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