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.

Integrated Lithium-Ion Battery Model Encompassing MultiPhysics in Varied Scales: An Integrated Computer Simulation 

Tool for Design and Development of EDV Batteries

Gi-Heon Kim*, Kandler 

Smith, Kyu-Jin Lee, 

Shriram 

Santhanagopalan, 

Ahmad Pesaran

*: gi-heon.kim@nrel.gov

The 11th International

Advanced Automotive Battery Conference

January 24 – 28, 2011, Pasadena, California

International Battery Modeling Workshop

NREL/PR-5400-50248
Innovation for Our Energy Future

CAEBAT

Program Coordinator NREL

Task 1:

Open Architecture

Development

(ORNL Lead)

Task 2

Pack Model

Development

(NREL Lead)

Task 4

Electrode/Material

Models

(LBNL Lead)

Major Activities and Responsibilities

Task 3

Cell Model

Development

(NREL Lead)

DOE’s CAEBAT Program

2

• To integrate the accomplishments of battery modeling 

activities in national lab programs and make them 

accessible as design tools for industry

• To shorten time and cost for design and development of 

EDV battery systems

Industry/University Participation (RFP)
Innovation for Our Energy Future

Contents

3

1. Introduction to the NREL’s MSMD model

• Multiphysics multiscale lithium battery model framework 

2. Model application to large Li-ion battery performance

• Stacked prismatic cell response simulation

• Spiral wound cylindrical cell response simulation

3. Model application to large Li-ion battery degradation

• Large tab-less cylindrical cell degradation simulation

4. Model application to large Li-ion battery safety

• Multiphysics internal short circuit simulation

5. Summary
Innovation for Our Energy Future

Performance, Durability and Safety

4

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
Innovation for Our Energy Future

Charge Conservation

r

η = (φs −φe )−U

Porous Electrode Performance Model

5

(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 in large cell systems
Innovation for Our Energy Future

Mesoscale Modeling Approach

6

Wang and Sastry, JES, 2007

• Model addresses correlation of composition, 

morphology, and processing conditions by 

resolving mesoscale geometry

• Captures mesoscale geometry impact on 

transport properties of composite electrodes

• Computationally expensive 

Liu and Siddique, 218th ECS , 2010

Micro-Structure Reconstruction

Computational domain generated by 

quasi-random reconstruction process

P.R. Shearinga et. al, Electrochemistry Communication, 2010

X-Ray Tomography (Nano CT)
Innovation for Our Energy Future

NREL’s Multi-Scale Multi-Dimensional Model Approach

7

Design of Materials

Design of 

Electrode Architecture

Design of Transport at

Electrode/Electrolyte

Design of Electron &

Heat Transport Operation & Management

MSMD-μ

NREL

MSMD-c

ξ1

ξ2

ξ3

x1

x2

x3

X1

X2

X3

ξ particle domain dimension x electrode domain dimension X cell domain dimension
Innovation for Our Energy Future

NREL’s Multi-Scale Multi-Dimensional Model Approach

8

Design of Materials

Design of 

Electrode Architecture

Design of Transport at

Electrode/Electrolyte

Design of Electron &

Heat Transport

MSMD-μ

NREL

MSMD-c

ξ1

ξ2

ξ3

x1

x2

x3

X1

X2

X3

ξ particle domain dimension x electrode domain dimension X cell domain dimension

• Introduce multiple computational domains for corresponding 

length scale physics 

• Decouple geometries between submodel domains

• Couple physics in two-way using predefined inter-domain 

information exchange

• Selectively resolve higher spatial resolution for smaller 

characteristic length scale physics

• Achieve high computational efficiency

• Provide flexible & expandable modularized framework
Innovation for Our Energy Future

The Model has Hierarchy Structure

MSMD: Modularized Framework: Flexible & Expandable

9

ξ1

ξ2

ξ3

x1

x2

x3

X1

X2

X3

ξ particle domain dimension x electrode domain dimension X cell domain dimension

p_module 1

p_module k

p_module 2

p_physics b

p_physics z

p_physics a

e_module 1

e_module 2

e_module k

e_physics b

e_physics z

e_physics a

c_module 1

c_module 2

c_module k

c_physics b

c_physics z

c_physics a
Innovation for Our Energy Future

Performance, Durability and Safety

10

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
Innovation for Our Energy Future

