Availableonlineatwww.sciencedirect.com
Journal of Applied Research and Technology
www.jart.ccadet.unam.mx JournalofAppliedResearchandTechnology15(2017)173–189
Original
Particle swarm optimization (PSO)-based tuning technique for PI controller for management of a distributed static synchronous compensator
(DSTATCOM) for improved dynamic response and power quality
T. Eswaran
∗, V. Suresh Kumar
DepartmentofElectricalandElectronicsEngineering,ThiagarajarCollegeEngineering,Madurai,TamilNadu,India Received20July2016;accepted24January2017
Availableonline2April2017
Abstract
Thedistributedstaticsynchronouscompensator(DSTATCOM)hasemergedasanindispensablecompensatorelementinthemanagementof reactivepowerdemandindistributedpowermanagementsystemsaswellasgridconnectedsystems.TheDSTATCOMmaintainsthevoltageat thepointofcommoncoupling(PCC)andattheDClinkvoltageacrosstheDClinkcapacitor.Forthesetwopurposes,therearetwoindependent controllersandthesecontrollersarepredominantlyofPItypes.TuningthePIcontrollerisachallengingexercise.Inthispaper,anovelmethod fortuningthePIcontrollersusingparticleswarmoptimizationispresented.ByMATLABSIMULINKsimulationitisshownthattheparticle swarmoptimization-tunedPIcontrollerperformsbetterthanthetraditionalZiegler-Nicholstechnique-tunedPIcontroller.Inordertovalidatethe proposedidea,anexperimentalsetuphasalsobeenconstructedwithaPIC16F877Amicrocontrollerasthecentralcontrolelementandasascale downphysicalmodeloftheDSTATCOM.
©2017UniversidadNacionalAutónomadeMéxico,CentrodeCienciasAplicadasyDesarrolloTecnológico.Thisisanopenaccessarticleunder theCCBY-NC-NDlicense(http://creativecommons.org/licenses/by-nc-nd/4.0/).
Keywords:DSTATCOM;PIcontroller;TuningtechniquesofthePIcontroller;Ziegler-Nicholstuningmethod;UseofparticleswarmoptimizationintuningthePI controller
1. Introduction
TheDSTATCOMcanbeusedinadistributionsystemwith theprimeobjectiveofcompensatingthereactivepowerdemand oftheloadthus,relievingthesourcethereactivepowerloading.
Thismayleadtobettervoltageregulationofthesourceandthe utilityofthesourcecanalsoberaisedtoitsfullcapacity,asthe powerfactoronthesourcesideisraisedtounity.DSTATCOM canalsobeusedforbalancingthecurrentsdrawnfromthesource inthefaceoftheloadcurrentsbeingunbalancedbecauseofthe unbalancedload.DSTATCOMcanalsobeusedformitigating harmonicsinthesourcecurrent,eveniftheloadisofnonlinear innature.Insuchapplications,theharmoniccurrentsdrawnby theloadwillbemetbytheDSATCOM.Acloseconsiderationof
∗Correspondingauthor.
E-mailaddress:[email protected](T.Eswaran).
PeerReviewundertheresponsibilityofUniversidadNacionalAutónomade México.
theliteraturerelatedtothedevelopmentshappeningaroundthe DTATCOMrevealsthattherehavebeenfourdifferentdirections ofresearchgoingon.Theyare:
a. Thedevelopmentspertainingtothetopologicalchangesof theDSTATCOMconverterincludingtheMultilevelConvert- ers.
b. The various Pulse Width Modulation techniques like the SinusoidalPWM,theSpaceVectorPWMandtheSelective HarmonicElimination(SHE).
c. Therearemanydevelopments intheunderlyingprinciples of electricalengineeringlikethe theoriesbasedonClarks, Parkstransformation,instantaneousrealandreactivepower theoryetc.
d. The fourth direction of the research concentrates on the developmentsofnoveltechniquesofcontrolsystemsforthe management of theDSTATCOM employinginultramod- erntechnologiesliketheAdvancedReducedInstructionSet
http://dx.doi.org/10.1016/j.jart.2017.01.011
1665-6423/©2017UniversidadNacionalAutónomadeMéxico,CentrodeCienciasAplicadasyDesarrolloTecnológico.Thisisanopenaccessarticleunderthe CCBY-NC-NDlicense(http://creativecommons.org/licenses/by-nc-nd/4.0/).
Microprocessor(ARM),DigitalSignalProcessor(DSP)and theVLSI(VeryLargeScaleIntegration)technologies.
Since theoutbreak of the technologicaldevelopments that happenwiththeadventofbothpowerelectronicsorpowersemi- conductorsandthe nearlysimultaneousdevelopments around digitalordiscretesignalprocessingandcontrolsystems,there havebeenvastdevelopmentsinthefieldofDSTATCOM-based powercompensationincludingtheactivepowerfilters.
