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.

Predictive Models of Li-ion 

Battery Lifetime

Kandler Smith, Ph.D.

Eric Wood, Shriram Santhanagopalan, Gi-Heon Kim, Ying Shi, Ahmad Pesaran

National Renewable Energy Laboratory

Golden, Colorado

Advanced Automotive Battery Conference &

Large Li-ion Battery Technology & Application Symposium

Detroit, Michigan• June 15-19, 2015 NREL/PR-5400-64622
2

Acknowledgements

Funding

• US DOE, Vehicle Technologies Office: Brian Cunningham, David 

Howell

• US DOE, Advanced Research Projects Agency-Energy (ARPA-E): Pat 

McGrath, Ilan Gur, Russel Ross

Collaborators

• Texas A&M: Prof. Partha Mukherjee & team

• Utah State: Prof. Regan Zane & team

o Ford: Dyche Anderson; UCCS: Plett & Trimboli; CU-Boulder Maksimovic

• Eaton Corporation: Dr. Chinmaya Patil & team
3

Outline

• Analysis of degradation mechanisms

• Modeling of particle fracture physics

• Cell-level prognostic control

• Pack-level prognostic control
4

NREL Battery Life Prognostic Model

• Physics-based surrogate models regressed 

to aging test data

• Li loss (SEI growth + cycling damage)

• Site loss (initial damage + continuous fatigue)

• Electrolyte decomposition

• Typical error across 20-50 test conditions

• Capacity: 3-4%

• Resistance: 6-12%

  Similar error for independent validation cases

• Next slides show examples for ironphosphate (FeP) 2.3 Ah cell from A123

No cooling

Air cooling

Air cooling, 

low resistance cell

Phoenix, AZ ambient conditions

33 miles/day driving, 2 trips/day

Liquid cooling, 

chilled fluid

Illustration by Josh 

Bauer, NREL

NCA = Nickel-Cobalt-Aluminum

FeP = Iron Phosphate

NMC = Nickel-Manganese-Cobalt

Example equations

Example systems analysis
5

Calendar/storage fade

• Li loss/SEI growth model1 captures t1/2 fade 

with rate dependent on

o Temperature

o Negative electrode equilibrium potential 

Fade rate

Model error

Model vs. data

1. H.J. Ploehn, P. Ramadass, R.E. White, “Solvent Diffusion Model for Aging of Lithium-Ion Battery Cells,” J. Electrochem. Soc. 151 (2004).
6

1. Additive Model (Schmalstieg, 2014)

2. Limiting mechanism model (NREL)

3. SEI micro-cracking model (Deshpande, 2012)

Coupled calendar/cycle life-predictive models

z p q = 1�� t � � N

z

Li q b b t = 0 � 1

min( , ) q = qLi qsites

( )

m

sei

sei k D

dN

dD = ×

( ) ,0

2

1

,0 1

2

1

sei

sei

q

b

dt

dq = × ×

( ) sei j

sei

sei j

q

b D

dt

dq

,

2

1

, 1

2

1 = × × ×

�

=

= �

N

j

Li sei j q t b q t

0

0 , ( ) ( )

Schmalstieg: z=1/2, p=1/2  no knee

Our experience: p=1.0  extends calendar life model for mild cycling

÷

÷

�

�

�

�

�

� = �

Sites

Sites

q

c

dN

dq 1

2

Described in previous presentations

Following slides
7

Cycling fade

• Causes apparent acceleration of t1/2 Li-loss/SEI growth rate

o Evidence for SEI damage (particle-to-particle displacement and/or surface cracking)

o Rate correlates best by including multiplicative term, (1+DODβ ) x t1/2

– discharge C-rate next best correlation

Model vs. all data Model error – Low error cases (33 of 45)

Model, shown here versus all data, 

was fit only to the portion of data 

before inflection point or “knee”
8

Cycling fade - knee 

• 12 of 45 cases show 

apparent “knee” not 

captured by t1/2 model

• Possible mechanisms

o Li-loss / SEI micro-cracking

o Site-loss / cycling fatigue

• Plotted vs. remaining 

capacity (bottom) seems to 

indicate similar mechanism 

across multiple cases

Model error – High error cases (12 of 45)
9

Cycling fade – SEI micro-cracking model1

• Matches individual aging tests well, especially at 60oC

• Difficult to justify model at T < 45oC. 

o 23oC, 60% DOD case not matched well

Good match Inconclusive

1. R. Deshpande, M. Verbrugge, Y.T. Cheng, J. Wang, P. Liu, “Battery cycle life prediction with coupled chemical degradation and fatigue mechanics,” J. Electrochem. Soc. 159 (2012).
10

Resistance growth

Typical mechanisms • SEI growth • Particle fracture • Site loss • Electrolyte 

decomposition
11

Outline

• Analysis of degradation mechanisms

• Modeling of particle fracture physics

• Cell-level prognostic control

• Pack-level prognostic control
12

Modeling of Particle Fracture Physics

with Texas A&M1

1. C.F. Chen, B. Vajipeyajula, P. Barai, K. Smith, P. Mukherjee, “Scaling of Intercalation Induced Damage in Electrodes,” Phys. Chem. Chem. Phys., submitted.