Model Prediction for a Large Stacked Prismatic Cell 

11

ξ1

ξ2

ξ3

x1

x2

x3

X1

X2

X3

1D spherical particle 

representation model 

ξ particle domain dimension x electrode domain dimension X cell domain dimension

r

1D porous electrode model 3D SPPC model

 Stacked prismatic design

 200 x 140 x 7.5 mm3 form factor

 20 Ah PHEV10 application

 Single side cooling 25W/m2K 25oC

SVM

Sub-model Choice 

Solution Method Choice 

SVM FVM
Innovation for Our Energy Future

Cell Design Evaluation

12

Case Description Lx [mm] Ly [mm] Lz [mm] Tab width [mm] Tab configuration

ND Nominal design 200 140 7.5 44 Adjacent tabs

CT Counter tab design 200 140 7.5 44 Counter tabs

ST Small tab design 200 140 7.5 20 Adjacent tabs

WS Wide stack-area design 300 140 5.0 44 Adjacent tabs

Nominal Design

Small Tab Design

Counter Tab Design

Wide Stack-area Design

ND

ST

CT

WS

Tab Location

Stack Area

Tab Size
Innovation for Our Energy Future

5C Discharge Voltage Response

13

• Identical discharge capacity: 18.9 Ah at 

5C

• Several mV difference in discharge 

voltage among the compared designs

• Tendency of a few millivolts voltage 

difference with design change cannot be 

easily confirmed by testing only

0 5 10 15 20

2.5

3

3.5

4

discharge capacity [Ah]

voltage [V]

ND

CT

ST

WS

9.8 9.9 10 10.1 10.2

3.43

3.44

3.45

3.46

3.47

 

ND CT ST WS
Innovation for Our Energy Future

0 5 10 15 20

2.5

3

3.5

4

discharge capacity [Ah]

voltage [V]

ND

CT

ST

WS

Cell Internal SOC Imbalance 

14

0 49.5

50

50.5

51

51.5

52

ND

ST

CT

WS
Innovation for Our Energy Future

SOC Deviation during Discharge

15

0 5 10 15 20

0

5

10

15

20

25

30

35

discharge capacity [Ah]

dQ/dV [Ah/V]

V

0 5 10 15 20

0

0.5

1

1.5

2

2.5

3

discharge capacity [Ah]

∆ SOC [%]

 

ND

CT

ST

WS

SOCmax-SOCmin dQ/dV

• Results imply that

 Flat voltage slope would promote cell internal SOC imbalance

 HEV cycling at “flat section” would cause larger internal imbalance

• Modifying thermodynamics vs Optimizing electrical/thermal configuration 

ND CT ST WS
Innovation for Our Energy Future

Thermal Response during Discharge

16

0 5 10 15 20

0

5

10

15

20

25

30

35

40

discharge capacity [Ah]

heat generation [W]

ND

CT

ST

WS

0 5 10 15 20

25

30

35

40

45

50

55

discharge capacity [Ah]

temperature (°C)

0 5 10 15 20

25

30

35

40

45

50

55

discharge capacity [Ah]

temperature (°C)

0 5 10 15 20

25

30

35

40

45

50

55

discharge capacity [Ah]

temperature (°C)

Total Heat Generation

CT ST WS

Temperature

• Similar average temperatures: ND, CT, ST

• Smaller ∆T at CT

• Larger ∆T at ST

• Heat generation is highest with WS, but the 

EOD average T is lowest

ND

Single side cooling on top surface

 With h = 25 W/m2K

 At Tamb= 25 oC
Innovation for Our Energy Future

CT

WS

Temperature Imbalance at EOD

17

X(mm)

Y(mm)

0 50 100 150 200

0

50

100

X(mm)

Y(mm)

0 50 100 150 200

0

50

100

X(mm)

Y(mm)

0 50 100 150 200

0

50

100

X(mm)

Y(mm)

0 50 100 150 200

0

50

100

X(mm)

Y(mm)

0 50 100 150 200

0

50

100

X(mm)

Y(mm)

0 50 100 150 200

0

50

100

X(mm)

Y(mm)

0 50 100 150 200 250 300

0

50

100

X(mm)

Y(mm)

0 50 100 150 200 250 300

0

50

100

46

47

48

49

50

47

48

49

46

47

48

49

50

51

43

44

45

46

47

48

ND

ST

Tavg= 48.1oC

∆T = 4.3oC

Tavg= 48.0oC

∆T = 2.9oC

Tavg= 48.5oC

∆T = 5.3oC

Tavg= 44.7oC

∆T = 6.0oC

Cooling 

Surface

Bottom

Surface
Innovation for Our Energy Future

Pulse Power Response Comparison

18

• HPPC at 20% SOC at 25oC initial temperature
Innovation for Our Energy Future

Vehicle Use Evaluation

19

0 5 10 15

0

0.5

1

1.5

2

2.5

3

time [minute]

