Availableonlineatwww.sciencedirect.com
ScienceDirect
JournalofElectricalSystemsandInformationTechnology3(2016)14–22
Application
of
flower
pollination
algorithm
for
optimal
placement
and
sizing
of
distributed
generation
in
Distribution
systems
P.
Dinakara
Prasad
Reddy
a,∗,
V.C.
Veera
Reddy
b,
T.
Gowri
Manohar
aaDepartmentofElectrical&ElectronicsEngineering,SriVenkateswaraUniversity,Tirupati,India
bDepartmentofElectricalEngineering,AITS,Tirupati,India
Received12December2014;receivedinrevisedform25July2015;accepted23October2015 Availableonline14April2016
Abstract
Distributed generator(DG)resourcesare small,self containedelectricgeneratingplants thatcanprovidepower to homes, businessesorindustrialfacilitiesindistributionfeeders.ByoptimalplacementofDGwecanreducepowerlossandimprovethe voltageprofile.However,thevaluesofDGsarelargelydependentontheirtypes,sizesandlocationsastheywereinstalledin distributionfeeders.ThemaincontributionofthepaperistofindtheoptimallocationsofDGunitsandsizes.Indexvectormethodis usedforoptimalDGlocations.Inthispapernewoptimizationalgorithmi.e.flowerpollinationalgorithmisproposedtodetermine theoptimalDGsize.ThispaperusesthreedifferenttypesofDGunitsforcompensation.Theproposedmethodshavebeentested on15-bus,34-bus,and69-busradialdistributionsystems.MATLAB,version8.3softwareisusedforsimulation.
©2016ElectronicsResearchInstitute(ERI).ProductionandhostingbyElsevierB.V.ThisisanopenaccessarticleundertheCC BY-NC-NDlicense(http://creativecommons.org/licenses/by-nc-nd/4.0/).
Keywords:Flowerpollinationalgorithm;Indexvectormethod;Distributedgenerationplacement;Radialdistributionsystem
Introduction
Distributionsystemisthatpartofthepowersystemwhichconnectsthehighvoltagetransmissionsystemtolow voltageconsumers.70%ofthetotallossesareoccurringintheprimaryandsecondarydistributionsystem,whilethe remaining30%intransmissionandsubtransmissionlines.Distributionlossesare15.5%ofthegenerationcapacity whereasthetargetlevelis7.5%.Thereforetheprimaryandsecondarydistributionsystemmustbeproperlyplanned toensurelosseswithinthetolerablelimits.
Distributionsystemshavemorelossesandpoorvoltageregulation.Almost13%ofthegeneratedpoweriswasted asI2Rlosses.Lossreductionindistributionsystemsbyapplyingtheoptimizationmethodsisthecurrentpotentialarea ofresearch.Thebasicrequirementsofagooddistributionsystemaregoodvoltageprofile,availabilityofpoweron
∗Correspondingauthor.Tel.:+919395112112.
E-mailaddress:[email protected](P.D.P.Reddy).
PeerreviewundertheresponsibilityofElectronicsResearchInstitute(ERI).
http://dx.doi.org/10.1016/j.jesit.2015.10.002
2314-7172/©2016ElectronicsResearchInstitute(ERI).ProductionandhostingbyElsevierB.V.ThisisanopenaccessarticleundertheCC BY-NC-NDlicense(http://creativecommons.org/licenses/by-nc-nd/4.0/).
demandandreliability.Theefficiencyofthedistributionsystemcanbeimprovedbyadoptingreactivepower compen-sation,networkreconfiguration,distributedgenerationandhybridmethods.Eachmethodhasitsownadvantagesand disadvantages.
Distributed generatorsare commonlyused toprovide the real andreactivepowercompensation indistribution systems. However, DG unit installation indistribution networks requires an appropriate location and size. Thus, optimalplacementplaysanimportantroleinminimizingthelossesthroughproperinstallationandsizingwhichcan beachievedbyusingoptimizationtechniques.
Hungetal.(2014)presentedamethodologyfor theintegrationof dispatchableandnon-dispatchablerenewable distributedgeneration(DG)units forminimizingannual energylosses. Jalalietal.(2014)presentedanew multi-stagemodel,basedonthemixedintegernonlinearprogramming(MINLP)approach,todeterminetheoptimal sub-transmissionsystemexpansionplanning(SSEP).Thismodelconsiderstheplacementofdistributedgeneration(DG) unitsindistributionnetworksovertheplanningperiods.
