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.

A Three-Dimensional Thermal-Electrochemical 

Coupled Model for Spirally Wound Large-Format 

Lithium-Ion Batteries

Kyu-Jin Lee*, 

Kandler Smith, 

Gi-Heon Kim

NREL/PR-5400-51151

Space Power Workshop

April 18, 2011

Los Angeles, CA

This research activity is funded by the US Department of Energy (Dave Howell)
2 Innovation for Our Energy Future

Objectives

• Develop thermal and electrochemical models resolving

3-dimensional spirally wound structures of cylindrical 

cells

• Understand the mechanisms and interactions between 

local electrochemical reactions and macroscopic heat 

and electron transfer

• Develop a tool and methodology to investigate 

macroscopic designs of cylindrical Li-ion battery cells
3 Innovation for Our Energy Future

Physics of Li-Ion Battery Systems in Different 

Length Scales

Li diffusion in solid phase

Interface physics

Particle deformation & fatigue

Structural stability

Charge balance and transport

Electrical network in 

composite electrodes

Li transport in electrolyte 

phase

Electronic potential &

current distribution

Heat generation and 

transfer

Electrolyte wetting

Pressure distribution

Atomic Scale

Particle Scale

Electrode Scale Cell Scale

System Scale

System operating 

conditions

Environmental conditions

Control strategy

Module Scale

Thermal/electrical

inter-cell configuration

Thermal management

Safety control

Thermodynamic properties

Lattice stability

Material-level kinetic barrier

Transport properties

Multi-Scale Physics in Li-Ion Battery Systems
4 Innovation for Our Energy Future

Porous Electrode Model of Li-ion Battery

• Pioneered by Newman group (Doyle, Fuller, 

and Newman 1993)

• Captures lithium diffusion dynamics and 

charge transfer kinetics across electrodes

• Predicts current/voltage response of a battery

• Provides design guide for thermodynamics, 

kinetics, and transport across electrodes

• Difficult to resolve heat and electron current 

transport in large cell systems

r Capacity [Ah] Voltage [V]

Capacity [Ah/m

Time

2]
5 Innovation for Our Energy Future

Computational Cost of Modeling Large Li-ion Cell

•Characteristic length of 

electrodes: Lelec

•Grids for the porous 

electrode model: Nelec

Characteristic length of 

a cell: Lcell

Number of grids for a full 3-D electrode porous model:

Ncell ~ (Lcell / Lelec *Nelec)3

Liu and Siddique, 218th ECS , 2010 Micro-structure Reconstruction

Number of grids in a model resolving mesoscale geometry: ~ 102-3

A full 3-D mesoscale cell model is extremely expensive. 
6 Innovation for Our Energy Future

ξ1

ξ2

ξ3

x1

x2

x3

Ɵ1

Ɵ2

Ɵ3

ξ: particle domain x: electrode domain : cell domain 

Multi-Scale Multi-Dimensional (MSMD) Model 

Ɵ

• Introduces separate computational domains for corresponding length 

scale physics 

• Decouples geometry between the domains

• Has independent coordinate systems for each domain

• Uses two-way coupling of solution variables using multi-scale model 

schemes

• Selectively resolves higher spatial resolution for smaller characteristic 

length scale physics

• Achieves high computational efficiency

• Provides flexible & expandable modularized framework

Description

Advantage
7 Innovation for Our Energy Future

Large Cell Design Differences

Prismatic cells Cylindrical cells

• Stacking / folding / semi-winding

• Complex and slow production 

processes

• Better packing efficiency for modules

• Better heat transfer

• Winding

• Simple and fast production processes

• Low manufacturing cost

Photo Credit:

http://en.wikipedia.org/wiki/List_of_battery_sizes Photo Credit: NREL-Dirk Long
8 Innovation for Our Energy Future

