International Journal of Emerging Trends in Engineering and Development
Available online on http://www.rspublication.com/ijeted/ijeted_index.htm
Issue 4, Vol.5 (Aug. -Sep. 2014)
ISSN 2249-6149
_____________________________
MODELLING AND SIMULATION OF PV CLOSED LOOP SYSTEM
TO REDUCE NONLINEARITIES WITH DECREASE IN
CAPACITOR SIZE USING MATLAB.
Anand.S1,Eranna2
1
Department ofEEE,StudentMtech, DR. AITBangalore
Department ofEEE,Assoc.Prof, DR. AITBangalore
2
Abstract—
Renewableenergygrowthleadstogreenpower,ithaswitnesseditsgrow
thoverpastdecade.Aphotovoltaicregulationisverynecessarytoobtain
maximumpower.Thispaperestimatesthedynamicresistanceforevery
changeinirradiance.Anadaptivevoltagecontrolmethodisusedbymod
elingthesystemsuchthatthefeedbackvoltageisbeentrackedwiththeM
PPTvoltageforeverychangeinirradiance,thiswillimprovetheperfor
manceofthecontrollerbyreducingtherisetime.ThustheMPPTcontrol
lerperiodisreducedminimizingthe
systemerrorusinga
proposedcontrollermethod.
Keywords—Adaptivevoltage
control,photovotaicpowersystems,signalmodelling,dynamicresistance
,MaximumPowerPointTracking(MPPT).
ED
I. INTRODUCTION
theconverter.ThevalueofPVvoltageiscontinuouslyupdatedbyMPPorLP
Ptracker.InMPPToperationthePVvoltageisveryclosetoMPPvoltage,inL
PPToperationthePVvoltagevariesfromMPPtoopencircuitvoltage.Thusa
fastandstableregulationintheentireoperatingrangeisrequiredforpropertra
cking.TheinfluenceofdynamicresistanceonPVvoltagecontrolforabuckc
onverterhasbeenstudied.Theauthorsanalyzethesingleandcascadedfeedb
ackloops.Itisshownthatsystemcanbecomeunstableifacorrectregulationa
ndcapacitorsizingnotcarriedout.Thispaperanalyzestheinfluenceofdyna
micresistancefordc/dcstepupstagesinglephasePVconverter.Thepaperpr
oposesanadaptivecontrolinordertoobtainaPVvoltageregulation.Thedyna
micresistanceestimationisdonefrommeasuredvariablesoftheconverter,n
amelyPVvoltageandinductorcurrentandthecontrolleriscontinuouslyada
ptedmaking useofthat estimation.
II. SYSTEMMODELLING
ThesystemtobeanalyzedisshowninFig.1.ItmainlyconsistsofaP
Varray,aninputcapacitorC,aboostconverter,abuscapacitorCbus,andasingl
ephaseinverter.Thispaperonlyabletoperformcascadedregulationofstepu
pconverter,whichwillconsistofouterPVvoltage
loopand
aninnerinductorcurrent loop.
IJ
ET
Renewableenergysourceshaslead
to
newresearchtechnologywhichaimstoprovideagoodscopetoemergethegr
owthandconsumptionofgreenpowerminimizingtheimpactofglobalwarm
ing.PVcellsareusedtoextracttheirradiancefromthesunandtoconvertintoel
ectricalenergy.Buttheoperatingpointofaphotovoltaic(PV)cellschangesw
ithchangeinirradiancesoa
propercontrolalgorithmisnecessarytoobtainmaximumpowerbyshiftingt
heoperatingpointofPVcell.SeveralMPPTalgorithmssuchasP&Omethod
,incrementalconductancemethod,anddirectmethodhavebeenused.These
lectionofalgorithmisdonebasedontheconvergingtime,response.ThePVa
rraypowerandcurrentcharacteristicsarehighlynonlinearandareaffectedb
y
irradianceandtemperaturevariation.Thereforeamaximumpowerpointtra
cking(MPPT)is
requiredto
handlesuchproblems
andensure
thatPVsystemis operating at MPP.
PVsystemssufferfromthreemainproblems

Highfabricationcost

Lowconversionefficiencywhenvariable weathercondition.

NonlinearitybetweenPVarrayoutputpower andcurrent.
AmongtheMPPTmethods,hillclimbing/perturbandobservefindsits
advantages in

Simplicity

Ease implementation

Low cost
Hillclimbingoperatesperturbingthesystembychangingtheconverterpow
erdutycycleandtoobserveitseffectonoutputarraypower.However it has
three majordrawbacks.