Power quality issues in power systems are analyzed by EwaldandMohammad(2008).Theuseof FACTSdevicesto addressthepowerqualityissuesintransmissionanddistribu- tionhasbeen presentedbyPadiyar (2008).Adetailed review on powerelectronic solutions topower qualityproblems has beenexplainedbySannino,Svensson,andLarsson(2003).The impactofharmonicsonpowerqualityissuesanditsacceptable limitarepresentedinIEEEStd519(1992).Inastudy,theauthors proposedtheanalysis,simulationandcontrolofDSTATCOMin isolateddistributedthree-phasefour-wiresystems(Singh,Adya, Mittal,&Gupta,2006).Inordertoimprovetheperformance,a studyusedtheparallelconnectedhybridpowerfilters,operated atdifferentswitchingfrequencies(Bhattacharya,Chakraborty,
& Bhattacharya, 2012). In Montero, Cadaval, and Gonzalez (2007), different control strategies, followed for the control of shunt active filters, are compared; A non-iterative opti- mizedalgorithm,forshunt activepower filterunderdistorted and unbalanced supply voltages, was proposed by Kanjiya, Khadkikar,andZeineldin(2013).Anadvancedcurrentcontrol strategyforthree-phaseshuntactivepowerfilterswasproposed byTrinhandLee(2013).Arobustadaptivecontrolstrategyof activepowerfiltersforvariousharmoniccompensation,power- factor correction and balancing of nonlinear loads has been proposed by De Araujo Ribeiro, de Azevedo, and de Sousa (2012). In Singh and Singh (2012), Longhui, Fang, Pengbo, Hongyu, and Zhaoan (2007), they simulated a DSTATCOM forvoltagefluctuation.ThedesignconsiderationsforDSPcon- trolled400Hzshuntactivepowerfilterwereproposedinastudy byHu,Shi,Lu,andXing(2012).Theoreticalinvestigationof originalandmodifiedinstantaneousPQtheoryhasbeendoneby Depenbrock,Staudt,andWrede(2003).PQtransformationto improvetheperformanceofsynchronousreferenceframecon- trollers inshunt activepowerfilters wasanalyzed byPigazo, Moreno,andEstebanez(2009).OperationofaDSTATCOMin voltagecontrolmodehasbeenpresentedinvariousstudiesby Mishra,Ghosh,andJoshi(2003).Aself-tuningPIController for aDSTATCOM using particle swarmoptimization (PSO) hasbeenproposedbyLiuandHsu(2010).Fuzzylogic-based controlofDClinkvoltageinaDSTATCOMwasproposedby SuryanarayanaandMishra(2008).
Thisresearchfocusesonthedevelopmentofarobustcontrol schemefor the DSTATCOM withjustthetraditional PI con- trollerbutwithabettertuningtechnique.Theresearchhasbeen carriedoutinanapplicationofDSTATCOMinabalancedand linearbutreactiveloadenvironment.Therefore,theobjectiveof theDSTATCOMunderconsiderationisjusttoinjectwherethe appropriatemagnitudeofthereactivecurrentrequiresloadwith thehelpofthetwoPIcontrollers.
OneofthetwocontrollerstakescareoftheDClinkvoltage.
TheothercontrollertakescareoftheACthree-phasevoltages atthepointofcommoncoupling.Thecontrollerthattakescare of theDClinkvoltagecanbeofthePItypewithfairlylower bandwidth.
Astheothercontrollermaintainsthevoltageatthepointof commoncoupling,themethodologyistoinjecttheappropriate reactivecurrentintotheACsystemsuchthattheexactquantity ofreactivepowerdemandoftheloadismetwithatafixedAC voltage.Thereactivepowerflowintotheloadfromthemains hasaninfluenceonthebusbarvoltage.Thechangesthatoccur atthe‘d’componentoftheorthogonallydisplaced‘d’and‘q’
components of thepark transformed three-phaseline voltage systemisafunctionofthereactivepowerdrawnbytheconnected load.
The paperhasbeenarranged asfollows. Nexttothisbrief Introductionsection,areviewoftheessentialsoftheDSTAT- COM isgiveninSection2.Theprinciplesof particleswarm optimizationare presentedinSection3.Thetuning ofthe PI controllerisdiscussedinSection4.Adetailedstudyoftheper- formance of the PI controller inthe light of frequency-based analysisisdepictedintheSection5.Resultsofthesimulation intheMATLABSIMULINKenvironmentarepresentedinSec- tion6.Anexperimentalverificationhasbeencarriedoutandthe resultsarediscussedinSections7–9followedbytheconclusion inSection10.
2. Structuremodelingandcontrolstrategiesofthe DSTATCOM
StructurallytheDSTATCOM,whetherforgrid-basedappli- cationsorforapplicationsinthedistributionsystems,assumes the three-phasethreelegsGraetzbridge arrangementconsist- ing ofsix powerelectronicswitches arrangedinthethreeleg converterasshowninFigure1.
The switches may be of the power MOSFET type or the IGBT type. Forlow-frequency switching butfor highpower applications,IGBTispreferred.Forlowtomediumpower,ifthe designuseshighswitchingfrequency,thenMOSFETswitches willbethechoice.
The DSTATCOM-based reactive power compensator has threefundamentalelementsandtheyaretheDSTATCOMcon- verter,theDClinkcapacitorandthereactor typefilter.There aretwosidesinDSTATCOM.ThetwoterminalDCsideiscon- nected tothe DClink capacitor andthe three-phaseAC side oftheconverterisconnectedtothepointofcommoncoupling throughasetofthreereactorsasshowninFigure1.
