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.

Advanced Models and 

Controls for Prediction and 

Extension of Battery Lifetime

Kandler Smith, Ph.D.

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

National Renewable Energy Laboratory

Golden, Colorado Presented at the

Large Lithium Ion Battery Technology & Application Symposia

Advanced Automotive Battery Conference

Atlanta, GA• February 4, 2014

NREL/PR‐5400‐61037
2

Thermal

NREL Electrochemical/Thermal/Life Models

Multi-Scale 

Multi-Domain 

(MSMD) model

• Inter-domain 

coupling of field 

variables, source 

terms

• Efficient, flexible 

framework for 

physics expansion

• Leading approach 

for large-cell 

computer-aided 

engineering models

Kim et al. (2011) “Multi-Domain Modeling of Lithium-Ion Batteries Encompassing Multi-Physics in Varied Length 

Scales”, J. of Electrochemistry, Vol. 158, No. 8, pp. A955–A969

Electrochemical

Current Collector (Cu)

Current Collector (Al)

p

Negative

Electrode

Separator

Positive

Electrode
3

Life-predictive model

• Physics-based surrogate 

models tuned to aging test data

• Implemented in system design 

studies & real-time control

• Regression to NCA, FeP, NMC 

chemistries

15°C

20°C

25°

C

30°C

10°C

Minneapolis

Houston

Phoenix

Li-ion graphite/nickelate life:

PHEV20, 1 cycle/day 54% ∆DoD

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

NREL Electrochemical/Thermal/Life Models

NCA = Nickel-Cobalt-Aluminum

FeP = Iron Phosphate

NMC = Nickel-Manganese-Cobalt
4

Challenges and Needs for Life/Degradation Models

Challenges:

• No standard process for life certification

• Predictive models must consider some 5 to 10 coupled 

degradation mechanisms

o Electrochemical/thermal/mechanical mechanisms not yet fully 

understood or modeled

• Lifetime uncertainty absorbed in excess design and warranty 

costs of xEV battery systems

Needs:

• Predict lifetime more accurately, with less test data

o Critical to capture accelerating fade effects nearing end-of-life

• Provide engineering feedback for cell, pack and system control 

designs
5

Outline

• Models

o Surrogate life models (cell level)

o Physics life models (cell level)

o System life (pack level)

• Lifetime extension

o Thermal control

o Charge control

o Cell electrochemical-based control

o Active cell balancing

o Prognostic-based supervisory control
6

Models

• Surrogate life models (cell)

o Present state of art for lifetime prediction

o Ranking of importance of mechanical-coupled 

degradation mechanisms on electrode site-loss

• Physics life models (cell)

o Coupling of solid mechanics with electrochemical/ 

thermal physics

• System life (pack)

o Vehicle & pack thermal models

o Cell performance & aging process variation
7

NREL Life Predictive Model

•Data: J.C. Hall, IECEC, 2006.

7

Relative Capacity 

(%)

Time (years)

r2 = 

0.942

Li-ion NCA chemistry

Arrhenius-Tafel-Wohler model 

describing a2(∆DOD,T, V)

NCA

• Statistical regression to experimental data

• Correct separation of calendar vs. cycling mechanisms

• In rate form, extensible to untested scenarios

Relative

Resistance

Relative

Capacity

Qsites = c0 + c2 N + ...

R = a1 t z + a2 N

Calendar fade

• SEI growth 

• Loss of cyclable lithium 

• Coupled with cycling

• a1, b1 = f(∆DOD,T,Voc,...)

Q = min ( QLi , Qsites )

QLi = b0 + b1 t z + ...

Cycling fade

• Active material structure 

 degradation and 

 mechanical fracture

• a2, c2 = f(∆DOD,T,Voc ,...)
8

NREL Life Model Framework

8

Relat

ive 

Capa

city 

(%)

NCA

A. Resistance growth during storage

 Broussely (Saft), 2007: 

• T = 20°C, 40°C, 60°C

• SOC = 50%, 100%

B. Resistance growth during cycling

Hall (Boeing), 2005-2006:

• DoD = 20%, 40%, 60%, 80%

• End-of-charge voltage = 3.9, 4.0, 4.1 V

• Cycles/day = 1, 4

C. Capacity fade during storage

Smart (NASA-JPL), 2009

• T = 0°C, 10°C, 23°C, 40°C, 55°C

Broussely (Saft), 2001

• V = 3.6V, 4.1V

D. Capacity fade during cycling

Hall (Boeing), 2005-2006: (see above)

Data

1. Fit local model(s)

2. Visualize rate-dependence on 

operating condition

3. Hypothesize rate-law(s)

4. Fit rate-laws(s)

5. Fit global model(s)

Regression of candidate models































 − − =

ref

a

T R T t T

E 1

( )