Slowconverging tooptimumoperatingpoint.

AtsteadystateconditiontheamplitudeofPVpoweroscillatesaro
undthemaximumpointthatcausessystempowerlosses.

During cloudydaysirradiancevariesquickly operatingpoint
movesaway from maximumoptimumpoint.
A. Inductorcurrentcontrol.
Insomeconditionsifthesystemastooperateunderlowpowerpoi
nttracking(LPPT),withlowinductorcurrent,thecontrolshouldbeabletoov
ercomebothcontinuousconductionmode(CCM)anddiscontinuouscondu
ctionmode(DCM).Soforthatpurpose acurrent controlis used based on
technique proposedin[6].
Making useofFig1applyingKirchhoff’svoltage law we have
Vpv– Vout=L.diL/dt
(1)
Vpv–(1-d).Vbus=L.diL/dt
(2)
Where dis the dutycycle.
Dividing(2)byVbusandreorganizing the equationwe have
d–(1-Vpv/Vbus) =d-dccm=L.diL/dt .1/Vbus
(3)
where dccmis definedas
dccm= 1-Vpv/Vbus
(4)
ThevalueofdccmcanbeestimatedfromvoltagesVpvandVbuswhic
haremeasuredvariables.Thevalueobtaineddccm,ffisusedasfeedforwardco
mpensation.Makinguseof(3)and(4)thisfeedforwardcompensationtheloo
pforinductorcurrentregulationinCCMisshowninFig.2whereCirepresent
sthecontroller,SicurrentdigitalsamplerandHiinductorcurrentsensing.Ab
usvoltagecompensationisalsoaddedforbusmeasurementVbus,fMakinguse
ofaleadlagcompensatorwhereTsithecurrentsampletime,thedigitalsample
rSicanbe approximatedas[4]
TheoutputreferenceofthesealgorithmscanbePVvoltage[1][3],thePVcurrentorjustdutycycleofdc/dcconverter.Thebestoptionistoco
ntrolthePVvoltagesinceitchangesslowlyandmorestable.ControllingtheP
Vcurrentmayresultinvoltagedropduringtransientsandcontrollingtheduty
cycleleadstoaninappropriatecontrolofPVvoltageandcurrentaswellasmor
elossesandstressin
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International Journal of Emerging Trends in Engineering and Development
Available online on http://www.rspublication.com/ijeted/ijeted_index.htm
Issue 4, Vol.5 (Aug. -Sep. 2014)
ISSN 2249-6149
_____________________________
WhereTvisthetimeconstantofPVvoltagesensingandKvisthescalingconsta
ntofPVvoltagesensingwhichwillbetakenas1forsimplicityofanalysis.Ifthe
innercurrentandoutervoltageloopsaretotallydecoupled,theinnerclosedloopcouldbemodeledas1.Althoughtheloopsaredecoupledinthispaper,the
innerclosed-loopwillbemodeledasafirst
orderformore
precision.Beingwictheangularcutofffrequencyofthecurrentcontrol,thetr
ansferfunctionisgivenby
Gicl(s) = 1/(s/wic+1)
(12)
Fig: 1.PV singlephase conversionsystem.
Fig: 3. ConventionalPV voltage control loop.
C. PVcellarray modeling.
ED
Fig: 2. Inductorcurrentcontrolloopfor CCM
Si(s)=1/(1.5.Tsi.s+1)
(5)
The inductorcurrentsensing transferfunction Hicanbe expressedasHi(s)
= Ki/(Ti.s+1)
(6)
IJ
ET
Where
Tiis
the
time
constant
ofinductorcurrentsensing
andKiisthescalingconstantofinductorcurrentsensingwhosevalueistaken
as1forsimplicity.
Thepresenceofsamplerandduetotheeffectofthemeasurementretardationo
f
VpvandVbustheforwardduty
cycledccm,ffdoesn’teliminatetheeffectofPVgeneratorforhighfrequency.A
simplePIcontrollerisusedtoobtainregulationindependentofdynamicresis
tance.
B. ConventionalModeling ofPVVoltage ControlLoop.
FromFig.1andKirchhoff’s currentlaw
ipv=ic+iL.
(7)
Byreplacing the capacitorcurrentin(7)
ipv= CdVpv/dt +iL
(8)
ApplyingLaplace transformto(8)weobtainthe
currenttovoltagetransferfunctionas
Vpv(s)/(-iL(s)+ipv(s))=1/(C.s)
(9)
Makinguseof(9),theloopforthePVvoltagevpvregulationisshowninFig.3,
whereCvrepresentsthecontroller,Sv the
