Tutorial-Lithium-Ion-Battery-Model

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TUTORIAL
Lithium‐IonBatteryModel
October2016

Lithium‐IonBatteryModel
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Thistutorialdescribeshowtousethelithium‐ionbatterymodel.
Somebatterymodelparameterscan be obtained from manufacturerdatasheets,whileothers
needtobeobtainedbytrial‐and‐error.Thistutorialdescribeshowtoobtaintheseparameters.
Theparametersneededbythemodelare:
NsNo.ofcellsinseries
N
p
No.ofcellsinparallel
KsVoltagederatingfactor
K
p
Capacityderatingfactor
Erate
d
Ratedvoltage,inV
Ecu
t
Dischargecut‐offvoltage,inV
Qrate
d
 Ratedcapacity,inAh(ampere‐hour)
Rbat
t
 Internalresistance,inOhm
Idischg Dischargecurrentofthecurveunderwhichmodelparametersareobtained,inA
Kc Capacityfactor
Eful
l
Full(ormaximum)batteryvoltage,inV
EtopExponentialpointvoltage(voltageattheendoftheexponentialzone),inV
EnomNominalvoltage,inV
Qma
x
 Maximumcapacitycorrespondingtothedischargecut‐offvoltageEcu
t
,inAh
Qtop Exponentialpointcapacity(capacityattheendoftheexponentialzone),inAh
QnomNominalcapacity,inAh
SOC Initialstate‐of‐charge
ParametersErated,Ecut,andQrated,canbedirectlyreadfrommanufacturerdatasheet.Someother
parameterscanbeobtainedfromthebatterydischargecurve.
AtypicaldischargecurveisshowninFigure1.
Capacity(Ah)
E
f
ul
l
Etop
Enom
Qto
p
Qnom
Exponential
Region
Voltage
Nominal
Region
Qmax
Ecu
t
0
Q0
Fig.1:Typicalbatterydischargecurve
ModelParameters:
DischargeCut‐offVoltage:Ecut
FullVoltage:Efull
ExponentialPointVoltage:Etop
NominalVoltage:Enom
MaximumCapacity:Qmax
ExponentialPointCapacity:Qtop
NominalCapacity:Qnom

Lithium‐IonBatteryModel
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Fromaspecificdischargecurve,onecanreadvaluesofEfull,Etop,Enom,Qtop,Qnom,andQmax.Note
thatthevaluesofEtop, Qtop, Enom, and Qnomarenotexactasthetransitionpointsareoftennot
definedexactly.Onemaytrydifferentvaluestoobtainabetterfitofthemodelcharacteristicsto
theactualcharacteristics.
ThecapacityfactorisroughlytheratiobetweenQ0(thecapacityat0V)andQmax.Itisavalueclose
to1,anditneedstobeadjustedsuchthatthebatteryvoltageisequaltoEcutwhenSOC=0.
For parameters that are not provided in the datasheet, one may ask manufacturers for the
informationormakeaninitialguessandadjustitbytrial‐and‐error.
Inthistutorial,therechargeablelithium‐ionbatteryVL34570fromSaftisusedtoillustratehowto
definetheparameterstofinetunethebatterymodel.Theprocessinvolvesthefollowingsteps:
 Entertheinformationfromthedatasheet.
 Makeaninitialguessofcertainparametersfromthedischargecurveofthedatasheet.
 Obtain the discharge and charge curves. Compare with the datasheet and experimental
datafordifferentoperatingconditions,andfinetunetheparameters.
1. EnteringDatasheetInformation
Fig.2showstheimageoftheexamplemanufacturerdatasheet.
Thefirststepistoobtainabatteryprofilebasedonthedatasheet.Thenumberofcellsinthe
stack,aswellasthederatingfactorsareallsetto1asthedefault.
Fig.2:SaftVL‐34570Rechargeablelithium‐ionbatteryelectricalcharacteristics
Thebatteryratingparameterscanbereaddirectlyfromthemanufacturer’sdatasheet.
Erated=3.7V
Qrated=5.4Ah
Ecut=2.5V
Erated
Qrated
Ecu
t

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In this case, the datasheet does not provide the battery internal resistance. One may make an
initial estimate from other Lithium‐Ion batteries of similar ratings. We will assume the battery
internalresistanceasRbatt=0.065Ohm.
2. EstimatingParameterValuesfromtheDischargeCurve
Thedischargecurveofthebatteryfromthedatasheetisshownbelow.Fromthedischargecurve,
onemaymaketheinitialestimatetheparameters.
Fig.3:DischargeandchargeprofileoftheSaftVL34570rechargeablelithium‐ionbattery
Usingthe+20otemperaturedischargecurve(1.1A),wehavetheinitialreadingsofthefollowing
parameters:
Efull=4.2V  [full(maximum)batteryvoltage]
Etop=3.75V  [valuesatthepointwheretheexponentialzoneends]
Qtop=2.5Ah
Enom=3.6V  [valuesatthepointwherethenominalzoneends]
Qnom=5.2Ah
Qmax=5.6Ah  [capacityatthecut‐offvoltageof2.5V]
ThecapacityfactorKcissetto1.02.NotethatexceptEfullandQmax,thesevaluesareapproximate.
Oneshouldadjusttheseparameterstobetterfitthesimulatedcurveswiththedatasheetcurves
orexperimentalresults.

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3. FineTuningtheParameters
Oncetheparametersareobtained,onecansetupcircuitstotestthecharginganddischarging
characteristics.Adischargetestcircuitisshownbelow.
V
V_battery
1.1A
A
I_battery
V
SOC
K
1.1/3600
V
Ah
+
-
2.5
Fig.4:Abatterydischargetestcircuit
Thecircuitusesa1.1Acurrentsourcetodischargethebatterythathasainitialstateofchargeof
1.Thetime,insec.,isdividedby3600toconverttohourandismultipliedtothe1.1Acurrentto
obtainthecapacityAh.
Achargetestcircuitisshownbelow.
V
V_battery
A
I_battery
V
SOC
4.2
1.1
K
1/3600
V
time_hr
+
-
Fig.5:Abatterychargetestcircuit
Usually an actual battery charge circuit consists of control circuitry that regulates the charge
currentandbatteryvoltage.Thecircuitaboveisanoversimplifiedversionofapracticalcircuit.
The charge process consists of two stages: constant‐current charging and constant‐voltage
charging.Intheinitialchargingstage,thechargingcurrentislimitedto1.1A.Whenthevoltageis
closetothefullvoltageof4.2V,itisconstant‐voltagecharging.