1 θ exp































 = −

ref

oc ref

V T

V

T t

V t

R

F

( )

( ) expα θ

β

θ 















∆

∆ ∆ =

ref

DoD DoD

DoD

NCA

PHEV10

Phoenix

Predictive model

Model selection based on statistics
9

Knee in Fade Critical for Predicting End of Life

Example simulation: 

1 cycle/day at 25°C 50% DOD:

Graceful fade

(controlled by lithium 

loss)

Hypothesis based on analysis of aging data: Transition from Li 

loss (chemical w/ weak mech. coupling) to site loss (mechanical)

80% DOD:

Graceful fade 

transitions to 

sudden fade ~2300 

cycles

Life over-predicted by 25% without “knee”

NCA
10

Sources of Mechanical Stress in Li-ion Cells Current Collector (Cu)

- +Current Collector (Al)

sep δ − δ δ + Negative Electrode Separator Positive Electrode

L

Li+

er

LixC6

r

Li

y

CoO2

eElectrolyte

x

cs,e

ce

cs

(r) cs

(r)

cs,e

Intercalation Strains

Thermal Strain

Residual stresses of 

manufacturing

Binder/Separator Swelling

Fracture

Delamination

External Loads, 

Cell Packaging

Winding Tension

Negative

Separator

Positive

cell

electrode

particle

Separator Visco-Elastic Creep
11

Open Areas in Mechanics Modeling

1) At which length-scale do stresses most impact battery life, e.g.:

• Particle-level fracture

• Active material bulk expansion/contraction

• Thermal expansion/contraction

• Polymer creep (binder, separator)

2) Optimal packaging of jellyroll (esp. pouch cells)

• Performance

• Lifetime

3) Multi-scale linkage to 3D automotive cell level

• Grains  particles  particles + PVDF + carbon black  composite 

electrode  neg./sep./pos. electrode sandwich  jellyroll  cell

• Accompanying property measurement

4) Linkage of mechanical stress with life (capacity, resistance)
12

Active Site Loss Visible in Cell Aging Data

Knee region (black) based on thresholds for dq/dt and d2q/dt2<0

• Iron-phosphate meta-dataset combines tests from multiple labs – 50+ tests

• In “knee-region” of capacity fade data below, graphite site loss (mechanical 

process) has exceeded Li loss (predominantly chemical process)

FeP
13

Dependence on 

operating parameters:

• C-rate (intercalation 

gradient strains)

• DOD (bulk 

intercalation strains)

• Low T (exacerbates Li 

intercalation- gradients)

• High T (exacerbates 

polymer creep of 

binder, separator)

• ΔT (thermal strains)

Mechanical Stress Effects Contributing to 

Active Site Loss
14

Hypothesized Active Site Loss Model

exp( ( ))[ ] exp( ( ))( ) . , ,

binder intercal.

1 1

1 2 3 R

1 1

2 2, 









 



 



 = − + ∆ + − − −

pulse ref

pulse

rate ref

rate

ref

a

ref

a

t

t

C

C

T T

E

R T T

E

c c ref m DOD m T m

min( , ). Li sites q = q q

q b b t b N z

Li

= 0 + 1 + 2 qsites

= c0 + c2N

accelerated 

polymer failure at 

high T

bulk

intercalation

strain

bulk

thermal

strain

intercalation gradient strain, accelerated 

by low temperature 

FeP

Model successfully 

describes 13 aging 

conditions from 0°C 

to 60°C
15

Bulk Strains Show Strongest Correlation 

with Capacity Fade in Knee Region

FeP

Particlefracture

IntercalationStrain (bulk)

Thermalstrain

%

Contribution to active site loss 

(23oC, 1C, 100% DOD reference condition)

Important factors to 

capture in 3D CAE 

models to optimize cell 

lifetime, mechanical 

constraint

Unstressed 

separator

Stressed 

separator

Princeton/Peabody (2014)

MSU/Xiao (2011)
16

3D Electrochemical/Thermal/Mechanical Model

• Objective: Create cell design 

tool to predict lifetime, 

optimize mechanical 

packaging of large format 

cells

Princeton/

Cannarella (2014)

NREL MSMD Electrochemical/Thermal

CU–Boulder Solid Mechanics

• Approach:

Multi-layer Li-ion battery discretized 

with solid shell elements
17

• ΔSOC & ΔT dependent stress (cell level) more 

significant contributor to capacity loss than 

diffusion-induced gradients (particle level)