∆ SOC [%]

ND

CT

ST

WS

0 5 10 15

0

20

40

60

80

100

time [minute]

State of Charge [%]

ND

CT

ST

WS

0 5 10 15

-1000

-500

0

500

1000

time [minute]

Power [W]

SOCavg SOCmax-SOCmin

Battery Power per Cell

• PHEV10 mid-size sedan 

• 15 minutes US06 Driving Profile

• Battery power from Vehicle simulation

Thermodynamics + Cell Design + System Control
Innovation for Our Energy Future

Thermal Response during Driving

20

0 5 10 15

0

2

4

6

8

10

12

time [minute]

∆ T [°C]

ND

CT

ST

WS

0 5 10 15

25

30

35

40

45

50

time [minute]

average temperature [°C]

ND

CT

ST

WS

• Similar average temperatures: ND, CT, ST

• Smaller ∆T at CT

• Larger ∆T at ST

• WS: lower average T during CS mode drive, but significant ∆T
Innovation for Our Energy Future

Cell Internal Kinetics Non-Uniformity 

21

0

12.8

13

13.2

13.4

13.6

13.8

14

14.2

6.0% 2.5%

6.9% 12.7%

CT

WS

ND

ST

• Ah Throughput

• PHEV10

• 15min US06
Innovation for Our Energy Future

Model Prediction for a Spirally Wound Cylindrical Cell 

22

ξ1

ξ2

ξ3

x1

x2

x3

X1

X2

X3

1D spherical particle 

representation model 

ξ particle domain dimension x electrode domain dimension X cell domain dimension

r

1D porous electrode model 3D SWC model

 Spirally wound cell design

 D40, H100 mm form factor

 10 Ah PHEV10 application

SVM

Sub-model Choice 

Solution Method Choice 

SVM FVM
Innovation for Our Energy Future

Spirally Wound Cell (SWC) Model

Stacking process: Forming a pair between inner electrodes 

current collector

current collector

Separator

Winding process: Forming a second pair between outer electrodes

electrode

electrode

Spirally Wound Cell : 

Paring Inner 

electrodes

Separator

electrode

electrode

Paring Outer 

Electrodes

• One pair of wide current collector foils

• Two pairs of wide electrode layers

• Complex electrical configuration

23
Innovation for Our Energy Future

Model Case

24

 Diameter 40mm, inner diameter 8mm, 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 = 25oC 

Tini = 25oC 

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 pairs

Positive current collector

Inner electrode pair

Outer electrode pair
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

SWC Model Results

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

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

 5 min after 5C discharge

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 

More energetic reactions 

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

26

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

SWC Model Results

Inner electrode pair

Outer electrode pair

 High rate of discharge with a moderate 

heat transfer condition

 Heat generation dominates temperature 

distribution in the system

 Temperature difference in the system is 

relatively small

- More usage of electrode 

near tabs
27 Innovation for Our Energy Future

Discharge kinetics rate comparison

Impact of # of tabs - Discharge Kinetics

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

120 121 122 123 124 125 126 127 128 129 130

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]

0.2%

2.2%

6.6%

32.2%

Δi

”/ i”

avg

2 tabs

5 tabs

Continuous tab

10 tabs

in the inner electrode pair at 5 min
28 Innovation for Our Energy Future

Impact of # of tabs - Temperature

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

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

T-Tavg[°C]

Temperature 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 discharge
Innovation for Our Energy Future

Performance, Durability and Safety

29

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
Innovation for Our Energy Future

Model Prediction for Cylindrical Cell Degradation

30

ξ1

ξ2

ξ3

x1

x2

x3

X1

X2

X3

1D spherical particle 

representation model 

ξ particle domain dimension x electrode domain dimension X cell domain dimension

r

1D porous electrode model

+ empirical life model 2D SPPC model

 Spirally wound cell design

 D40, H100 mm form factor

 10 Ah PHEV10 application

SVM

Sub-model Choice 

Solution Method Choice 

SVM FVM
Innovation for Our Energy Future

Life Modeling Approach

NCA datasets fit with empirical, yet physically justifiable formulas

31

Resistance

Growth

Relative

Capacity

•Data shown above: J.C. Hall, IECEC, 2006.