voltagedigitalsampleHvthePVvoltagesensingGiclthecurrentclosedloop,gtheirradiance,andTthearraytemperature.ItcanbeobservedintheFig.
3.thatprocessisinfluencedbythePVcurrentipv..BeingTsvthevoltage
sampletime,the digitalsamplerSvcanbe approximatedasSv(s) =
1/(1.5Tsv.s+1)
(10)
The PV voltage sensing transferfunction Hvcanbe expressedas
Hv(s) = Kv/(Tv.s+1)
(11)
Fig:4.PVcellequivalent circuit.
The Fig.4shows the equivalentcircuit ofPVcellasIpv=Iph–
Io.exp[(Vpv+Rs . ipv)/ Vt–1]–(Vpv+Rs .ipv) / Rp (13)
WhereIphandIoarephotogeneratedandsaturationcurrentofarray,Rsistheeq
uivalentseriesresistance,Rpistheequivalentshuntresistance andVtis the
terminalvoltage givenby
Vt=Ns m.(K.T)/q
(14)
Where Ns is the cells connectedin series, mis the ideality factor
ofthediode,kistheBoltzmannconstant,Tisthegeneratortemperatureandqi
sthe
electroncharge.Toobtaina
linearequationforPVcurrentIpvasafunctionofPVvoltageVpvandirradiati
ong.Thevariationofcurrentwithtemperatureisnotconsideredsinceitchang
esveryslowlyandbeingeasilycompensatedbyregulator.Thedynamicresis
tanceofPVarrayRpvwhichwillrepresentthevoltageinfluence
is
calculatedusing (13)as
Rpv= - Vpv/ipv.=Rd// Rp+Rs
(15).
III. CONVENTIONALCONTROL
Inthissectionthevariationofregulationperformanceisobservedforboostst
ageofatypicalPVconverterwhosefeaturesareshowninTable1.Thespecific
ationsofthePVarrayusedforanalysisareshownintable2.Theinductorcurre
ntcanbecontrolledbymodeldevelopedinsection2A.For
thePVvoltageregulationaPIcontroller
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International Journal of Emerging Trends in Engineering and Development
Available online on http://www.rspublication.com/ijeted/ijeted_index.htm
Issue 4, Vol.5 (Aug. -Sep. 2014)
ISSN 2249-6149
_____________________________
isusedintheconverter.IntheconventionalmethodfromFig.3.therisetimeof
thevoltageresponseshouldbeconstantandcloseto9.5ms.Buttherisetimeis
muchhigheranditishighlydependentonvoltagelevel.soinconventionalsys
temthereisnoovershootasthephasemarginishigh.Souseofsmallcapacitor
stheregulationbecomespoorsuchasbecauseofMPPTControllerperiodism
ore.Andnorejectionofirradiance,soonemustuseanewtechniqueso
thatcontrollertimeis reducedandthus increasing the systemstability,
thereby estimatingthechangeinresistanceforachangeinintervaloftime
andirradiance(g).givesriseto implementationofproposed
controller.
(16)
Wherei pv100 ,g 100 andV pv100 arerespectivelythePVcurrent,irradia
nceandPVvoltageobtainedafterapplyinga
type1Chebyshev100Hzbandpassfilter
(
100HzBPF)totheoriginalsignal.
Now,anestimationofthedynamicresistance,Rpv,estcanbeeasilyfoundb
ydividingtherms value ofvpv100(V pv100 )bythermsvalueof
Rpv100=Vpv100/Ipv100
(17)
But generallythemeasuredcurrent is iLinstead ofipv.Howeveripv100
canbeworkedoutbymeansof100HzrippleofiL(iL100)andVpv100asfollows:
TABLEI
Ipv100= iL100+C .Vpv100(K) –Vpv100(K-1)/ Tsv
Features ofDC/DC booststage commercial PVConverter.
Nominalpower
5000W
Input capacitor C
40µF
Boost inductor L
750µH
16KHz
Commutationfrequency fc
250µs
PVvoltage sample timeTsv
125µs
Inductor current sampletimeTsi
(18)
B.ControllerDesign
Theproposedcontroller is a
secondorderonewithtwoconstantparameters KpandTn, andone
variableparameterTmCv(s)=Kp.(Tn.s+1/Tn.s).(Tm.s+1/Tm.s)
(19)
So from(19) it is observedthat, once the dynamicresistance
isKnown,thevariabilityofthesystemcanbeeliminatedbycontrollerparam
eter Tmby forming
Tm=C.Rpv,est
(20)
The belowfig 5showsabout proposedcontrollerblock
74µs
2π.450rad/s.
350V
IJ
ET
TABLEII
Specifications ofPVarrayformedbyfour
