

∂ ′′′ = − − + ln

Charge Transfer Kinetics at Reaction Sites

Species Conservation

Energy Conservation • Difficult to resolve heat and electron current 

transport

National Renewable Energy Laboratory 8 Innovation for Our Energy Future
Integrated Model Resolving Different Scale Physics

National Renewable Energy Laboratory Innovation for Our Energy Future

Li Transport &

Charge Transfer Kinetics

Electron Transport &

Heat Transport

To expand knowledge of the impacts of designs in different scales, 

usages, and management on performance, life, and safety of battery 

systems

Simply Work?

Extend model domain size up to cell scale to capture macroscopic design 

features, while maintaining model resolution to capture Li diffusion dynamics 

in electrode level scale ???  huge computational complexity and cost

9
Approach

National Renewable Energy Laboratory 10 Innovation for Our Energy Future

Multi-Scale Multi-Dimensional (MSMD) Model Current Collector (Cu) Current Collector (Al) Negative Electrode Separator Positive Electrode

Simulation

Domain

X

R

x

= Macro Grid Micro Grid

(Grid for Sub-grid Model)

+

• Captures macroscopic electron/heat transports, electrode scale Li 

diffusion dynamics/charge transfer kinetics in separate domains

• Physically couple the solution variables defined in each domain using 

multi-scale modeling schemes

• Runs in tolerable calculation time, practical for battery and system 

engineering design
Present Study

National Renewable Energy Laboratory 11 Innovation for Our Energy Future

“Poorly designed electron and heat transport paths can cause excessive 

spatial non-uniformity in battery physics, and then deteriorate the 

performance and shorten the life of the battery.” 

Fixed Microscopic Designs Macroscopic Features as Design Variables

Objectives

Demonstrate the impact of macroscopic design factors on battery ...

• Performance : B2 abs# 252 (Kim & Smith)  This talk

• Life: B2 abs# 255 (Smith & Kim)
Nominal Design – 10C discharge for 30 sec

National Renewable Energy Laboratory 12 Innovation for Our Energy Future 15 mm

 Stacked prismatic design

 140 x 100 x 15 mm3 form factor

 Tabs on a same side

 20 Ah

 PHEV10 application

 10C constant current discharge

 socini = 90%

 Surface and tab cooling

 hinf = 20 W/m2K

 Tamb = 30oC

 Tini = 30oC

0 5 10 15 20 25 30

3.2

3.4

3.6

3.8

4

t (s)

(V)

V(t)

OCV(t)

evaluated from volumetric

average of composition
Electrical Response – 10C Discharge

Current density field at metal collector foils 

after 30 sec discharge at mid-plane

X(mm)

Y(mm)

0 20 40 60 80 100 120 140

0

20

40

60

80

100

X(mm)

Y(mm)

0 20 40 60 80 100 120 140

0

20

40

60

80

100

Al foil

Cu foil

Working potential between electrode planes

after 30 sec discharge at mid-plane

National Renewable Energy Laboratory 13 Innovation for Our Energy Future
Electrical Response – 10C Discharge

Current density field at metal collector foils 

after 30 sec discharge at mid-plane

X(mm)

Y(mm)

0 20 40 60 80 100 120 140

0

20

40

60

80

100

X(mm)

Y(mm)

0 20 40 60 80 100 120 140

0

20

40

60

80

100

Al foil

Cu foil

0

50

100

0

50

100

3.34

3.35

3.36

3.37

Y(mm) X(mm)

Working Potential [V]

Working potential between electrode planes

after 30 sec discharge at mid-plane

3.34

3.345

3.35

3.355

3.36

3.365

3.37

...

...

