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.

Ahmad A. Pesaran, Gi-Heon Kim, Kandler Smith

(ahmad_pesaran@nrel.gov)

National Renewable Energy Laboratory

Eric C. Darcy

NASA Johnson Space Center

NREL/PR-540-45388

Designing Safe Lithium-Ion Battery 

Packs Using Thermal Abuse Models
National Renewable Energy Laboratory 2 Innovation for Our Energy Future

Background

– For powering spacesuits, 

NASA is considering using a 

battery pack consisting of 

arrays (16P-5S) of 18650 Liion cells.

– These cells are equipped with 

a positive temperature 

coefficient (PTC) device 

proven effective for control of 

overcurrent hazards at the Liion cell and small battery level.

– However, PTC devices are not 

as effective in high-voltage 

battery designs.

– A fire in a 2004 Memphis 

FedEx facility suspected to be 

due to a PTC device failure in 

a large-capacity (66p-2s) 

battery shorted while at 50% 

SOC. 
National Renewable Energy Laboratory 3 Innovation for Our Energy Future

PTC Device: Background

• Commercial lithium-ion 18650 cells 

typically have a current-limiting PTC 

(positive temperature coefficient) device 

installed in the cell cap to limit external 

currents in the event of an external short to 

the cell.

• The PTC device consists of a matrix of a 

crystalline polyethylene containing 

dispersed conductive particles, usually 

carbon black.* The resistance of the PTC 

device increases with temperature.

• The PTC resistance increases sharply with 

temperature. When a short is applied to a 

cell, the elevated currents cause the PTC 

to self-heat and move to a high-resistance 

state in which most of the cell voltage is 

across the PTC but the current is 

significantly reduced. 

• As long as the short is maintained, the PTC 

device produces enough heat to keep itself 

in this tripped state (lower current is offset 

by greater voltage drop across PTC).

Single Cell Short:

*Doljack, F., IEEE Transactions on Components, Hybrids, and Manufacturing Technology, 4, 732, 1981
National Renewable Energy Laboratory 4 Innovation for Our Energy Future

Cell Design Features for Abuse Tolerance

Crimped

Can

Gasket Seal

PTC ring

+ Top Cover

CID Button CID ring

polymer

+ Tag mounting

disk 

Scored Disk Vent

Sony HC Cell Moli ICR-18650J
National Renewable Energy Laboratory 5 Innovation for Our Energy Future

Motivation for this Work

• Can NASA’s spacesuit battery design (16p-5s) array 

depend on cell PTC devices to tolerate an external 16p 

short?

• Is there a range of smart shorts that can be hazardous?

Gasket Seal

PTC ring

+ Top Cover

CID Button CID ring

polymer + Tag mounting

disk 

Scored Disk Vent

Gasket Seal

PTC ring

+ Top Cover

CID Button CID ring

polymer + Tag mounting

disk 

Scored Disk Vent
National Renewable Energy Laboratory 6 Innovation for Our Energy Future

Objectives

• Create an engineering model to 

guide the design and to verify the 

safety margin of a battery using high 

specific energy COTS cells

• Use the model to provide input for designing a NASA 16p-5s 

18650 spacesuit battery

– Cell model must include the electrical and thermal behavior of the cell 

PTC device

– Use cell model as building block to model multi-cell battery behavior 

under short-circuit conditions

– Assess the range of smart short conditions that push cells close to 

the onset of thermal runaway temperature
National Renewable Energy Laboratory 7 Innovation for Our Energy Future

Utilizing NREL’s Multi-physics Battery Modeling

• Electrical Performance Modeling 

– Cells & multi-string modules

• Thermal Modeling

– Cells & modules

• Thermal/Electrochemical Modeling

– Cells

• Thermal/Chemical Abuse Modeling*

– Cells and modules

*G.-H. Kim, A. Pesaran, “Analysis of heat dissipation in Li-ion cells and modules for modeling of thermal runaway,” 3rd International Symposium on Large Lithium Ion Battery Technology and Application, Long Beach, 

CA, May 2007. Available: www.nrel.gov/vehiclesandfuels/energystorage/

0 20 40 60 80 Sec

External Temp Internal Temp 

Current Density

Temperature

Current Collector (Cu)

Current Collector (Al)

p

Negative

Electrode

Separator

Positive

Electrode







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
National Renewable Energy Laboratory 8 Innovation for Our Energy Future

Overview

• Modeling

– Approach

– PTC device 

– Cell

• Electrical 

• Thermal (5-node)

– Module

• Electrical (multi-node network)

• Thermal (multi-node network)

• Validation with experiments from SRI

– 16P module with 10 mΩ external short

• Parametric study

– Resistance of external short

– Heat rejection rate to ambient

• Conclusions

Photo: Symmetry Resources Inc. (SRI)
National Renewable Energy Laboratory 9 Innovation for Our Energy Future

Modeling Approach

Previous Work:

• Design module to prevent 

thermal runaway propagation

Present Work:

• Verify module design tolerant 

to external electrical short







0 10 20 30 40 50 60 70 80 90 100 0

100

200

300

400

500

600

700 1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

Thermal

Network

Model

Chemical

Reaction

Model

+

Thermal

Network

Model

Electrical

Model +

Photo: Symmetry Resources Inc.