Large Cell Design can Lead to Large Temperature Difference

• Anisotropic thermal conductivity of electrodes coated on current 

collectors

Negative current collector

Positive current collector

Separator

Anode electrode 

Cathode electrode

Kin-plane 10-100W/mK

Kthrough-plane ~1W/mK

Prismatic cell Cylindrical cell

• Stacked electrodes 

• Thin and wide shape helps thermal 

uniformity

Kthrough-plane

Kin-plane

Kthrough-plane

Kin-plane

Kin-plane

• Wound electrodes 

• Center region of cell heats up easily 

due to the poor radial thermal 

conductivity
9 Innovation for Our Energy Future

Prismatic cell Cylindrical cell

• Large number of small metal 

current collectors

• Electric current flows through 

small distance

• A pair of long continuous metal current 

collectors

• Electric current flows through long distance.

• Tab design can critically impact on cell 

performance

Example:

Prismatic cell: 200 mm x 150 mm x 7 mm

Cylindrical cell: radius: 25.85 mm height: 100 mm 

Thickness of an electrode pair: 300 μm Length of current collectors: ~ 7 m

tab

Cell volume: 0.21 mL

Current

Large Cell Design can Lead to Large Electric Potential Difference

Unwinding electrodes
10 Innovation for Our Energy Future

1-D spherical particle 

representation model 

r

1-D porous electrode model

Sub-model choice for 2-D cylindrical cell model 

2-D Cylindrical Cell Model

X

R

2-D axisymmetric cell model

Particle domain sub-model Electrode domain sub-model Cell domain sub-model

– Previous study

Applicable to continuous tab design

Continuous tab design

Extended foil

Axisymmetric 

assumption

Cylindrical cell Unwinding jellyrolls
Innovation for Our Energy Future

Continuous Tab Cell Design Evaluation

Large H D[mm]: 14 H[mm]: 350 Nominal D[mm]: 50 H[mm]: 107

Large D 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

• Large H design has almost 10% less power capability.

10s pulse power capability comparison

X (mm)

0 20 40 60 80 100

5

10

15

20

25

X (mm)

0 20 40 60 80 100

5

10

15

20

25

0 20 40 60 80 100

5

10

15

20

25

∆i[%]

V

T-Tavg

0 50 100 150 200 250 300

4

6

8101214

0 50 100 150 200 250 300

4

6

8101214

∆i[%]

0 50 100 150 200 250 300

4

6

8101214

V

T-Tavg

X (mm)

0 10

5

10

15

20

25

30

35

40

45

50

55

X (mm)

0 10

5

10

15

20

25

30

35

40

45

50

55

-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

X (mm)

0 10

5

10

15

20

25

30

35

40

45

50

55

3.318

3.32

3.322

3.324

3.326

3.328

T-T V ∆i[%] avg

9 min 5C discharge

Effects of “Aspect Ratio” of a Cylindrical Cell – Previous study

11

14

7

0

14

7

0

14

7

0

 Nominal D[mm]: 50 H[mm]: 107

 

 

 

20

25

 

0 20 40 60 80 100

5

10

15

20

25

X (mm)

0 20 40 60 80 100

5

10

15

20

25

0 20 40 60 80 100

5

10

15

20

25
Innovation for Our Energy Future

Continuous Tab Cell Design Evaluation

Large H D[mm]: 14 H[mm]: 350 Nominal D[mm]: 50 H[mm]: 107

Large D 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

• Large H design has almost 10% less power capability.

10s pulse power capability comparison

X (mm)

0 20 40 60 80 100

5

10

15

20

25

X (mm)

0 20 40 60 80 100

5

10

15

20

25

0 20 40 60 80 100

5

10

15

20

25

∆i[%]

V

T-Tavg

0 50 100 150 200 250 300

4

6

8101214

0 50 100 150 200 250 300

4

6

8101214

∆i[%]

0 50 100 150 200 250 300

4

6

8101214

V

T-Tavg

X (mm)

0 10

5

10

15

20

25

30

35

40

45

50

55

X (mm)

0 10

5

10

15

20

25

30

35

40

45

50

55

-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

X (mm)