2.1. Realpowertransaction
ThoughtheDSTATCOMismeantforreactivepowercom- pensation, it needs a steady DC voltage across the DC link capacitor.Becauseoftheleakageofthecapacitor,theDClink voltagemaytendtofall.Thishastobetopedupcontinuously bydrawingrealpowerfromtheACmainssource.Besides,the lossesoccurringinthesemiconductorswitchesandthelosses occurringintheseriesreactoraretobemet.Asaresultofthese
Fig.1.StructureofDSTATCOM.
losses,acertainrealpoweristobedrawnfromtheACmains.
Therefore,theDSTATCOMshouldbecapableofdrawingreal powerfromthe mains, whileit hastosupplyreactivepower.
Itis tobenoted thatbothreal andreactivepowerscan cross across the DSTATCOM in oppositeor inthe samedirection andthisfeaturesthecontrollabilityofrealandreactivepowers simultaneously.
Thereareactuallytwodegrees offreedomassociated with theDSTATCOMandthesetwoarethemodulationindexandthe phaseangleofthereferencesignalwhichareusedforPWMin theswitchingofthepowersemiconductorsoftheDSTATCOM.
Themodulationindexcontrolisusedforthereactivepower controlandthephaseanglecontrol isused fortherealpower control. The currents associated with the DSTATCOM obey Kirchhoff’scurrent law andvectorsandthe waveformsasso- ciatedwiththeDSTATCOMareshowninFigures2and3.
Therealpowertransactionhappeningoverareactorisafunc- tionofthepotentialdifferenceandthephaseangledifference existingbetweentheendsofthereactor.Also,therelationship between the voltages, phase angles and the reactance of the reactoraregiveninEq.(1).
TherealpowertransferredfromV1toV2is P =V1∗V2 cosδ
X (1)
whereXisthereactanceofthereactorbetweenV1andV2. In ordertodrawthe requiredquantity of real powerfrom theAC mains, thephase angleof the terminalvoltageof the
Fig.2.CurrentsassociatedwithDSTATCOM.
convertorshouldlagbehindthephaseangleofthevoltagepre- vailingatthepointofcommoncoupling(PCC).Now,thisangle oflagcanbeintroducedintheterminalvoltageoftheDSTAT- COMconverterbyprovidingtherequiredlagofthereference signalused.Theangleoflagisderivedfromacontrollertypi- callyofPItypeoranFLCorwhateveritcouldbeandwherever theinputtothecontrollerusedistheerrorbetweenthesetpoint DClink voltageandthe actualDClink voltage. The general structure of thecontrollerthat producesthe angle θof lagor lead,isshowninFigure4.
Fig.3.Therealpowertransactionhappeningoverareactorisafunctionofthe potentialdifferenceandthephaseangledifferenceexistingbetweentheendsof thereactor.
Fig.4.Generalstructureofcontroller.
2.2. Reactivepowercompensation
Inreactivepowercompensationtechniques,thereactivecom- ponentofcurrentdrawnfromthe loadissuppliedtotheload fromtheDSTATCOM.Thisrelievesthemainsourcefrombeing loadedwithreactivecomponentofcurrent.Theactualquantity of reactivecomponentof current tobeinjectedis carriedout indirectlybyconsideringthe‘d’component ofthe‘dq’trans- formedVabcatthepointofcommoncouplingusingthePark’s transformation.
Withapurelyresistiveloadd componentof thevoltageat thepointofcommoncouplingwillbepracticallyverycloseto theunit.Withtheinclusionofreactivepowerload,thisquantity fallsdownandtheDSTATCOMwillinjectreactivecurrentinto theloadthroughthebus.Thisactiontakesthedcomponentof thevoltageatthepointofcommoncouplingbacktonearunity condition.
ThephasordiagramshowninFigure5showsthemechanism ofreactivepowerflowbymaintainingtheappropriatevoltages atthe point of common coupling andat the terminalsof the converter.
ThereactivepowertransferredfromV1toV2is Q=V1∗V2sin δ
X (2)
whereXisthereactanceofthereactorbetweenV1andV2. According to Eq. (2), the reactive power transaction is a function of the voltage difference between the terminals of theDSTATCOMconverterandthepointofcommoncoupling.
Fig.5.Reactivepowertransformation.
Fig.6.Generalcontrolstructureforreactivepowercompensation.
Theequationrevealsthateventhoughthereisphasedifference betweenthenodesV1andV2,thereactivepowertransactioncan happenwithdifferenceinthemagnitudeofthevoltagelevelsat V1andV2.
InthePWMdrivenDSTATCOM,thedifferenceinthevol- tagesprevailingacrossthereactorcanbeachievedbyadjusting themodulationindexofthereferencesignalusedinPWM.The generalcontrolstructureofthereactivepowercompensationis showninFigure6.Thus,usingthetwocontrolsystems,thetwo degrees offreedomaremanipulatedandthisleadstorealand reactivepowertransactioninrequiredmanner.
The varioussteps involved in the reactiveand real power compensationaresetoutinthefollowingsteps.