stringof12BP585modules.
ED
Timeconstant of the
PVvoltage sensing
Angularcutofffrequencyofthec
urrent controlwic
Bus voltage Vbus
I pv100 =K g .g 100 –V pv100 /R pv =-V p v 100 /R pv
IV. PROPOSEDCONTROL.
Tosolvetheproblemsof
thedynamicresistancevariation,anadaptivecontrolisproposedinthispaper
.ForeachvoltagesampletimeTsv,thecontroltimeatthedynamicresistancea
ndusesthis
valueinordertoadaptoneparameterofthecontrolleraccordingtothedynami
cresistancevariation.Inthisway,thenonlinearsystemvariabilityiscompens
ated.
A.Dynamic ResistanceEstimation
Itcanbeseenthatipvvariationiscausedbybothvpvandgvariations.The
irradiance
variationis
unknownbut
canhave
importanteffectonthecurrentduringacloudpassage.Thisfacthinderstheest
imationofdynamicresistancewhichrepresentscurrentvariationcausedbyv
oltagevariation.Forthisreason100Hzrippleisused.Inrealsystemstheirradi
ancecomponentaround100Hzisnegligible.Asaresultevolutionof100Hzri
ppleofipvisusedby100Hzrippleofvpv. It follows that
Fig: 5. Proposedcontroller.
C.MATLAB SIMULATION AND RESULTS.
ThesimulationiscarriedoutbyusingMatlabSimulink.TheFig:1isusedt
oanalyzethecomponentswhichplayaroletoobtainthedesiredoutput.Anew
modelingtechniqueiscarriedoutbymodeling thecontrolblocks.
Thepaperalsoaimstoprovideanestimationofdynamicresistanceevenfora
verylowfrequency
of100Hzmeansthesystemiscapableofestimatingthechangeinresistancec
orrespondingtothechangeinvoltage values.
An100HzBPFfilterisprovidedtoestimatetheresistancewithinthisbandoff
requency.TheFig:6showsthecircuitarrangementusingMatlabSimulink.
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International Journal of Emerging Trends in Engineering and Development
Available online on http://www.rspublication.com/ijeted/ijeted_index.htm
Issue 4, Vol.5 (Aug. -Sep. 2014)
ISSN 2249-6149
_____________________________
Fig:6 Circuitarrangement usingMatLab.
Fig:7 PVvoltage regulation.
ED
Fig.9 Traditional PV closed loop.
IJ
ET
InproposedcontroltheMPPTtimecanbereducedwhichwillleadt
oimprovementintheperformance.TheMPPTcycletimecanbereducedto40
ms.FromFig:7.Therisetimeofthevoltageresponse
should
beconstantandcloseto23.9ms.Howeverduringthetransientfrom260Vto2
50Vthatisneartoopencircuit,therisetimeis18.4ms,whereasfrom220Vto2
10VaroundtheMPPitis15.1ms.Soinanycasewhenusingtheproposedcontr
ol,therisetimeismuchclosertothedesigntimethanincaseofconventionalco
ntrol.Sobyusingtheproposedcontrol,theMPPTcontrollerperiodcanbeco
nsiderablyreducedwhichleadstothe
improvementintheperformance.Theproposedcontrollercanreducethetim
euptoabout40ms.
Fig.10 simulation result for reduction in ripple(non
linearities)
V.CONCLUSION
Thedynamicresistanceisfirstlyestimatedfrommeasuredvariable
softheconverter.Thencontrolleriscontinuouslyadaptedmakinguseofdyna
Fig.8 Conventional PV voltage closed loop
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International Journal of Emerging Trends in Engineering and Development
Available online on http://www.rspublication.com/ijeted/ijeted_index.htm
Issue 4, Vol.5 (Aug. -Sep. 2014)
ISSN 2249-6149
_____________________________
micestimation.Theresistanceisaccuratelycalculatedbyvoltageandcurrent
100ripplepresentinthesinglephaseinverters.Thisavoidsmisestimationsca
usedbyabruptirradiancevariations.Theoutputvoltageistracedwiththefeed
backvoltagetohaveabettervoltageregulation.TheMPPTcontrollertimeis
reducedsuchthatresponse ofsystemis increased.
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