GopiyaNaiketal.(2013)proposedsensitivitybasedsimultaneousoptimalplacementof capacitorsandDG.In thispaperanalyticalapproachisusedforsizing.InjetiandPremaKumar(2013)developedsimulatingalgorithmfor optimalplacementofDGunits.Kansaletal.(2013)inthispaperusesparticleswarmoptimizationalgorithmisused forDGallocation.Theresultsobtainedarepromisingwhencaperedtoanalyticalmethod.KayalandChanda(2013)
proposedanewconstrainedmulti-objectiveparticleswarmoptimization(PSO)basedwindturbinegenerationunit (WTGU)andphotovoltaic(PV)arrayplacementapproachforpowerlossreductionandvoltagestabilityimprovement ofradialdistributionsystem.
Alonsoetal.(2012)proposedageneralizedoptimizationformulationisintroducedtodeterminetheoptimallocation ofdistributedgeneratorstoofferreactivepowercapability.Junjieetal.(2012)proposedadynamicmodelofdistributed generationinthesmartgrid,basedonenvironmentalcompensationcosts,traditionalDGcapacitycost,DGoperation andmaintenancecosts,purchasedpowercostandnetworklosscost.Amanetal.(2012)proposedagoldensectionsearch (GSS)algorithmfordistributedgenerator(DG)placementandsizingfordistributionsystemsbasedonanovelindex.A novelcombinedgeneticalgorithm(GA)/particleswarmoptimization(PSO)ispresentedinMoradiandAbedini(2012)
foroptimallocationandsizingofDGondistributionsystems.Improvedgroupsearchoptimizer(iGSO)isproposedin thispaper(Kangetal.,2012)byincorporatingparticleswarmoptimization(PSO)intogroupsearchoptimizer(GSO) foroptimalsettingofDGs.
SinghandGoswami(2010)presentednewmethodologybasedonnodalpricingforoptimallyallocatingdistributed generation for profit,loss reduction,andvoltageimprovement including voltagerisephenomenon.A value-based methodis proposedinTenget al.(2007)toenhance thereliability andobtain the benefitsfor DGplacement.An analyticalapproachbasedonexactlossformulahasbeenpresentedinAcharyaetal.(2006)tofindtheoptimalsize andlocationofDGhowevervoltageconstrainthasnotbeenconsidered.
DifferenttypesoftheDG’scanbecharacterizedas
TypeI DGcapableofinjecting real poweronly.Forinstance,photovoltaic,microturbines,fuel cells whichare integratedtothemaingrid withthehelpof converters/invertersare goodexamplesof typeI,if theyare runningatunitypowerfactor.
TypeII DGcapableof injecting reactivepower onlytoimprove thevoltageprofile fallintype-II DG,e.g.kvar compensator,synchronouscompensator,capacitors,etc.
TypeIII DGcapableofinjectingbothrealandreactivepower,e.g.synchronousmachines(cogeneration,gasturbine, etc.).
TypeIV DGcapableofinjectingrealbutconsumingreactivepower,e.g.inductiongeneratorsusedinthewindfarms. Inthispapernewoptimizationalgorithmi.e.flowerpollinationalgorithm(FPA)isusedforsizingofDGs.Inthis papertype-I,type-IIandtype-IIIDG’sareconsideredforoptimalplacement.Optimalplacementproblemhasbeen solvedusingflowerpollinationalgorithm(FPA)approachbytakingtheexactlossformulaasobjectivefunction.As theFPAtechniqueisaheuristicglobaloptimizationmethodwhichisbasedonflowerpollinationprocess.
Thealgorithmisnewandrapidlydevelopedforitseasyimplementationandfewparticlesrequiredtobetunedas comparedtootherheuristicapproaches.Theproposedtechniquehasbeentestedon15bus,34-busand69-bussystems. TheresultsobtainedfromthetechniquehavealsobeencomparedonthebasisofdifferenttypesofDGunits.
OptimallocationofDGbasedonindexvectormethod
Indexvector methodhas beenutilized for optimalallocation of DGinradial distributionsystem(Murthyand Kumar,2013).Indexvectorisformulatedbyrunningthebasecaseloadflowonagivenradialdistributionnetwork, andcalculatingreactivecomponentofcurrentinthebranchesandreactivepowerloadconcentrationateachnode.In thispaper,theindexvectormethodhasbeenusedforoptimallocationproblem.Basedontheelementsoftheindex vector,thismethodidentifiesasequenceofnodestobeconnectedwithDG.
