Sensitivity Based Volt/Var Control and Loss Optimization

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Sensitivity Based Volt/Var Control and Loss Optimization
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Katti, Anurag R
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Master's ( M.S.)
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University of Florida
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Electrical and Computer Engineering
Committee Chair:
Khargonekar, Pramod
Committee Members:
Barooah, Prabir
Hammer, Jacob

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Subjects / Keywords:
control -- distributed -- generation -- loss -- optimization -- penetration -- pso -- siting -- sizing -- voltage
Electrical and Computer Engineering -- Dissertations, Academic -- UF
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Electrical and Computer Engineering thesis, M.S.
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Abstract:
The objective of this study is to control voltage at different points in a distribution grid to within a specified range and minimize power loss. Sensitivity coefficients are used to determine the reactive power dispatch of distributed generators connected in the grid. Power loss is also represented in terms of sensitivity coefficients to simultaneously optimize the voltage profile and power loss. Two variants of the optimization algorithm are discussed - a centralized control algorithm based on the complete state of the system and a decentralized algorithm using only the local information. To study the influence of the location of generators in the grid, the properties of sensitivity and its variation for different generator locations are studied. Two different sensitivity coefficients - current and power loss sensitivity with respect to location of generator are developed from the voltage sensitivity values. The use of these sensitivity coefficients in siting and sizing of generators are discussed. And finally the influence of the number of generators and penetration of distributed generation on voltage and distribution loss are discussed through simulations.
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In the series University of Florida Digital Collections.
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by Anurag R Katti.
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Thesis (M.S.)--University of Florida, 2012.
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Adviser: Khargonekar, Pramod.
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SENSITIVITYBASEDVOLT/VARCONTROLANDLOSSOPTIMIZATIONByANURAGR.KATTIATHESISPRESENTEDTOTHEGRADUATESCHOOLOFTHEUNIVERSITYOFFLORIDAINPARTIALFULFILLMENTOFTHEREQUIREMENTSFORTHEDEGREEOFMASTEROFSCIENCEUNIVERSITYOFFLORIDA2012

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c2012ANURAGR.KATTI 2

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Tomyparents 3

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ACKNOWLEDGMENTS Ithankallthepeoplewhohavesupportedmeoverthedurationofthisthesisandbeyond.InparticularIwouldliketothankmyparentsandmyadvisorDr.PramodKhargonekarattheDept.ofElectricalandComputerEngineering.IwouldalsoliketothankDr.WonsukDanielLeeattheDept.ofAgricultureandBiologicalEngineering,UniversityofFloridaforgivingmetheopportunitytoworkoninterestingprojects,myfriendsandcolleaguesinthePrecisionAgricultureLaboratory.Andlastbutnottheleast,IwouldliketothankmyfriendsandpastroommatesDiwakarRaghunathan,KiranTumkur,NikiNachappaandUgandharReddyandallmyfriendsovertheyears. 4

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TABLEOFCONTENTS page ACKNOWLEDGMENTS .................................. 4 LISTOFTABLES ...................................... 6 LISTOFFIGURES ..................................... 7 ABSTRACT ......................................... 8 CHAPTER 1INTRODUCTION ................................... 9 2OVERVIEW ...................................... 12 2.1Motivation .................................... 12 2.2DistributedGeneration ............................. 13 2.3DistributionNetworks ............................. 16 2.4VoltageandReactivePowerControl ..................... 18 3PROBLEMDESCRIPTION ............................. 22 4LITERATUREREVIEW ............................... 25 5VOLTAGE-VARCONTROLANDLOSSMINIMIZATION ............. 32 5.1VoltageSensitivity ............................... 32 5.2CentralizedVoltageControlandLossOptimization ............. 34 5.2.1ObjectiveFunction ........................... 36 5.2.2ConstraintsandOptimizationProblem ................ 39 5.3DecentralizedVoltageControlandLossOptimization ............ 39 5.4OptimizationAlgorithm ............................. 42 5.4.1QuadraticProgramming ........................ 42 5.4.2ParticleSwarmOptimization ...................... 43 5.5ResultsandObservations ........................... 44 6GENERATORSITINGANDSIZING ........................ 49 6.1GeneratorSiting ................................ 49 6.2GeneratorSizing ................................ 53 6.3ImpactofDGPenetrationonLoss ...................... 55 7CONCLUSION .................................... 57 APPENDIX:FEEDERCONFIGURATIONS ....................... 59 REFERENCES ....................................... 61 5

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BIOGRAPHICALSKETCH ................................ 65 6