• CU-Boulder and NREL developed multi-physics 3D 

model of commercial pouch cell

• Calibrated model versus electrical/thermal 

performance and measured changes in cell 

thickness with SOC, T, age

• Largest stresses at edge of electrode stack with 

separator wind

• Non-negligible in-plane displacements

• More significant stress/strain effects induced by 

electrochemical/thermal bulk changes rather than 

3D gradients across the cell

• Temperature rise from electrochemical/thermal 

model important for capturing magnitude of 

mechanical strain

17

Echem/Thermal/Mechanical Model – Pouch Cells

Displacement in 

thickness direction 

during charging
18

Capturing Vehicle & Ambient Impacts on Life

Time (hr)

Temperature (

o

C)

Vehicle thermal model fit to 3 days 

of Gen II Prius data recorded in 

Golden, CO in winter

Same model predicts Prius battery 

temperature fluctuation in 

Phoenix, AZ 

• Winter: within 1⁄2 oC

• Summer: within 1oC

 (Passenger cabin fluctuations

 within 6oC)

Photo credits: Kandler Smith NREL
19

Ambient Effects on Battery Average Temperature

0

5

10

15

20

25

30

35

Phoenix, AZ Los Angeles,

CA

Minneapolis,

MN

Temperature (C)

BEV75

Passive cooling

Average Ambient w/ solar effects

w/ driving effects

0

5

10

15

20

25

30

35

Phoenix, AZ Los Angeles,

CA

Minneapolis,

MN

Temperature (C)

PHEV35

Chilled liquid cooling

Average Ambient w/ solar effects

w/ driving + active TMS

• Ambient conditions dominate

• Thermal connection with passenger 

cabin, parking in shaded structures 

strongly influence battery life

• Battery temperature and 

lifetime weakly coupled to 

ambient conditions
20

PHEV Life Variability – Phoenix, Arizona

Simulation of 782 drive cycles. Error bars show 5th to 95th percentile drive cycles

Baseline:

TBattery = Ambient

Forced 

ambient air

Chilled liquid

Chilled liquid

+

Frequent 

charging

0 2 4 6 8 10 12 14 16 18

Years Life 

to 75% Remaining Capacity

PHEV10

PHEV40 Drive cycle/annual mileage: ±25%

Value of chilled liquid vs. forced 

air battery thermal 

management: 

• PHEV10: +34%

• PHEV40: +42%

(equates to $500-$600 savings in 

reduced pack total energy at $300/kWh)

Frequent charging:

• PHEV10: -8% (more cycles)

• PHEV40: +4% (shallower cycles)

Lifetime Variation
21

Sub-Ambient Standby Cooling Topologies

• Options: Chilled liquid, air, refrigerant 

evaporative plate or thermoelectrics (TE)

• Shown here: TE device 

 on busbars

HEV

10 yr target life

Photo and figure 

credit: Gentherm
22

Optimized Charging Strategies

• Reduce time spent at high SOC (delay charging)

• Avoid high C-rates to lower peak temperatures

Cost 

function

CU-Boulder/Hoke (2014) 
23

Optimized Charging Strategies

• Delayed charging best • Response to price signals

• No V2G energy exported until electricity price $0.50/kWh

Begin charge End charge Begin charge End charge

A) Constant energy cost B) Variable energy cost
24

ARPA-E AMPED: Battery 

Management

24

Utah State/Ford

Project: 20% reduction in 

PHEV pack energy content 

via power shuttling system 

and control of disparate 

cells to homogenous endof-life

NREL: Requirements 

analysis; life model of 

Ford/Panasonic cell; 

controls validation of Ford 

PHEV packs

Eaton Corporation

Project: Downsized HEV 

pack by 50% through 

enabling battery prognostic 

& supervisory control while 

maintaining same HEV 

performance & life

NREL: Life testing/modeling 

of Eaton cells; controls 

validation on Eaton HEV 

packs

Washington Univ.

Project: Improve available 

energy at the cell level by 

20% based on real-time 

predictive modeling & 

adaptive techniques

NREL: Physics-based celllevel models for MPC; 

implement WU 

reformulated models on 

BMS; validate at cell & 

module level

Advanced Management and Protection of Energy Storage Devices

• Develop advanced sensing and control technologies to provide new innovations in 

safety, performance, and lifetime for grid-scale and vehicle batteries.
25

• US Dept. of Energy – Vehicle Technologies Office: 

Brian Cunningham, David Howell

• US Dept. of Energy – Advanced Research Projects Agency: 

Ilan Gur, Russel Ross

• US Army Tank Automotive Research, Development & Engineering 

Center: 

Yi Ding, Sonya Zanardelli, Matt Castanier

• Gentherm:

Alfred Piggott, Todd Barnhart, Dmitri Kossakovski, Madhav 

Karri

• University of Colorado at Boulder:

Kurt Maute, Reza Behrou, Dragan Maksimovic, Andrew Hoke

• Japan Aerospace Exploration Agency:

Makoto Kawase

Acknowledgements