Theindexvectorforbusnisgivenby:(MurthyandKumar,2013) Index(n)= 1 V(n)2 + Iq(k) Ip(k)+ Qeff(n) TotalQ (1)
whereIndex(n)=“Index”fornthbus;V(n)=voltageatnthbus;Iq(k)=imaginarycomponentofcurrentinkthbranch; Ip(k)=realcomponentofcurrentinkthbranch;Qeff(n)=effectiveloadatnthbus;TotalQ=totalreactiveloadofthe givendistributionsystem.
Thus,the potentiallocationsof DGare obtaineddirectly. ArrangetheIndexvectorindescending orderso that highestprioritybuswillcomefirstandthelowestprioritybuswillcomeattheend.Normalizedvoltagemagnitudes arecalculatedforallthebusesbythefollowingformula:V(i)=V(i)/0.95.Buses,whosenormalizedvaluesarelessthan 1.01areconsideredasoptimallocationsforoptimalsizingofDGs.
Theoptimallocationsareatbus6,26andbus61for15,34and69-bussystemsrespectivelysinceatthesebuses normalizedvoltageisbelow1.01.TheflowerpollinationalgorithmhasbeenusedforoptimalsizingofDGsatthese locations.
Flowerpollinationalgorithm
Inthispapernewoptimizationalgorithmbasedonflowerpollinationprocesshasbeenusedforoptimalsizingof DGunits.ThisalgorithmwasproposedbyYangetal.(2014).Theobjectiveoftheflowerpollinationprocessisthe optimalreproductionofplantsintermsofnumbersaswellasfittest.Itiscompletelynewoptimizationbasedonflower pollinationcharacteristics.
Theidealizedcharacteristicsofflowerpollinationalgorithm(FPA)are
1. Bioticandcross-pollinationisconsideredasglobalpollinationprocesswithpollencarryingpollinatorsperforming Levyflights.
2. Abioticandself-pollinationareconsideredaslocalpollination.
3. Flowerconstancycanbeconsideredasthereproductionprobabilityisproportionaltothesimilarityoftwoflowers involved.
4. Localpollinationandglobalpollinationiscontrolledbyaswitchprobabilityp∈ [0,1].
Duetothephysicalproximityandotherfactorssuchaswind,localpollinationcanhaveasignificantfractionpin theoverallpollinationactivities.
Inrealityeachplantcanhavemultipleflowersandeachflowerpatchoftenrelease millionsandevenbillionsof pollengametes.Howeverforsimplicityassumethateachplantonlyhasoneflower,andeachfloweronlyproduceone pollengamete.Thus,thereisnoneedtodistinguishapollengamete,aflower,aplantorsolutiontoaproblem.This simplicitymeansasolutionxiisequivalenttoaflowerand/orapollengamete.
Therearetwostepsi.e.globalpollinationandlocalpollination.Intheglobalpollinationstep,flowerpollensare carriedbypollinatorssuchas insects,andpollenscantraveloveralongdistancebecauseinsectscanoftenflyand moveinamuchlongerrange.Thisensuresthepollinationandreproductionofthefittest,andthuswerepresentthe mostfittestasg*.Thefirstruleplusflowerconstancycanberepresentedmathematicallyas
whereXtiisthepolleniorsolutionvectorXiatiterationt,andg*isthecurrentbestsolutionfoundamongallsolutions
atthecurrentgeneration/iteration.TheparameterListhestrengthofthepollination,whichessentiallyisastepsize. Sinceinsectsmaymoveoveralongdistancewithvariousdistancesteps,wecanusealevyflight.ThatisforL>0 fromaLevydistribution
L≈λΓ(λ)sin(
λ/2)
1
s1+λ (3)
whereΓ(λ)isthestandardgammafunction,andthisdistributionvalidforlargestepss>0.Hereλ=1.5isused. Thelocalpollination,bothrule2andrule3canberepresentedas
Xti+1=Xti+ε(Xtj−Xtk) (4)
whereXtj andXtk are pollen from differentflowersof the sameplantspecies. Thisessentially mimicsthe flower constancyinalimitedneighborhood.Mathematically,ifXtjandXtkcomesfromthesamespeciesorselectedfromthe samepopulation,thisequivalentlybecomesalocalrandomwalkifwedrawεfromauniformdistributionin[0,1]. Thoughflowerpollinationactivitiescanoccuratallscales,bothlocalandglobal,adjacentflowerpatchesorflowers inthenot-so-far-awayneighborhoodaremorelikelytobepollinatedbylocalflowerpollenthanthosefar away.In ordertomimicthis,wecaneffectivelyuseaswitchprobability(rule4)orproximityprobabilityptoswitchbetween commonglobalpollinationtointensivelocalpollination.TheflowchartofthealgorithmisshowninFig.1.Thedetailed algorithmisasfollows.