Reactivepowercompensation:
1. Forthepurposeoftesting,tostartwith,athree-phaseresistive load isconnectedonthe loadside.The STATCOM isnot connectednow.
2. Measurethethree-phasevoltageatthePCC.
3. Afterthelow-passfilter,thethree-phasevoltagewaveform obtained.
4. Get thefrequencyand sineandcosine components of the threephasevoltageprevailingatthePCC.
5. PerformParktransformationandseparated,qand0compo- nents.
6. Thedcomponentvalue,withresistiveloadontheloadside willbethesetpointforreactivepowercompensation.
7. WiththeSTATCOMconnected,theactualRLload,theactual d component andthe setpointof the d component of the voltageatthepointofcommoncouplingareusedtofindthe error.
8. Thiserroris usedinthe first PIcontroller togeneratethe modulationindextobeusedinthereferencesinewavegen- eration.
RealPowerCompensation:
Thereal power canflow through the STATCOM ineither directionfromthe DClinkcapacitortothepointof common couplingorfromthepointofcommoncouplingtowardtheDC linkcapacitor.Dependinguponthedirectionoftheflowofreal power,thevoltageacrosstheDClinkcapacitormayeitherriseor fall.ItisnecessarythattheDClinkcapacitoristobemaintained ataconstantDClevelsothat,thereactivepowercompensation iscarriedoutsatisfactorily.
Duringtheoperation,itispossiblethatthecapacitorlooses chargecausedbytheinternallossesinthecapacitorresultingin reductionoftheDClinkvoltageacrossthecapacitor.
ThesecondPIcontrollerthatisresponsibleformaintaining DClinkvoltageworksasperthefollowingsteps.
1. AcceptsetpointDClinkvoltage 2. MeasuretheactualDClinkvoltage.
3. Findtheerror.
4. ApplyerrortothePIcontroller.
5. GettheoutputofthePIcontrollerwhichliesbetween+1.57 and−1.57(radians).
6. Usethisangleinthethreephasereferencesinewavegener- ationunit.
2.3. Parktransformation
Thevoltageatthepointofcommoncouplingisathree-phase balancedvoltagesystemdisplacedby120◦betweenthephases.
Thethree-phasevoltagesaretimevaryingaccordingtothesine law.Directdecoupledcontrolofreactiveandrealpowerisnot possiblebysimplevoltagecontrol.Adecoupledcontrolsystem is needed.The Park transformationhas two advantages. The firstoneisthetimevaryingthree-phasevoltagesystem,Vabcis transformedintoanontimevaryingdandqcomponentssuch thatthecontrollersoflowbandwidthcanbeused.Thesecond advantageisthatadecoupledcontrolschemecanbeachieved sothat,independentrealandreactivepowerflowcanbecarried outwithoutdisturbingeachother.
⎡
⎢⎣ vd
vq
v0
⎤
⎥⎦=
⎡
⎢⎢
⎢⎢
⎢⎢
⎢⎣
sinθ sin
θ− 2π
3
sin
θ+2π
3
cosθ cos
θ− 2π
3
cos
θ+2π
3
1 2
1 2
1 2
⎤
⎥⎥
⎥⎥
⎥⎥
⎥⎦
⎡
⎢⎣ va
vb
vc
⎤
⎥⎦ (3)
⎡
⎢⎢
⎣ va
vb
vc
⎤
⎥⎥
⎦ =
⎡
⎢⎢
⎢⎢
⎢⎣
sinθ cosθ 1
sin
θ−2π
3
cos
θ−2π
3
1
sin
θ+2π
3
cos
θ+2π
3
1
⎤
⎥⎥
⎥⎥
⎥⎦
⎡
⎢⎢
⎣ vd
vq
v0
⎤
⎥⎥
⎦ (4)
Eqs. (3) and(4) givethe transformation matricesfor Park transformationandreverseParktransformation,respectively.In thisresearch,aParktransformationiscarriedoutforthethree- phase voltageVabc atthe point of commoncoupling and the
‘d’and‘q’quantitiesareseparated.The‘d’quantityisusedfor reactivepowercontrol.However,the‘q’quantityisnotused.
Afterderivingthecontrolleroutputs,themodulationindex and the phaseangle ‘θ’ from the two controllers areference signal isrestructured using the fundamentalequation of sine wave
V(t)=Vmax∗sin(ωt+θ)
whereω=2*π*fandfisderivedfromaphaselockedloop(PLL) unit.
3. Particleswarmoptimization
Particleswarmoptimizationisaheuristicsearchoroptimiza- tiontechniqueinspiredbythecooperativebehaviorofflocksof birdsorschoolsoffish.Withanextremelyintricatesystemof communication,thebirdsor fishhereaftertermed asparticles interactwitheachother.Inadditiontothecommunicationskills, theparticlesarecharacterizedbyasortofupdatingthebestof thepastperformancesinthecurrentflight.