Large Overpotential

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Thermal Response – 10C Discharge

National Renewable Energy Laboratory Innovation for Our Energy Future

0 5 10 15 20 25 30

30

32

34

36

t [s]

T(t) [°C]

avarage temperature

maximum temperature

minimum temperature

0

50

100

0

50

100

30

32

34

36

Y(mm) X(mm)

Temperature [°C]

0

50

100

0

50

100

30

32

34

36

Y(mm) X(mm)

Temperature [°C]

0

50

100

0

50

100

30

32

34

36

Y(mm) X(mm)

Temperature [°C]

0

50

100

0

50

100

30

32

34

36

Y(mm) X(mm)

Temperature [°C]

0

50

100

0

50

100

30

32

34

36

Y(mm) X(mm)

Temperature [°C]

0

50

100

0

50

100

30

32

34

36

Y(mm) X(mm)

Temperature [°C]

30

32

34

36

5s 10s 15s 20s 25s 30s

Temperature Evolution at Mid-Plane

15
X(mm)

Y(mm)

0 20 40 60 80 100 120 140

0

20

40

60

80

100

Thermal Response – 10C Discharge

Temperatures after 30 sec discharge

X(mm)

Y(mm)

0 20 40 60 80 100 120 140

0

20

40

60

80

100

Y(mm)

Z(mm)

0 20 40 60 80 100

0

5

10

15

Y(mm)

Z(mm)

0 20 40 60 80 100

0

5

10

15

Y(mm)

Z(mm)

0 20 40 60 80 100

0

5

10

15

34

34.5

35

35.5

mid-plane

surface

35.9

33.6

 Tini =30.0 oC

 Tavg=34.3 oC  ∆T=2.3 oC

National Renewable Energy Laboratory 16 Innovation for Our Energy Future
Electrochemical Response – 10C discharge

National Renewable Energy Laboratory 17 Innovation for Our Energy Future

0

50

100

0

50

100

270

275

280

285

Y(mm) X(mm)

i [A/m2]

0

50

100

0

50

100

270

275

280

285

Y(mm) X(mm)

i [A/m2]

0

50

100

0

50

100

270

275

280

285

Y(mm) X(mm)

i [A/m2]

0

50

100

0

50

100

270

275

280

285

Y(mm) X(mm)

i [A/m2]

0

50

100

0

50

100

270

275

280

285

Y(mm) X(mm)

i [A/m2]

0

50

100

0

50

100

270

275

280

285

Y(mm) X(mm)

i [A/m2]

0

50

100

0

50

100

-0.4

-0.2

0

0.2

0.4

Y(mm) X(mm)

soc-soc

avg(%)

0

50

100

0

50

100

-0.4

-0.2

0

0.2

0.4

Y(mm) X(mm)

soc-soc

avg(%)

0

50

100

0

50

100

-0.4

-0.2

0

0.2

0.4

Y(mm) X(mm)

soc-soc

avg(%)

0

50

100

0

50

100

-0.4

-0.2

0

0.2

0.4

Y(mm) X(mm)

soc-soc

avg(%)

0

50

100

0

50

100

-0.4

-0.2

0

0.2

0.4

Y(mm) X(mm)

soc-soc

avg(%)

0

50

100

0

50

100

-0.4

-0.2

0

0.2

0.4

Y(mm) X(mm)

soc-soc

avg(%)

0 5 10 15 20 25 30

80

85

90

t [s]

soc(t) [%]

avarage soc

maximum soc

minimum soc

soc- socavg

discharge current density

5s 10s 15s 20s 25s 30s
Virtual 

Battery Design

Vehicle Simulator

-10

0

10

20

30

40

50

60

70

80

90

0 100 200 300 400 500 600

Time (s)