0 10

5

10

15

20

25

30

35

40

45

50

55

3.318

3.32

3.322

3.324

3.326

3.328

T-T V ∆i[%] avg

9 min 5C discharge

Effects of “Aspect Ratio” of a Cylindrical Cell – Previous study

12

T-T V [V] ∆i[%] avg [K]

14

7

0

14

7

0

14

7

0

T-Tavg [K]

V [V]

∆i[%]

 Nominal D[mm]: 50 H[mm]: 107

 

 

 

20

25

 

0 20 40 60 80 100

5

10

15

20

25

X (mm)

0 20 40 60 80 100

5

10

15

20

25

0 20 40 60 80 100

5

10

15

20

25

T-Tavg [K]

V [V]

∆i[%]
Innovation for Our Energy Future

Present Study:

Current flows along the winding direction

3-D spiral wound cell model

tab

tab

• 2-D axisymmetric model is not 

applicable to a wound cell .

• Geometries and materials of 

electric current paths in spirally 

wound layer structure must be 

properly resolved.

13

Electrical Design Issue-Tab Configuration

1-D spherical particle 

representation model 

r

1-D porous electrode model

Sub-model choice for 3-D cylindrical cell model 

Particle domain sub-model Electrode domain sub-model Cell domain sub-model
Innovation for Our Energy Future

Cell Domain Model:

14

Unit structure: Double-paired electrodes on single-paired current collectors

Negative current collector

Positive current collector

Separator

Winding: Alternating radial placement of double-paired electrodes 

 Two electrode pairs are formed 

when the unit structure is wound

Double-sided anode electrode 

Double-sided cathode electrode

Spirally Wound Cell Model

Outer 

electrode 

pair

Inner 

electrode 

pair

Outer 

electrode 

pair

 Two points with a distance of a 

winding cycle of outer electrode pair 

are matched in the wound structure
15 Innovation for Our Energy Future

Spiral Cell Structures: Alternatively layered jelly roll

Positive current collector

Negative current collector

Anode electrode

Separator

Cathode electrode

Outer electrode pair Inner electrode pair

A current collector has two electrode pairs in both sides
16 Innovation for Our Energy Future

Spiral Cell Structures:

φi

φi+1

φi-1

φ+

i

φ+

i+1 jLi,i

out

i+

i+

iiiNon-uniform potential along the current collectors occurs from electric current 

in the winding direction 

Non-uniform electrical potential along current collectors

Non-uniform charge transfer reaction across electrodes

Electrical potential fields

and charge transfer reaction
17 Innovation for Our Energy Future

Modeling Case

 Diameter 40 mm, inner diameter 8 mm, height 100 mm form factor

 Positive tabs on the top side, negative tabs on the bottom side

 10-Ah capacity

5C constant current discharge

SOCini = 90%

Natural convection:

hinf = 5 W/m2K

Tamb = 25°C 

Tini = 25°C 

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

0

0.05

0.1

X [m]

]m[Y

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

0

0.05

0.1

X [m]

]m[Y

Tab locations for 5-tab case

Negative current collector

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

0

0.05

0.1

X [m]

]m[Y

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

0

0.05

0.1

X [m]

]m[Y

Tab configuration of each electrode pair

Positive current collector

Inner electrode pair

Nickel oxide-based cathode Outer electrode pair

Graphite-based anode
Innovation for Our Energy Future

X [m]

Y [m]

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

0

0.05

0.1

122

124

126

128

18

Modeling Results

X [m]

Y [m]

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

0

0.05

0.1

0

0.01

0.02

X [m]

Y [m]

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

0

0.05

0.1

122

124

126

128

Electrochemical reaction rate

Electric potential

X [m]

Y [m]

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

0

0.05

0.1

-0.02

-0.01

 5 tabs in each current collector

 5C discharge for 5 min

Inner electrode pair

Outer electrode pair

Positive current collector

Negative current collector

0 2 4 6 8 3

3.2

3.4

3.6

3.8

Time [min]

Vout [V]