InthePSOmodelusedinindustrialoptimization,eachparti- cleisassociatedwithasetofparameters.Thesetofparameters associatedwitheachparticleisavector.Thisvectorisofequal numberofelementsforalltheparticlesandthesizeofthisvector isequaltothesizeofthevectortobeoptimizedintheapplica- tion.Tostartwith,theelementsofthevectorsofeachparticleare assignedwitharbitraryvalueswithintheallowablerange.With thearbitraryvaluesforthevectorelements,theperformanceof eachofthevectorsiscalculated.ThePSOtechniqueisaheuris- ticsearchtechniquewhichisusedtolocateaparticularpointin amultidimensionalspace,wherethispointisultimatelypointed outbyalltheparticleswhichsatisfytheobjectivetobereached.
InatypicalPSOsetup,afixednumberparticleisinvolved.
Eachparticleisassociatedwithavectoroffixednumberofele- ments.Tostartwith,theseelementsarerandomlyinitializedand thewholesystemofparticlesentersintoaniterativeprocess.At the endof each iteration,the performanceof eachparticle is calculatedintermsoftheclosenesstotheobjectivefunctionby substitutingthevaluesoftheelementsofthevectorintheobjec- tivefunction.Attheendofeveryiteration,itmaysohappenthat oneamongoftheparticlescomesoutwiththebestresults.That particleisreferredasthegloballybestparticleoftheiteration.
Inthenextiteration,anotherparticlemaybecometheglobally bestparticle.
Besides,eachparticleoveranumberofiterationsmayexhibit differentperformancesineachiterationandbyconsideringthe
past andthe present iteration,the certain combinationof the elementsofthevectorforaparticulariterationmightstandthe bestperformingvectorpertainingtothatparticularparticle.This particularvectoristhepersonalbestofthesaidparticle.Allthe particlesare updated withthe best vector that givesthe best results.
Thus,aftertheupdatingtheprocessthathappensattheend ofeveryiteration,alltheparticleswillassumetheirbestvectors sofar,respectivelytheirpersonalbestandoneamongthemwill bethegloballybestparticle.
Basedonthevectorofthepersonalbestofeachparticleand basedonthevectorofthegloballybestperformingparticle,a velocityisestimatedandthisvelocityisaddeduprespectively withtheupdatedbestperformingvectorofeachparticle.Thus, attheendofeachiteration,thevectorsofalltheparticlesare updatedandtheperformanceevaluatedwithEqs.(5)and(6).
vid =w(G)×vid+c1×rand1di ×
pbestid−Xdi
++c2×rand2di ×
gbestid−Xdi
(5)
Xdi =Xdi +Vid (6)
As the iterative process is under process, the elements of thevectorofeachparticlearemodifiedlittlebylittleandthey allmovetowardthecommongoalfromdifferentdirectionsto ultimatelymeetattheuniquepoint.Atthisunique,theelements ofthe vectorsofallthe particleswillbe thesameandallthe particlesshowupalmostthesameperformancewithrespectto theobjectivefunction.
Theelementsofthevectorofallparticleswillbethesameat thepointofconvergenceandthatistherequiredsolution.
InthecaseoftuningaPIcontroller,itisatwodimensional searchspacewheretheelementstobeestimatedaretheKpand Kivalues.AflowchartwhichdescribestheoperationofaPSO isgivenherewith(Charts1–3).
4. ThePIcontrollertuningtechniques
Theobjectiveofanycontrolsystemistomaketheerrorten- dingtozerobetweenthesetpointandtheactualvalue.InaPI controller,theerroristheinputtothecontrollerandincourseof time,thisinputshouldbecomezero.Dependinguponthechar- acteristicsoftheplantandthatoftheKpandKiparametersused inthePIcontroller,thetrajectoryoferrorisdictatedfromthe maximumvaluetothefinalminimumorzerovalue.
ThelocationofatypicalPIcontrollerinafeedbackcontrol systemappliedtoaplantisshowninFigure7.
Fora plant withgiven transferfunction, the constantsKp
andKiusedinthePIcontrollersplaythemainroleoftracking the errorsuch that the performanceparameterssuch as over- shoot,transientperiod,oscillationsandthesteadystateerrorare minimum.
TheappropriateselectionoftheKpandKiconstantsofthe PI controllers can be done using the trial and error method, if the plant under considerationis linear. However, for more
Chart1.Proposedwork.
Chart2.PIfunction.
complicatedplantswithhigherordersoftransferfunction,spe- cializedtuningtechniquesarerequired.
The Ziegler-Nichols method for tuning PI controllers is supported partiallybyamathematicaldeterministicbasisand partiallybyexperienceandempiricalrules.TheZiegler-Nichols
Chart3.PSOalgorithm.
Fig.7.TypicalPIcontroller.
methodfortuningPI controllersisfairlygoodinmost ofthe systems.However,forsystemssuchasDSTATCOM,wherenon linearitiesareobserved,theZiegler-Nicholsmethodshowsinfe- riorperformance.Undersuchcircumstances,morerobusttuning techniquesareneeded.
Particleswarmoptimizationisatechniquethatcanhandlea numberofgoverningequationsandconstraintsandarriveatan optimalsolutionfortheproblemathand.ThePSOtechniquecan beusedtofindtheKpandKivaluesusingarepetitiveprocess, whichiswhathasbeenattemptedinthiswork.ThefinalKpand Ki values,as suggestedby the PSO,provetooutperform the
Table1
Performanceparameters.
