Temperature-DependentBattery Models for High-Power

Lithium-Ion BatteriesValerie H. Johnson, Ahmad A. PesaranNational Renewable Energy Laboratory

Thomas Sack Saft America

At-A-Glance• What?

– Two battery models (Matlab/Simulinkenvironment) for a high-power 6 Ahlithium-ion battery

– Initial model based on available modelfrom NREL’s Advanced VehicleSimulator (ADVISOR)

• Who?– National Renewable Energy Laboratory

(NREL) and Saft America, underDOE’s PNGV program

• Why?– To be used in simulations of hybrid-

electric vehicles

• When?– Testing in Spring 1999

– Model development through Summer2000

• Where?– NREL, Golden, Colorado

Test Data

Model Parameters

ADV RC

CompareModels

ValidateModels

Conclusions

Resistive Model (ADV)

• Model consists of an open circuit voltage (Voc) and an internalresistance (R)

– parameters are functions of State Of Charge (SOC), Temperature (T),and direction of current flow (Rint only)

– SOC:

• External load is a power request

• Called ADV model, stands for ADVISOR

+- Voc = f(SOC,T)

R = ∆V/I =f(SOC,T,charge/discharge) External

LoadP

Battery Terminals

<>

==t

coulomb

coulomb

Adt

A

0used

max

usedmax

charge 0A

discharge 0Afor Ah where

Ah)(Ah-Ah

SOCη

η

Capacitance Model (RC)

Rt(1.2 mΩ)

Re(1.1 mΩ)

Cb(82 kF)

Cc(4.074 kF)

Rc(0.4 mΩ)

Is

Vo

VCc

VCb

Battery Terminals

• Model consists of two capacitors (Cb,Cc) and three resistors(Re, Rc, Rt)

– parameters are constant

– SOC estimated from capacitor voltage (Vcb)

• External load is a current request

• Called RC model

• State-space representation in Simulink

Laboratory Test Setup

• Testing gives parameters for either the ADV or RC model

Bitrode Battery Tester

AmbientTesting

TemperatureTesting inNESLAB

Liquid Bath

Test Procedures

660 680 700 720 740

-30

-25

-20

-15

-10

-5

0

5

Time (min)D

ata

Begin NoResidualEnd NoResidualBegin ResidualEnd Residual

CurrentVoltage

Ah

1. ResidualCapacity Testfor maximumAh capacity

40 60 80 100 120 140 160 180 200

-6

-4

-2

0

2

4

6

CurrentAhVoltageeval pts

Time (min)

Dat

a

2. Open CircuitVoltage Testfor Voc versusSOC

Vfuzzy

Time

Voltage

V1

V2

V3

18 sec

Rest untildV/dt=0

Current0 A

Discharge

IVV

IVV

R

23

terminalocint

−=

−=

3. InternalResistance Testfor:• Rint (ADV)• potentially R

and C values(RC)

Model Parameters vs. Temperature

0 20 40 60 80 1004

4.5

5

5.5

6

6.5

7

7.5

Discharge Current (A)

Cap

acity

(A

h)

0C20C40C0C resid20C resid40C resid0C P.line20C P.line40C P.line

-10 0 10 20 30 40 50 60

8

Temperature (C)

Max

Cap

acity

(A

h)

7.5

7

6.5

6

5.5

5

data

2nd order fit

Ah increase 6%

Ah drop 15%

-10 0 10 20 30 40 50 607.2

7.4

7.6

7.8

8

8.2

8.4

8.6

8.8

9x 10

4

Temperature (C)

Bul

k C

apac

itanc

e (F

arad

s)2nd order fitdata

F increase 2%

F drop 10%

Capacity

0 20 40 60 80 1003

3.1

3.2

3.3

3.4

3.5

3.6

3.7

3.8

3.9

4

SOC (%)

VO

C (

V)

0C data25C data41C data0C model25C model41C modelManuf HP data

0C

25C

40C

3 3.2 3.4 3.6 3.8 40

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

Voltage (V)

Rdi

scha

rge

(ohm

s)

0C model25C model41C model0C Manuf25C Manuf40C Manuf

0C model

0C Manuf

40CManuf

25CManuf

25C model

41Cmodel

3 3.2 3.4 3.6 3.8 40

0.005

0.01

0.015

0.02

0.025

0.03

Voltage (V)

Rch

arge

(oh

ms)

0C data20C data40C data0C model20C model40C model

Open Circuit Voltage

InternalResistance

Model Parameters vs. Temp, cont.