Step1 Readlineandloaddataofthesystemandsolvethefeederlineflowforthesystemusingloadflowmethod. Inthispaperbranchcurrentloadflowmethodisused.
Step2 FindthebestDGlocationsofthebusesusingtheindexvectorbasedmethod.
Step3 Initializethepopulation/solutionsanditmax,proximityprobabilityp=0.8,λ=1.5.NumberofDGlocations d=1,DGmin=60,DGmax=3000.
Step4 Generatethepopulation/solutionsDGsizesrandomlyusing
Sol(i,:)=DGmin+(DGmax−DGmin)∗rand(1,d) (5)
Step5 Determineactivepowerlossforgeneratedpopulationbyperformingloadflow. Step6 SelecttheDGvaluewhichgiveslowlossascurrentbestsolution.
Step7 Generatenewlocalandglobalpopulation/solutionsbasedonpusingEqs.(2)and(4). Step8 Determinethelossesforupdatedpopulationbyperformingloadflow.
Step9 Replace thecurrentbest solutionwiththeupdated valuesifobtained lossesareless thanthecurrent best solution.Otherwisegobacktostep7.
Step10 Ifmaximumnumberofiterationsisreachedthenprinttheresults. Problemformulation
TheobjectiveoftheoptimalplacementandsizingofDGistominimizetheactivepowerlossinthedistribution networkandtoimprovethevoltageprofile.
Theobjectivefunction:
minf =min(TLP) (6)
whereTLPisthetotalpowerlossoftheradialdistributionsystem. Constraints: Equalityconstraints Powerconstraints PLoss+ PDi= PDGi (7)
Start
Initia liz e a ll va riabl es Pop , p, Itma x, DGmin,Dgma x,
λ
Gene rate random
popula tion usi ng (5)
Is t<Itma x Com pute t he be st solut ion for ini tia l
pop (g*)
St op and print t he
resul ts
If Ra nd<p
Gene rate new globa l
popula tion usi ng (2)
Gene rate new loc a l
popula tion usi ng
(4)
Com pute t he be st
solut ion for ge nerat ed
popula tion
Is new pop
be st
Updat e the pop No Yes No Yes Yes No
Fig.1.Flowchartofflowerpollinationalgorithm.
Inequalityconstraints Voltageconstraints
|Vimin|≤Vi ≤|Vimax| i=1,2,......N (8)
wherePDGiistherealpowergenerationusingDGatbusi,PDiisthepowerdemandatbusi.ViminandVimaxarethe
minimumandmaximumvoltagesoftheithbus,respectively.Inordertominimizethetotalpowerlosssubjectedto theconstraintsgiveninEqs.(7)and(8),flowerpollinationalgorithmisdevelopedandtheresultsareanalyzed. Implementationofalgorithm
ThecompletestructureoftheworktosolvetheoptimalDGplacementandsizingofthethreetestsystemsusing FFAisshowninFig.1.Atfirstthetotalpowerlossiscalculatedfromloadflowmethod.AfterthatplacetheDGand varythesizeinstepsusingFPAalgorithm.FordifferentDGsizescomputethelosses.Theprocedureisrepeateduntil nofurtherminimumlossesfromtheDGplacementareachieved.
Table1
Resultsfor15bussystem. Testsystem Optimal
location
DGtype Optimalsizeofdifferent typesofDG
Activepowerlosses Minimumvoltageinp.u.
kW kVAR kVA Without
DG(kW) WithDG (kW) Without DG(p.u.) WithDG (kW) 15bus 6 I 675 – – 61.7933 45.8035 0.9445 0.9527 II – 682 – 45.3228 0.9544 III – – 681 29.9108 0.9607 Casestudies
Simulationsresultsandanalysis
Inordertoevaluatetheproposedalgorithm,threedifferenttestsystemsaretakenfromDeviandGeethanjali(2014)
andReddyetal.(2014).TheoptimumsizeandplaceofDGsforthetestsystems15,34,and69busesaredetermined byFPA.ThesimulatedresultsaretabulatedandanalyzedusingMATLAB,version8.3.Inthisworktheparameters forFPAhasbeentakenaspop=20,proximityprobabilityp=0.8,λ=1.5,DGmin=60,DGmax=3000.