Parameters ZN PSO
Peakovershoot 58.5 19.5
Transientperiod 0.0024 0.0019
ISE 482.5 335.8
Fig.8.StepresponseforPIcontrollerusingZiegler-Nicholstuningmethod.
Ziegler-Nicholstuningmethodintermsofthecomparisonsof theperformanceparametersastabulatedinTable1.
Ofthemanyavailableoptimizationtechniques,thePSO is preferablebecause ofits easeimplementingintheembedded systemenvironments.
5. AnalysisofthePIcontrollerinthefrequencydomain The performance of the PI controller canbe judgedafter gettingtheresultsofsimulationinthetimedomain.Thetime domainanalysisistheanalysisoftheresultsofthesimulation after arrivingattentativeparameters. However,thefrequency domainconsiderationgivesmoreinsighttothe systemandit is usefulinarrivingat the controlsystem parametersbefore- hand.Thefrequencyresponsecharacteristicsgiveanideaofthe dynamicresponseofthesystemtobedesigned.
With reference toFigures 8 and 9, the comparisonof the dynamic response of the system can be made. A typical PI controller tuned by the Ziegler-Nichols method offers more overshoot, more transient period, more oscillations andlittle oscillationsinthesteadystatetoo.However,inthesameplant, thePSO-tunedcontrolleroffersabetterdynamicresponsewith minimumovershoot,lessoscillationsandlesstransientperiod anditdoesnotshowminuteripplesinthesteadystate,asshown inFigures8and9.
ThebodeplotsofthePIcontrollerswithtwotuningmethods consideredareshowninFigures10and11.Thegainmarginof thePSO-tunedcaseisobviouslyhigherthanthatoftheZiegler- Nicholstuningmethod.Thisleadstomorestablecontrollability withawiderangeofdisturbancesinthePSO-basedtuningtech- nique.
Fig.9.StepresponseforPIcontrollerusingPSO.
6. MATLAB/SIMULINKsimulation
The proposed method of designing the PI controllers for the management of the DSTATCOM is implemented in the SIMULINK/MATLABenvironment.
Thespecificationsofthesystemare:
Operatingvoltage380V50Hz3phase Load:P=5KW,Q=5KVARandPF=0.707.
DSTATCOM:10KVARandVDC=1200V ReactorL=1mHandR=3Ohms.
PWM:SinusoidalPWM6Pulse Switches:MOSFETs6Nos.
Switchingfrequency1050Hz.
With thepurpose ofdemonstratingtheperformanceof the proposedmethod,anRLloadisselected,suchthatthepower factorisnearly=0.707.WithouttheDSTATCOMinactionwith
Fig.10.BodeplotforPIcontroller1(ISE1)usingZiegler-Nicholstuningmethod.
Fig.11.BodeplotforPIcontroller2(ISE2)usingPSOtuningmethod.
Fig.12.MATLABsimulinkmodelofproposedsystem.
Fig.13.MATLAB/SIMULINKmodelofPIcontroller.
Fig.14.Thehardwaresetup.
Fig.15.VoltageandcurrentofDSTATCOMusingZiegler-Nicholstuningmethod.
thesourceside,itisburdenedwithrealandreactiveloadsof5kW and5KVAR,respectively.Theloadandthesourcesidepower factorare close toeach other=0.707. With the DSTATCOM inaction, the reactivecomponent of the loadQ=5KVAR is fullysupportedandthemainsourceisrelievedfromthereactive demand.Theloadsidepowerfactorbeing0.707,thesourceside
powerfactorisimprovedtonearly0.93.Thesourcecurrentis alsoreducedaccordingly.
ThemanagementoftheDSTATCOMinvolvesthemanage- mentoftwocontrollers.Oneisresponsibleformaintainingthe DClinkvoltageandtheothercontrollerisresponsibleformain- tainingthevoltageatthepointofcommoncoupling.Forboth
Fig.16.VoltageandcurrentofDSTATCOMusingPSO-PITuningmethod.
Fig.17.THDforsourcecurrentusingZNmethod.
ofthesecontrollers,PItechniqueisadopted.Tostartwith,the Ziegler-Nichols-tuned PI version is tried and the results are recorded. Then, the PSO tuned PI versionis attempted. The resultsofthePSOtunedPIversionarealsorecordedandatable ofcomparisonismade.ItisdiscussedintheResultssection.
ThemainblocksoftheMATLABSIMULINKmodelofthe proposedsystemand the model of PI controllerare given in Figures12and13,respectively.Detaileddisplaysystemsofall theparametersareincludedinthemodel.Thecontroltechnique ofthe DSTATCOMinvolvesparktransformation andfor that purpose,the estimations of the sourceside frequencyandits phaseare required.Figure12 showsthe blocksinterconnect- ingthePLLunit,theParktransformationunit,thecontrollers pertainingtoDClinkvoltageandVpcc.
Fig.18.THDofsourcecurrentusingPSO-PItuningmethod.
The construction of the reference signal follows the con- trollers.Theoutput ofthecontrollerismeantformaintaining theDClinkvoltageandthatofthecontrollerismeantformain- tainingthe Vpcc isused for constructing thereferencesignal.