Model-to-Model Comparison

0 10 20 30 40 50 60 70 80 90 100-4000

-3000

-2000

-1000

0

1000

2000

3000

4000

5000

6000

Discharge

Time (sec)

Pow

er (

W)

ADVRC

Power Command

Charge

0 10 20 30 40 50 60 70 80 90 1005

6

7

8

9

10

11

12

13ADVRC

2

1 2

1

Time (sec)

Vol

tage

(V

)

• A demanding power requestwas given to the battery

• ADV model reached voltagelimits, while RC modeldoesn’t currently includevoltage limits

• RC predicts higher restingvoltages

• The RC voltage stays withinthe allowable voltage range

1. discharge at 10 seconds andcharge 90 seconds

• The RC voltage exceeds theallowable safe voltage range

2. discharge at 51 seconds andcharge at 35 seconds

Limiting Cases

Overview

ADV & RC Model Validation

0 100 200 300 400 500 600 700-800

-600

-400

-200

0

200

400

600

800

1000

1200ExperimentADV modelRC model

Discharge

Time (sec)

Pow

er (

W)

Charge

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

-40

-20

0

20

40

60

80

100

120

ExperimentADV modelRC model

Experiment

ADV model

RC model

Time (sec)

Cur

rent

(A

)

0 10 20 30 40 50 60 70 80 90 1008.5

9

9.5

10

10.5

11

11.5

12

ExperimentADV modelRC model

Experiment

ADV model

RC model

Time (sec)

Vol

tage

(V

)

• The experimental values liebetween the ADV model and theRC model

• Neither discharge (6 V) norcharge (11.7 V) voltage limits areexceeded

• The ADV model substantiallyovershoots the experimentalvoltage on both discharge andcharge

• During rests (e.g. 56 - 64 sec),the RC voltage slowly drops, asdoes the experimental voltage,while the ADV model is constantas it has no time dependentbehavior

• During rests, the ADV voltage isslightly lower than experimentalvalues

Observations

• US06 derived battery powerprofile

Model Validation, cont.

0 20 40 60 80 100 1200.34

0.36

0.38

0.4

0.42

0.44

0.46

0.48

ExperimentADV modelRC modelRC model Vcc

Experiment

ADV model

RC model

RC model Vcc

Time (sec)

SO

C (

-)

0 100 200 300 400 500 600 7000.25

0.3

0.35

0.4

0.45

0.5

0.55

0.6

0.65

ExperimentalSOC after1200 sec rest= 0.48

Experiment

ADV model

RC model

RC model Vcc

ExperimentADV modelRC modelRC model Vcc

Time (sec)

SO

C (

-)• ADV more accurately predicts instantaneous SOC than RC

• Final ADV SOC was closer to the true SOC than the RC model

Observations

Cycle Validation ADV model RC modelOverall US06 cycle (600seconds) Vol tage Error

Avg: 1.4% + Std dev 2%,Max: 15%, over-predict

voltage swings

Avg: 1.2% + Std dev 0.7%,Max: 5%, under-predict

voltage swingsInstantaneous SOC Close tracking, slightly

over-predict SOCSlower tracking, similar

behavior patternsFinal SOC (after resting) 3% below 3.7% below

Results & Future Work

• NREL plans on developing a capacitance-based modelin ADVISOR– Advantages of including cap’s: smooth performance

behavior, better voltage tracking

• Issues to address with the future Saft/ADVISOR Model:– SOC estimation– Model to work on a power request basis (not a current

request)– Operation within safe voltage limits– Maintain ADV’s parameter (R and C) variation with

temperature and SOC

• Saft approved release of the current Saft model inADVISOR 3.0, available free on the web:www.ctts.nrel.gov/analysis