Testsystem1:15bussystem
For 15 bus system without installation of DG real, reactive power losses are 61.7933kW and 57.2977kVAR respectively. Thistestsystemconsists of15 busesand14 branches.Table1shows thereal powerlossesafterthe placementofdifferenttypesofDGs.FromtableitisinferredthatusingDGtypeIIIthelossesarereducedmorewhen comparedtoothertypeofDGs.ThelossesaftertheplacementofDGtypeI,IIandIIIare45.8035kW,45.3228kW and29.9108kWrespectively.AlsofromFig.2itisinferredthatthevoltageprofileofthesystemisimprovedmore whenDGtypeIIIisused.
Testsystem3:34bussystem
For34bussystemwithoutinstallationofDGreal,reactivepowerlossesare168.3kWand48.0083kVAR respec-tively.Thistestsystemconsistsof34busesand33branches.Table2showstherealpowerlossesaftertheplacementof differenttypesofDGs.FromtableitisinferredthatusingDGtypeIIIthelossesarereducedmorewhencomparedto othertypeofDGs.ThelossesaftertheplacementofDGtypeI,IIandIIIare82.4297kW,132.9023kWand58.8298kW respectively.AlsofromFig.3itisinferredthatthevoltageprofileofthesystemisimprovedmorewhenDGtypeIII isused.
Table2
Resultsfor34bussystem. Testsystem Optimal
location
DGtype Optimalsizeof differenttypesofDG
Activepowerlosses Minimumvoltageinp.u.
kW kVAR kVA Without
DG(kW) WithDG (kW) Without DG(p.u.) Without DG(p.u.) 34bus 26 I 2086 – – 168.3 82.4297 0.9417 0.9802 II – 1250 – 132.9025 0.9619 III – – 1675 58.8298 0.9801
Fig.3.Voltageprofilesof34bussystemusingdifferentDGunits.
Testsystem4:69bussystem
For69bus systemwithoutinstallation ofDGreal,reactivepowerlossesare 225.0446kWand102.2059kVAR respectively.Thistestsystemconsistsof 69busesand68branches.Table3 showsthereal powerlossesafter the placementofdifferenttypesofDGs.FromtableitisinferredthatusingDGtypeIIIthelossesarereducedmorewhen comparedtoothertypeofDGs.ThelossesaftertheplacementofDGtypeI,IIandIIIare83.2279kW,160.0838kW and48.1969kWrespectively.AlsofromFig.4itisinferredthatthevoltageprofileofthesystemisimprovedmore whenDGtypeIIIisused.
Theplotbetweenvoltagesateachbusandbusnumberiscalledthevoltageprofileofthesystem.Tables1–3show theminimumvoltagesforwithandwithoutDGsforallthecasesof 15,34and69-bus testsystems.Inallthetest systemsminimumvoltage(p.u.)ismorewhentypeIIIDGisplaced.Hencevoltageprofileimprovementismorewhen typeIIIDGisplaced,becauseitinjectsbothrealandreactivepower.
Table3
Resultsfor69bussystem. Testsystem Optimal
location
DGtype Optimalsizeof differenttypesofDG
Activepowerlosses Minimumvoltageinp.u.
kW kVAR kVA Without
DG(kW) WithDG (kW) Without DG(p.u.) Without DG(p.u.) 69bus 61 I 1873 – – 225.0446 83.2279 0.9092 0.9682 II – 1384 – 160.838 0.9277 III – – 1640 48.1969 0.9722
70 60 50 40 30 20 10 0 Bus Number 0.92 0.93 0.94 0.95 0.96 0.97 0.98 0.99 1 Voltages in p.u
Voltage profiles of 69 bus system
DG TypeI DG TypeII DG TypeIII
Fig.4.Voltageprofilesof69bussystemusingdifferentDGunits.
Conclusion
InthispapertheoptimumDGlocationandsizeforlossreduction andtoimprovevoltageprofileisdetermined throughtheindexvectormethodandflowerpollinationalgorithm.HereindexvectormethodisusedtofindtheDG locationsinordertominimizethesearchspace.TheoptimumDGsizeisevaluatedbasedontheobjectivefunction whichminimizesthetotalactivepowerlossusingflowerpollinationalgorithm.Flowerpollinationalgorithmisnew optimizationtechniquewhichisusedtofindtheoptimumDGsize.Ithasbetterconvergence characteristicswhen comparedtootheralgorithms.Thesimulationresults indicatedthatthe overallimpactofthe DGunitsonvoltage profileispositiveandproportionatereductioninpowerlossesisachieved.Itcanbeinterferedthatbestresultscanbe achievedwithtypeIIIDG.
Acknowledgments
TheauthorsarethankfultotheauthoritiesofSriVenkateswaraUniversity,Tirupati517502,India,forprovidingall thefacilitiestodoresearchwork.
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