Vehicle Speed

Vehicle Design Vehicle Driving Profile

Virtual

0 10 20 30 40 50 60

-600

-400

-200

0

200

400

600

800

Battery Power Profile

Multi-Scale

Multi-Dimensional 

Li-ion Battery Model

Battery Responses Feedback

Embedded 

Battery Model

National Renewable Energy Laboratory 18 Innovation for Our Energy Future

Virtual Design Evaluation
Alternative Cell Designs

National Renewable Energy Laboratory 19 Innovation for Our Energy Future

Nominal Design

• 140 x 100 x 15 mm3

• Tabs on a same side

• 20 Ah

Small Capacity

Thin and Wide

Counter Tab

• 3 x (140 x 100 x 5) mm3

• Same tab design

• 3 x 6.67 Ah

• Same electrode area/stack layer

• 1/3 thickness

• ~ 3x surface area

• 200 x 140 x 7.5 mm3

• Same tabs

• 20 Ah

• 2x electrode area/stack layer

• 1/2 thickness

• ~ 2x surface area

• 250 x 120 x 7 mm3

• Wide-counter tab design

• 20 Ah

• ~2x electrode area/stack layer

• ~1/2 thickness

• ~2x surface area

SC

TW

CT
Thermal Behavior Comparison

National Renewable Energy Laboratory 20 Innovation for Our Energy Future

0 5 10 15

30

35

40

45

50

55

60

t [min]

T(t) [°C]

0 5 10 15

30

35

40

45

50

55

60

t [min]

T(t) [°C]

3 x

0 5 10 15

30

35

40

45

50

55

60

t [min]

T(t) [°C]

0 10 20 30 40 50 60

-600

-400

-200

0

200

400

600

800

• 15-minute drive (CD + CS)

• socini = 90%

• Surface and tab cooling

• hinf = 20 W/m2K

• Tamb = 30oC

• Tini = 30oC

SC TW CT

Battery Power Profile

mid-size sedan PHEV10 US06 drive
Temperature Imbalance during CD Drive

National Renewable Energy Laboratory 21 Innovation for Our Energy Future

0 5 10 15

0

2

4

6

8

10

12

14

t [min]

∆T(t) [°C]

0 5 10 15

25

30

35

40

45

50

55

t [min]

T

avg(t) [°C]

SC

TW

CT

Nominal

42

44

46

48

50

52

54

0 20 40 60 80 100 120 140 0

20

40

60

80

100

0 20 40 60 80 100 120 140 0

20

40

60

80

100

0 20 40 60 80 100 120 140 160 180 200 0

20

40

60

80

100

120

140

0 20 40 60 80 100 120 0

50

100

150

200

250

Nominal

TW

CT SC

@ t = 6 min
0 20 40 60 80 100 120 140 160 180 200 0

20

40

60

80

100

120

140

0 20 40 60 80 100 120 140 0

20

40

60

80

100

0 20 40 60 80 100 120 140 0

20

40

60

80

100

0 20 40 60 80 100 120 0

50

100

150

200

250

Temperature Imbalance during CS drive

National Renewable Energy Laboratory 22 Innovation for Our Energy Future

0 5 10 15

0

2

4

6

8

10

12

14

t [min]

∆T(t) [°C]

0 5 10 15

25

30

35

40

45

50

55

t [min]

T

avg(t) [°C]

SC

TW

CT

Nominal

Nominal

TW

CT SC

@ t=15 min

36

38

40

42

44

46

48
X(mm)

Y(mm)

0 20 40 60 80 100 120 140 160 180 200

0

20

40

60

80

100

120

140

X(mm)

Y(mm)

0 20 40 60 80 100 120

0

50

100

150

200

250

Ah Throughput Imbalance TW vs CT

National Renewable Energy Laboratory 23 Innovation for Our Energy Future

TW

CT

0 5 10 15

3.4

3.5

3.6

3.7

3.8

3.9

t [min]

V

ocv [V]

TW

CT

25.5

26

26.5

27

27.5

28

Ah/m2
National Renewable Energy Laboratory 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 used for evaluating 

large format prismatic automotive cell designs by integrating microscale electrochemical process and macro-scale transports.

Thin form factor prismatic cell with wide counter tab design would 

be preferable to manage cell internal heat and electron current 

transport, and consequently to achieve uniform electrochemical 

kinetics over a system. 

Engineering questions to be addressed in further discussion include ...

What is the optimum form-factor and size of a cell?

Where are good locations for tabs or current collectors?

How different are externally proved temperature and electric signals from nonmeasurable cell internal values? 

Where is the effective place for cooling? What should the heat-rejection rate be?

24
National Renewable Energy Laboratory Innovation for Our Energy Future

Acknowledgments

Vehicle Technology Program at DOE

• Dave Howell

NREL Energy Storage Task

• Ahmad Pesaran

25