17500

0

690

55

Temperature [oC]

Heat Generation [oC/min]
National Renewable Energy Laboratory 10 Innovation for Our Energy Future

PTC Resistance versus Temperature; 

Moli ICR-18650J

Cell header removed from cell without disturbing closure configuration

Resistance measurements taken from rupture disk surface to positive button

1.0E-02

1.0E-01

1.0E+00

1.0E+01

1.0E+02

1.0E+03

1.0E+04

1.0E+05

1.0E+06

0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180

Temperature (deg. C)

Resistance (ohms)

PTC 71A06 virgin PTC 71A07 virgin PTC 71A08 virgin PTC 71A09 tripped

Phase

Transition
National Renewable Energy Laboratory 11 Innovation for Our Energy Future

Behavior Principles of PTC Devices

Cell can be in 40°C range with two possible PTC device states

– Low-resistance current conducting state (<50 mΩ)

– Current-limiting state with high resistance (>1 kΩ)

Minimum and maximum base resistance (given ambient T)

– Minimum is for virgin (never been tripped) devices

– Maximum is for once (or more) tripped devices

Ultimate trip current, Iu, is the highest equilibrium current possible in 

the low-resistance state of the device for a given temperature

– It’s the maximum current achieved in an I vs. V curve for a given 

ambient temperature, for example, at 45°C

• Moli J‘s Iu = 7 A

• LV’s Iu = 9 A

Power generated in device = power dissipated in device

– The trip time depends on size of the overcurrent, ambient T, thermal 

mass of the device, its specific heat, its heat dissipation coefficient, 

and its base resistance

– Steady-state trip current is inversely proportional to voltage applied 

and ambient temperature
National Renewable Energy Laboratory 12 Innovation for Our Energy Future

16P Bundle External Short Test

• Performed by Symmetry 

Resources, Inc.

• Moli ICR18650J cells

• 16 parallel

• 10 mΩ external short

Model needs to capture important physics 

happening during an experiment

• PTC device behavior

– RPTC(T)

– Thermal connection with the 

cell

• Cell electrical behavior

– Current/voltage/temperature 

relationship

• Cell-to-cell heat transfer

– Conduction 

• air gaps

• electrical tabs

– Radiation

• Cell-to-ambient heat transfer

– Convection to air

– Conduction through wire 

leads

Photos: SRI
National Renewable Energy Laboratory 13 Innovation for Our Energy Future

Model Development Approach

Unit Cell Model

R1(SOC,TJR)

VOCV(SOC)

C1(SOC,TJR)

Rs(SOC,TJR) RPTC(TPTC)

+

-

I(t)

V(t)

Jelly Roll PTC

5.Jelly

Bottom

4.Jelly

Middle

3.Jelly

Top 2.PTC 1.TopButton

Ambient

K45 K34 K23

K5a

K12

K4a K3a K1a

5.Jelly

Bottom

4.Jelly

Middle

3.Jelly

Top 2.PTC 1.TopButton

Ambient

5.Jelly

Bottom

4.Jelly

Middle

3.Jelly

Top 2.PTC 1.TopButton

Ambient

K45 K34 K23

K5a

K12

K4a K3a K1a

5 4 3 1

2

Multi-Cell T&E Network Model

T10

T9

T8 T7

T6

T5

T4

T2 T3

T1

Rptc

Rjr

V0 +

-

+

-

+

-

Vmeas Rshort

Imeas

1 2 16

5-Node

Thermal 

Model

Electrical 

Performance 

Model

Thermal 

Network 

Model

Electrical 

Network 

Model

electrical/thermal interaction electrical/thermal interaction

Integrated Thermal and Electrical Network Model of a Multi-Cell Battery

for Safety Evaluation of Module Design with PTC Devices during External Short
National Renewable Energy Laboratory 14 Innovation for Our Energy Future

Unit Cell Model: Electrical Performance Model

Equivalent 

Circuit Model

and Relevant 

Parameters

)()()()(

)(

/1

0

00

1

1 11 11

VtV SOC tIRRV

tI

R

Q

V

SOC

V

SOC

dt

d

= OCV s PTC ×+−+





 