•Model also fit to DOE/TLVT, Southern CA Edison & NASA data

Qactive = e0 + e1 N

R = a1 t1/2 + a2 N

Calendar fade

• SEI growth (partially

suppressed by cycling)

• Loss of cyclable lithium 

• a1, d1 = f(∆DOD,T,V)

Q = min ( QLi , Qactive )

QLi = d0 + d1 t1/2

Cycling fade

• active material structure 

degradation and 

mechanical fracture

• a2, e1 = f(∆DOD,T,V)

• Portability + Physical interpretation

• Applicable to complex real-world storage and cycling scenarios Relative Capacity (%)

Time (years)

r2 = 0.942

Li-ion NCA chemistry

Resistance 

Growth (m

Ω)

Tafel-Wohler model 

describing a2(∆DOD,V)
Innovation for Our Energy Future

US06 – Nonuniform Capacity Loss

• Regions near terminals 

suffer most significant 

capacity loss

Large overpotential  Excessive cycling

• Inner core loses capacity 

faster than outer cylinder 

wall

0 months: High temperature  Material degradation

8 months:

16 months:

+

-

+

-

+

-

US06

32
Innovation for Our Energy Future

US06 – Ah Imbalance (Nonuniform Cycling)

33

0 months:

0.7% Ah Imbalance 8 months:

1.7% Ah Imbalance 16 months:

4.8% Ah Imbalance

• Later in life, those same areas are 

most degraded and are cycled least

+

-

+

-

+

-

Preferentially cycled regions shift early in life

Imbalance continually grows throughout life

• Early in life, inner 

core and terminal 

areas are cycled 

the most
Innovation for Our Energy Future

Performance, Durability and Safety

34

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
Innovation for Our Energy Future

Modeling Thermal Runaway

35

 Constructed empirical reaction models using calorimetry data for 

component decompositions: approach practiced by J. Dahn’s group

 Enhanced understanding of the interaction between heat transfer 

and exothermic abuse reaction propagation for a particular 

cell/module design 

 Provided insight on how thermal characteristics and conditions can 

impact safety events of lithium-ion batteries

8 20 28 40 sec

Total Volumetric Heat Release from Component Reactions

4 12 16 24 32 36

Internal T External T

(°C)

0 20 40 (sec)

SEI decomposition positive/electrolyte negative/electrolyte
Innovation for Our Energy Future

Multi-Physics ISC Model

36

• Developed an integrated model for multi-physics internal short circuit 

(ISC) of lithium-ion cells by linking and integrating NREL’s unique 

electrochemical, electrothermal, and abuse reaction kinetics models

• Performed 3D multi-physics internal short simulation study to 

characterize an internal short and its evolution over time

Current Density

Temperature

Electrothermal Model

Abuse Kinetics Model Electrochemical Model

0

50

100

150

200

0

50

100

150

59.5

60

60.5

61

61.5

62

X(mm)

soc [%]

Y(mm)

Internal Short Model Study

T soc
Innovation for Our Energy Future

40 mm

35 mm

3 mm

Shorted Spot

Shutdown Separator for Large Cells ?

37

Short Between Al & Cu Metal Foils

Al

Cu

• Cell Capacity: 20 Ah 0.4 Ah

Rshort ~ 10 mΩ

Ishort ~ 300 A (15 C-rate)

Rshort ~ 7 mΩ

Ishort ~ 34 A (85 C-rate)

Joule Heat for Short Temperature @10 sec after short

800oC

25oC

surface temperature

internal temperature

T

Q

30 sec

T

Q

40 sec

T

Q

50 sec

T

Q

60 sec

 

 

T

Q

20 sec

100 110 120 130 140

0

0.1

0.2

100 110 120 130 140

0

0.1

0.2

110

140

120

130

100

surface temperature

temperature [oC] 

volume fraction volume fraction

0 2 4 6 8 10 12 14 16 18

0

200

400

600

800

without shutdown

shutdown functioned
Innovation for Our Energy Future

Summary

38

1. Introduction to the NREL’s MSMD model

• The MSMD model is a modularized multiphysics multiscale lithium battery 

model framework 

2. Model application to large Li-ion battery performance

• The model enhances understanding of interactions among varied scale physics 

beyond what’s possible with experimentally measurable quantities only

• Thermal/electrical design variation of a cell impacts internal battery kinetics

3. Model application to large Li-ion battery degradation

• Internal imbalance of cell use grows continually throughout life

4. Model application to large Li-ion battery safety

• Cell heating pattern is affected by cell characteristics (e.g. Ah, rate)
Innovation for Our Energy Future

Acknowledgments

39

Vehicle Technology Program at DOE

• Dave Howell

CAEBAT operation at DOE

• Stephen Goguen, Brian Cunningham

Thank you for your attention!