The referencesignalis asine wavewiththe samefrequency asof thesource.Theoutputof theDClinkvoltagecontroller willbe thephaseangleof thereferencesignal. Theoutputof theVpcccontrollerwill betheamplitudeofthe referencesig- nal.Aftergeneratingthereferencesignal,thesinusoidalPWM isimplementedusingthediscretePWMblockavailableinthe SIMULINK.
Fig.19.RealandreactivepowerofDSTATCOMusingZiegler-NicholsTuningmethod.
Fig.20.RealandreactivepowerofDSTATCOMusingPSO-PITuningmethod.
7. Experimentalverificationusingahardwaresetup Anexperimentalverificationsetupinthehardware formis executedtovalidatetheproposedmethodology.Ascaleddown hardwaresetupisconstructedwithaPICmicroprocessorasthe
central controldevice. The specifications of theexperimental setuparegivenbelow:
1. System voltage and frequency: Three-phase 380V 50Hz utilityoutlet.
Fig.21.PowerfactorandDClinkvoltage.
Fig.22.(a)HandheldclamptypeTHDmeter.(b)ThethreephaselinesynchronizedthreephasetriggeringpulsesgeneratorconstructedusingLM741operational amplifierICs.
2. Linear reactive load: Three-phase 100W/230V with 100VAR/230Vreactiveloadsateachphase.
Thehardware setup,whichhasbeen constructedandused for the validation of the proposed technique, is presented in Figure14.
With reference to the hardware setup as presented in Figure14,threelampsocketsareused totestthethreelamps ofunequalwattageinordertostudytheloadunderunbalance condition.Thefiguredepictstheconditionwhenthesystemis studiedforanonlinearloadwithoneRLloadusingonelamp andachokedrivenbyathree-phaserectifier.
AnLCDdisplayisprovidedtoindicatethepowerfactoron thesourceandloadsides.
The STATCOM unit is constructed using aGraetz bridge comprisingsixnumbersofMOSFETSoftypeIRF840andthey
havereversediodes.TheseMOSFETSarearrangedintheform oftheGraetzBridge.TheyactuallybridgetheDClinkcapac- itor andthe point of common coupling through the reactors.
PICmicrocontrollerPIC16F877isthecentralcontrolunitthat drivesthesixMOSFETSthroughsixoptocouplersoftypeMCT 2E.IC741-basedcomparatorswhichareusedforthedetectionof thephaseanglebetweenthesourcevoltageandsourcecurrent.
Similarly,theloadpowerfactorisalsomeasuredanddisplayed.
Variousexperimentsareconductedtovalidatetheproposedidea andtheresultsoftheexperimentsarepresentedinSection8.
8. Resultsanddiscussions
Twoapproacheshavebeenusedinthisworkfortheestima- tionof KpandKi valuesofthetwoPIcontrollersinvolvedin themanagementofreactivepowerusingtheDSTATCOMand
Fig.23.Atriangularcarrieroffrequency1kHzusedforthesinusoidalPWM.
Fig.24.Thecomparisonofthereferencewaveandthecarrier.
Table2
KpandKivaluesfortwocontrollers.
Parameters ZN PSO
Kp1 0.1 0.0643
Ki1 2.513 0.0712
Kp2 0.13 0.0352
Ki2 0.8622 0.0513
theyaretheZiegler-Nichols approachandthePSO approach.
Table2givesthevaluesofKpandKiforthetwocontrollersas derivedfromthetwoapproaches.
UpongettingthevaluesforKpandKi,thesimulationsarecar- riedoutandthevariousresultsobtainedareshowninthissection.
Figure15givesthewaveformsofthesourcesidevoltage,source current,loadsidevoltage,loadcurrent,theterminalvoltageof theDSTATCOMconverterandtheDSTATCOMcurrent–with theZiegler-Nichols-tunedPIcontrollers(Fig.16).
InthecompensationofthereactivepowerusingtheDSTAT- COM, being a switched system, there are chances of the line gettingpolluted. Therefore, comparisonsof the THD of the source voltage with both the approaches are shown in Figures17and18.ItisevidentthattheTHDofthesourcecur- rentislessinthecaseofthePSO-tunedPIcontrollersthanfor the Ziegler-Nichols-tunedPI controllers.Thematricesof real andreactivepowerflowinboththecasesareshowngraphically inFigures19and20.Thesimulationresultsarecomparedand showninTable3.
Finally, a comparisonof the DClink voltageis shownin Figure21.TheQualityoftheDClinkvoltageobtainedinthecase ofusingPIcontrollerswithZiegler-Nicholstuningtechniqueis inferioranditcontainsmoreripplesthanthatofPIcontrollers tunedbythePSOmethod.
Considering thedifferencesinthe controlsystem, theper- formanceparametersandthepowerflowparameters,itcanbe
Fig.25.ThesinewavereferenceandtriangularwavecarriertothePWMcomparatorwiththecorrespondingsquarepulseoutput.
Table3
Simulationresultscomparison.
Parameter ZN-PI PSO-PI
PDemand 0.25 0.25
QDemand 0.25 0.25
PfromSources 0.2806 0.2822
QfromSources −0.00897 −0.001151
PtoDSTATCOM −0.0288 −0.03602
QfromDSTATCOM 0.2632 0.2533
PFatSource 0.9995 0.9997
THDofsourcecurrent 1.58% 1.49%
inferredthatthePSO-basedtuningtechniqueisfarsuperiorto theZiegler-NicholstuningmethodinthecaseofaDSTATCOM, meantforreactivepowercompensation.