+ 



 









 



 = 



 





λ λ

11

1

1

CR

− λ = Q = 2.345 A-h

R1(SOC,TJR)

VOCV(SOC)

C1(SOC,TJR)

Rs(SOC,TJR)

V1

RPTC(TPTC)

+

-

I(t)

V(t)

Jellyroll PTC
National Renewable Energy Laboratory 15 Innovation for Our Energy Future

Unit Cell Electrical Model Agrees Well with Data

Validation of Equivalent Circuit Model

• Model compared with constant current 

discharge data from manufacturer (21C)

• Model compared with mission power 

profile data from NASA (25C and 65C)
National Renewable Energy Laboratory 16 Innovation for Our Energy Future

Unit Cell Model: Thermal Model

T [oC] MESH

• Finite Volume Method

• 41,250 computational grid

...and validated it with data from PTC device 

withstanding voltage test. (NASA/SRI)

Developed detailed cell model based 

on cell cross-cut measurements...

Detailed Cell 

Thermal 

Model
National Renewable Energy Laboratory 17 Innovation for Our Energy Future

Unit Cell Model: 5-nodeThermal Model Validated

∑ ( ) −=

j

i ij TTKQ ji

( ) dt

dT MCpTTKQ i

i

j

i ∑ ij ji +−=

Steady Form

Unsteady Form

A PTC:3.38W, Jelly:0.0093W

B PTC:3.0W, Jelly:0.0093W

C PTC:2.0W, Jelly:0.0093W

D PTC:1.0W, Jelly:0.0093W

E PTC:1.0W, Jelly:1.0W

40

60

80

100

120

140

160

temperature [oC]

Fluent

5-Node Aprox

Top buttonPTCJelly topJelly middleJelly bottom

A

B

D

C

E

40

60

80

100

120

140

160

temperature [oC]

Fluent

5-Node Aprox

Top buttonPTCJelly topJelly middleJelly bottom

A

B

D

C

E

Detailed Cell Thermal Model • Large computational requirement

• Not suitable for multi-cell modeling

5.Jelly

Bottom

4.Jelly

Middle

3.Jelly

Top 2.PTC 1.TopButton

Ambient

K45 K34 K23

K5a

K12

K4a K3a K1a

5.Jelly

Bottom

4.Jelly

Middle

3.Jelly

Top 2.PTC 1.TopButton

Ambient

5.Jelly

Bottom

4.Jelly

Middle

3.Jelly

Top 2.PTC 1.TopButton

Ambient

K45 K34 K23

K5a

K12

K4a K3a K1a

5 4 3 1

2

5-Node Cell Thermal Model

• Low order dynamic model

• Suitable for multi-cell modeling

Comparison of Detailed and 5–Node Models 

For Different Heat Generation Conditions
National Renewable Energy Laboratory 18 Innovation for Our Energy Future

Rptc

Zjr

V0 +

-

+

-

+

-

Vmeas Rshort

Imeas

1 2 16

Rjr = 6.172e-5 exp(2178/T)

Rjr = 1.04e-2 exp(651/T)

Jellyroll Resistance

as a function of cell temperature

PTC Resistance

as a function of PTC temperature

Open-Circuit Voltage

as a function of cell SOC

Multi-Cell Network Model

Electrical Network Model

The Model Solves Voltage and Current Interactions 

among the Components in a Multi-Cell Circuit

Data: SRI
National Renewable Energy Laboratory 19 Innovation for Our Energy Future

Multi-Cell Network Model

Thermal Network Model

Thermal Mass: Identifying thermal mass at each node

Heat Generation: PTC heat, charge transfer heat (future: abuse reaction heat) 

Heat Transfer: Quantifying heat exchange among the nodes

radiationij ij connector conduction ij convection  ijj

Qtransport i ijij QQQ , Q _, Q ,

,1

, ∑ , +=−= +

≠=

)(

44 Q ,radiationij ij

−= TTAF ji ε

Radiation Heat Transfer 

D

d

F2 F1 F2 F3 F4

d/D

F

Radiation Heat Transfer 

D

d

F2 F1 F2 F3 F4

d/D

F
Multi-Cell Network Model

Thermal Network Model

Thermal Mass: Identifying thermal mass at each nodeHeat Generation: PTC heat, charge transfer heat (future: abuse reHeat Transfer: Quantifying heat exchange among the nodes

radiationij connectorij conduction ij co

ijj

Q itransport ijij QQQ , Q _,

Q ,

,1

,  , 





dT

Heat Rejection Through Wires 

8 0

100120140160

T [oC]