Top

view

Bottom

view

Current mainly flows in 

the winding direction 

High generation rate of 

transfer current near tabs
Innovation for Our Energy Future

0 2 4 6 8

25

30

35

40

45

50

Time [min]

Temperature [oC]

X [m]

Y [m]

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

0

0.05

0.1

0.3

0.3

19

State of Charge

Temperature

X [m]

Y [m]

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

0

0.05

0.1

0.32

0.34

Modeling Results

Inner electrode pair

Outer electrode pair

 Radial heat transfer from tabs

 Temperature difference is relatively 

small 

More usage of 

electrode near tabs
20 Innovation for Our Energy Future

Modeling Results: Parametric Study 

SOCini = 90% 

2 tabs

10 tabs

continuous tab

5 tabs

 Different tab numbers (2, 5, 10 and continuous tab) on cell performance 

 10-Ah capacity, 5C discharge

Output voltage

10 tabs

5 tabs

2 tabs

2-D model

Continuous tab 
21 Innovation for Our Energy Future

Modeling Results:

Temperature 2 tabs

5 tabs

10 tabs

2-D model

Continuous tab 

Natural convection:

hinf = 5 W/m2K

Tamb = 25°C 

Tini = 25°C 

Temperature

Parametric Study 
22 Innovation for Our Energy Future

Generated Heat

2 tabs

5 tabs

10 tabs

2-D mode

Continuous tab 

Natural convection:

hinf = 5 W/m2K

Tamb = 25°C 

Tini = 25°C 

Modeling Results: Parametric Study 
23 Innovation for Our Energy Future

 High rate of discharge with a moderate heat transfer condition

 Heat generation dominates temperature distribution in the system

2 tabs

5 tabs

10 tabs

Continuous tab 

Rejected Heat

Modeling Results: Parametric Study 
24 Innovation for Our Energy Future

Electrochemical reaction rate comparison

X [m]

Y [m]

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

0

0.05

0.1

X [m]

Y [m]

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

0

0.05

0.1

X [m]

Y [m]

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

0

0.05

0.1

X [m]

Y [m]

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

0

0.05

0.1

i

” [A/m2]

2 tabs

5 tabs

Continuous tab

10 tabs

in the inner electrode pair at 5 min

0 3 5 6 8 9 30

120

130

122

121

124

129

128

127

126

125

123

Δi

”

/ i

”

avga

32.2%

6.6%

2.2%

0.2%

Modeling Results: Parametric Study 
Innovation for Our Energy Future

-0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4

25

X [m]

Y [m]

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

0

0.05

0.1

X [m]

Y [m]

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

0

0.05

0.1

T-Tavg [°C]

Temperature deviation comparison

0.19°C

0.37°C

0.78°C

3.25°C

2 tabs

5 tabs

Continuous tab

10 tabs

ΔT

at 5 min

-0.4

0.1

-0.3

-0.2

0

-0.1

0.2

0.3

0.4

Modeling Results: Parametric Study 
Innovation for Our Energy Future

Conclusions

26

• Used Multi-Scale Multi-Dimensional model to evaluate largeformat cell designs by integrating micro-scale electrochemical 

processes and macro-scale heat and electrical current transport.

• Spatial non-uniformity of battery physics, which becomes 

significant in large batteries, requires 3 dimensional model.

• Developed macro-scale domain model resolved spirally 

wound structures of lithium-ion batteries.

• Modeled effects of tab configurations and the doublesided electrode structure.

• Increasing the number of tabs in spiral-wound cells would be 

preferable to manage internal heat and electron current 

transport, and to achieve uniform electrochemical kinetics.

• The spiral-wound cell model provides quantitative 

information regarding optimization of cell design including tab 

location and number.
Innovation for Our Energy Future

US. Department of Energy, Vehicle Technology Program

Dave Howell, Hybrid Electric Systems Team Leader

Brian Cunningham, CAEBAT Coordinator

National Renewable Energy Laboratory

Ahmad Pesaran, Energy Storage Team Leader

Acknowledgments

27