9. Resultsofexperimentalverification
Theexperimentalsetupalongwiththespecificationsispre- sentedinthepreviousSection7.
1. Theloadsideandsourcesidepowerfactors.
2. TheloadandthesourcesideTHDofthecurrent.
Variousassociatedwaveformsarealsorecorded(Fig.22).
Figure23(b)showstheexperimentalsetupfortheimplemen- tationofthethree-phaseSTATCOMcontrolledbyaPIcontroller tunedbytheZNtechniqueandthePSO-basedtuningtechnique.
Fortheobservationof theresults,theDSOUTD4104Cis used. For the indication of power factor, an LCD display is incorporatedandtheestimationofpowerfactoriscarriedout insidethePICmicrocontroller.TheTHDofthesourcecurrent isobserved using the handheld clamptypeTHDinstrument UNITmodelUT243whichisshowninFigure23(a).
The carrier wave of 1kHz is generated using an opera- tional amplifier-based triangular wave generator. The typical waveformof the triangular waveis showninFigure 24.The three-phasereferencewaveisgeneratedusingthethree-phase sample waves derived from the line at the point of common couplingsoastoenablelinesynchronousoperation.
Theoperationalamplifier-basedcomparatorsareusedforthe generationofPWMpulses.Thewaveformsassociatedwiththe comparatorareshowninFigures25and26.Figure26illustrates thesinusoidalPWMprocessforamodulationindexof.65.The distributionofthe dutycycle asper thesine lawis shownin Figure26.
Thesignalspertainingtothesourcevoltage,sourcecurrent, loadsidevoltage andcurrent areschimit triggeredtoget the correspondingsquarewavestobefedasinputtothemicrocon- trollertomeasurethephaseangleandhence,thepowerfactor (Fig.27).
Figures 28–32 shows the phase relationships between the sourcecurrentandthesourcevoltagewithandwithouttheSTAT- COM.Figures 31 and32 specifically illustrate the improved performanceof the PSO-tunedPI controllercompared tothe ZN-tunedPIcontroller.
Fig.26.Thesinewavesaturatedatthepeakresultinginovermodulation.
Fig.27.Theloadsidevoltageandcurrentwaveforms.
Fig.28.ThesourcesidevoltageandcurrentwaveformswithoutSTATCOM.
Table4 isthe comparisonof the keyparametersof power transaction. The real and reactive power demands are setas 250Wand250VAR.Itisevidentfromtablethatalthoughboth theZN-tunedPIcontrollerandthePSO-tunedPIcontrolleroffer
Fig.29.Thesquarewaverepresentationofthesourcevoltageandcurrentused formeasurementofPFaftertheconnectionoftheSTATCOM.
Fig.30.ThesourcevoltageandcurrentwaveformsforanRLloadoperated througharectifierwithtraditionallytunedPIcontroller.
Fig.31.ThesourcevoltageandcurrentwaveformsforanRLloadoperated througharectifierwithPSOtunedPIcontroller.
Fig.32.ComparisonofTHD.
Table4
Experimentalresultscomparison.
Parameter ZN-PI PSO-PI
PDemand 250 250
QDemand 250 250
PfromSources 212.6 252.2
QfromSources −0.412 −0.1258
PtoDSTATCOM −3.74 −0.22
QfromDSTATCOM 254.12 251.3
PFatSource 0.9871 0.9848
THDofsourcecurrent 4.66% 2.89%
practicallyacceptableresults,thePSO-tunedPIcontrolleroffers muchbetterresultsthantheZN-tunedPIone.
10. Conclusion
Inthispaper,particleswarmoptimizationhasbeenproposed foroptimallytuningthecontrollersassociatedwiththeDSTAT- COM.TheperformanceparametersoftheDSTATCOMwithPI controllers tunedby theZiegler-Nichols methodandthepro- posed tuningmethodusing thePSO techniquearecompared.
TheresultsrevealthatPSO-tunedPIcontrollershavesomedefi- niteedgeovertheZiegler-Nicholstuningmethod.Theproposed method has been validated using the MATLAB/SIMULINK environment.Anexperimentalsetupisconstructedinorderto validate the proposed idea and the results are recorded. The experimental resultsconfirm thatthe proposedideaof tuning thePIcontrollerforthedistributedSTATCOMwithKpandKi
valuesas suggestedbythePSO-basedtuning algorithmisfar superiorthantheconventionalZiegler-Nicholstuningmethod.
Conflictofinterest
Theauthorshavenoconflictsofinteresttodeclare.
Acknowledgments
Theauthorsaregratefultothemanagementandtheprinci- palofThiagarajarCollegeofEngineeringfortheircontinuous encouragement and for providing the facilities for doing research. This research was supported by University Grants Commissions, Government of India through Rajiv Gandhi
NationalFellowshipforSCCandidate(RGNF)scheme(RGNF Fileno:RGNF-2015-17-SC-TAM-4006).
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