 

dx

dT kAQ 

base b

TT 

 

 

 

TT 

 

Heat Transfer to Ambient

(

)

T 

T

Qi a hAi a i

0 5 1 0 1 5 

2 04 06 0

Conduction Through Bus 

(

)

Qi

a i

a i 

jiji

ji

connector ji Ak

L

R





, 



Heat Conduction Throu

gh Air-Ga

p

National Renewable Energy Laboratory 20 Inno

g

p
National Renewable Energy Laboratory 21 Innovation for Our Energy Future

Experimental Model Validation 

10 mΩ External Short

1) t = 0 sec: Circuit closed

2) t ≈ 12 sec: PTC devices trip

– TPTC ≈ 130°C

3) t ≈ 1 hr: Steady state reached

~ C/5 discharge

Data & Photo: SRI
National Renewable Energy Laboratory 22 Innovation for Our Energy Future

Model Validation – Current & Voltage

Peak inrush current readily predicted with knowledge of cell & short resistances.

PTC device trip time affected by – PTC thermal mass

– PTC conductive path to jellyroll & can.

Steady-state behavior affected by jellyroll and PTC device temperature, indirectly – PTC conductive path to jellyroll & can

– Thermal boundary conditions to ambient.

1

2

3

2

3

1
National Renewable Energy Laboratory 23 Innovation for Our Energy Future

Model Prediction – Heat Generation

PTC devices at steady-state

1.35 to 1.86 W

• Pre-trip: Jellyroll heat generation dominates.

• Post-trip: PTC device heat generation dominates.
National Renewable Energy Laboratory 24 Innovation for Our Energy Future

Is this design safe under other short conditions?

Rshort

Max Temperature

PTC

-limited

SOC

-limited

Adequate 

thermal 

dissipation 

required

small large
National Renewable Energy Laboratory 25 Innovation for Our Energy Future

/ Simulation Results at Various Values of Rshort

• Rshort ≤ 40 mΩ: PTC-limited

• Rshort ≥ 50 mΩ: SOC-limited

• Tripped PTC device serves as 

thermal regulator

[dRPTC/dT]130 ̊C = 3Ω/ ̊C

(5 orders of magnitude > than at 25 ̊C)

• Large pre-trip heat rates are 

safe provided they are of

– short duration

– sufficient thermal mass

– sufficient heat dissipation

Steady-State Temp

Average Heat

before and after Trip

PTC

Jellyroll

Post-trip

Pre-trip

Max Temp
National Renewable Energy Laboratory 26 Innovation for Our Energy Future

Red lines: h = hnominal / 2

Black lines: h = hnominal

How much heat rejection is required for safety?

• PTC device trip time 

decreases only slightly 

with less heat rejection 

from cells.

• Less rejection leads to 

hotter PTC device 

(higher resistance) and 

slower discharge of cell.

Additional simulations run with various 

values of h (convective heat transfer 

coefficient to ambient).
National Renewable Energy Laboratory 27 Innovation for Our Energy Future

PTC

Jellyroll

Post-trip

Pre-trip

How much heat rejection is required for safety?

• Less rejection causes an 

increase in jellyroll 

temperature.

• Pre-trip heat generation rate is 

largely unaffected by thermal 

boundary conditions.

• Post-trip, the PTC device 

reduces heat generation rate 

as heat rejection decreases.

Red lines: h = hnominal / 2

Black lines: h = hnominal
National Renewable Energy Laboratory 28 Innovation for Our Energy Future

Conclusions

Rshort

Max Temperature

PTC

SOC-limited

-limited

• Moli ICR18650J cell design has promise to be 

tolerant to a wide range of external shorts for 

the 16p configuration of a spacesuit battery, as 

long as

– No damage occurs due to the in-rush current 

transient

– Nominal tripping of cell PTC devices and steadystate conditions occur

– External short does not excessively heat battery.

• PTC device is an effective thermal regulator. 

Maximum cell temperature (final state) is very 

similar for a variety of initial and boundary 

conditions.

• Created & validated a new multi-cell math model capturing electrical and 

thermal interactions of cells with PTC devices during abuse. Suitable for

- Assessing battery safety design margins 

- Supplementing and guiding verification tests

Data: SRI
National Renewable Energy Laboratory 29 Innovation for Our Energy Future

Acknowledgements

NASA Johnson Space Center

• Funding for this work was provided by NASA JSC 

under Inter-Agency Government Agreement 

NNJ08HC04I

• Technical Guidance: Frank Davies

Symmetry Resources Inc.

• Brad Strangways