• Strain of electrochemical cycling 

causes stress and fracture in particles

o Micro-cracks inhibit solid phase 

diffusivity

• Texas A&M has developed high-order 

mechanical-electrochemical models 

of micro-cracking + transport

• Goal: Develop reduced-order scaling 

laws that can be integrated with 

fatigue models & validated with 

aging data
13

Reduced-order particle 

fracture model

• Developed from 

numerical 

experiments run 

with full order model 

for various

o C-rates (constant)

o Particle sizes

o Temperatures

• Validated for drive- cycle simulations

PHEV BEV HEV
14

Outline

• Analysis of degradation mechanisms

• Modeling of particle fracture physics

• Cell-level prognostic control

• Pack-level prognostic control
15

Utah State ARPA-E AMPED Project

Approach Benefits

Team: USU (Zane), Ford (Anderson), NREL (K. Smith), UCCS (Plett & Trimboli), UC-Boulder (Maksimovic)
16

Hardware Architecture
17

Pack Validation Test Setup

• Goal: Reduce cell capacity imbalance over 1 year test using heterogeneous 

cell control, optimized for life

o Simultaneously supply 1.5 kW auxiliary load

USU Control Modules

17

Side view Top view

• 1 year aging test underway at NREL (4 US06 cyc/day, 35oC)

o Lower Half Pack: Cell#1-42, passive balancing

o Upper Half Pack: Cell# 43-84, heterogeneous/life active balancing

o Each half-pack purposely imbalanced with 50% new cells and 50% pre-aged cells
18

Life Benefit: Capacity at Year 10 (PHEV) / 8 (BEV)

• PHEV20: +2% to 5% additional capacity (up to 20% life extension)

• BEV75: +3% to 7% additional capacity (up to 40% life extension)

o Active balancing provides benefit greater than liquid cooling

% Remaining Capacity

NREL BLAST-V Model 

Predictions

PHEV20

15kmi/yr

BEV75 – Passive cool.

12.5kmi/yr

BEV75 – Liquid cool.

12.5kmi/yr
19

Outline

• Analysis of degradation mechanisms

• Modeling of particle fracture physics

• Cell-level prognostic control

• Pack-level prognostic control
20

Eaton/NREL ARPA-E 

AMPED Project

• Goal: 50% downsized HEV battery

OOOOOOOOOOOOOOOOOO ffffff ffff: 

JJ XX,UU = � ww1 ∙ ffffffff + ww2 ∙ dddddddddddddd dddddd + ww3 ∙

kk+NNPP

tt=kk

...meet the driver demand using 

least amount of fuel, without 

violating system constraints...

...while meeting target battery life

Medium-duty Commercial HEV

Photo credit: Eaton

Team: Eaton Corporation (Chinmaya Patil), NREL (K. Smith)
21

Online Life Prognostic Model Development

21

1) Cell life test data - Constant temperature & duty cycle

3) Pack life test data

 - Variable temperature & duty cycle

2) Regress life model parameters

4) Validated pack life model

 - Forward looking prognosis based 

 on observed I,V,T,SOC,...

5) Control strategy 

 prototyping

6) Closed-loop 

HIL testing

-20 0 20 40 60 80 100 0

2

4

6

8

1

2

4

6

SOC (%)

discharge

charge

Pulse Power Resistance Growth
22

Life Prognostic Model Accuracy

• Current Status

• Secondary verification (EOL tests) underway

• Verification of iEPM algorithm based on battery health model

• Next Steps

• Complete HIL validation testing of closed-loop performance for 

HEV application

• Application to ES with smart grid & renewables

Pack Aging Model Error (Validation)

0 2 4 6 8 10 12 14

-6

-3

0

3

6

Resistance Model Error (%)

0 2 4 6 8 10 12 14

-2

0

2

4

Time (months)

Capacity Model Error (%)

0 50 100 150 200 250

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1 x 10-3

55oC, Storage50

45oC, hCmDoD50

30oC, hCmDoD

30oC, hCmDoD

30oC, hChDoD

30oC, hChDoD

45oC, mCmDoD

30oC, mCmDoD

55oC, Storage100

45oC, hChDoD50

45oC, Storage100

45oC, Storage50

45oC, Storage100

0oC, mClDoD

45oC, utility

45oC, Storage50

45oC, hCmDoD

0oC, mCmDoD

30oC, mClDoD

55oC, Storage20 30oC, utility 30oC, Storage100

45oC, mClDoD

0oC, utility

g ( )

+10% Error Bound

-10% Error Bound

Resistance Model Error (%)

Capacity Model Error (%)

Cell Aging Model Error (Model Identification)
 NATIONAL RENEWABLE ENERGY LABORATORY

Conclusions & Next Steps

23

• Applications show promise for

• 50% downsized HEV battery

• Up to 20% PHEV life extension

• Up to 40% BEV life extension, relaxing need for liquid cooling

• For mature cell designs, modeling of 3-5 physics-based 

mechanisms predicts aging within

• 3-4% capacity error

• 6-12% resistance error

 Long-term validation still needed

• Major degradation mechanisms are now reasonably well 

understood, ready for

• Standardization of battery testing/modeling for determining warranty

• Integration into computer-aided engineering design tools
24

Thank you