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LISTOFTABLES Table page 2-1Comparisonofvoltage,currentandlosswithandwithoutDG .......... 19 5-1Comparisonofoptimizationperformanceforcase1 ............... 45 5-2Comparisonofoptimizationperformanceforcase2 ............... 46 5-3Comparisonofoptimizationperformanceforcase3 ............... 47 7

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LISTOFFIGURES Figure page 2-1SchematicofaPowergrid .............................. 16 2-2N+1loadfeederwithadistributedgeneratorconnectedatthelastnode .... 19 2-3Currentdrawnatdifferentvoltagesfordifferentloadtypes ............ 20 5-1Sensitivityof34nodefeederforfourdifferentDGpositions ........... 33 5-2Variationofsensitivity ................................ 35 5-3Noresultconditionofthe13nodefeeder ..................... 47 6-1Sensitivityof34nodefeederforsixdifferentDGpositions ............ 50 6-2Sensitivityforadecreasingvoltageprole ..................... 50 6-3Sensitivityforanincreasingvoltageprole ..................... 51 6-4SensitivityofcurrenttoDGlocation ........................ 52 6-5SensitivityofpowerlosstoDGlocation ...................... 53 6-6VariationoflossesfordifferentpenetrationlevelsandnumberofDGs ..... 55 A-1SchematicofIEEE13nodetestfeeder ...................... 59 A-2SchematicofIEEE34nodetestfeeder ...................... 60 8

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AbstractofThesisPresentedtotheGraduateSchooloftheUniversityofFloridainPartialFulllmentoftheRequirementsfortheDegreeofMasterofScienceSENSITIVITYBASEDVOLT/VARCONTROLANDLOSSOPTIMIZATIONByANURAGR.KATTIMay2012Chair:PramodKhargonekarMajor:ElectricalandComputerEngineeringTheobjectiveofthisstudyistocontrolvoltageatdifferentpointsinadistributiongridtowithinaspeciedrangeandminimizepowerloss.Sensitivitycoefcientsareusedtodeterminethereactivepowerdispatchofdistributedgeneratorsconnectedinthegrid.Powerlossisalsorepresentedintermsofsensitivitycoefcientstosimultaneouslyoptimizethevoltageproleandpowerloss.Twovariantsoftheoptimizationalgorithmarediscussed-acentralizedcontrolalgorithmbasedonthecompletestateofthesystemandadecentralizedalgorithmusingonlythelocalinformation.Tostudytheinuenceofthelocationofgeneratorsinthegrid,thepropertiesofsensitivityanditsvariationfordifferentgeneratorlocationsarestudied.Twodifferentsensitivitycoefcients-currentandpowerlosssensitivitywithrespecttolocationofgeneratoraredevelopedfromthevoltagesensitivityvalues.Theuseofthesesensitivitycoefcientsinsitingandsizingofgeneratorsarediscussed.Andnallytheinuenceofthenumberofgeneratorsandpenetrationofdistributedgenerationonvoltageanddistributionlossarediscussedthroughsimulations. 9

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CHAPTER1INTRODUCTIONDistributionsystemsarethelaststageinthedeliveryofpowertothecustomer.Powerproducedbygeneratorsistransportedthroughthetransmissionnetworkathighvoltagestodistributionnetworksanddeliveredtothecustomerattheutilityvoltagetypicallyaround120V/240Vforresidentialcustomersandpossiblyforothertypesofcustomerswithlargerpowerrequirements.Thetransferofpowerfromthesubstation-thebeginningofthetraditionaldistributionsystemtothecustomercausescurrenttoowdownstreaminthedistributiongrid.Currentsinacircuitcauseavoltagedropbetweennodesandpowerlossintheconductorjoiningthem.Todeliverthemaximumpowertotheenduser,thepowerlostduringthetransferofenergymustbeminimized.Utilitycompaniesmustalsoensurethequalityofpowerattheoutputterminals.Oneaspectofpowerqualitydealswiththevoltagemagnitudevoltageattheoutletsmustnotvarymorethan5%ofthenominalvoltage(120V)accordingtoANSIstandards[ 1 ].Toensurequalityofpowerandprovidethemostefcienttransferofpower,thedistributioncompanyhastoperformvoltagecontrolandlossminimizationrespectively.Inthetraditionaldistributiongrid,controlwasachievedbyadjustingthetapsontheonloadtapchangetransformerandvoltageregulatorsoradjustingthereactivepowercompensationofanycapacitorbanksorothercompensationdevices.Toensurethemosteconomicalcompensation,optimizationwasnecessary.Becauseoftheuseofreactivepower(VAR)sourcesforcompensation,theoperationiscalledVolt/VARcontrol.Theoptimizationfunctioncouldbethecostofcompensation,thenumberoftapchangessincethelifetimeoftapchangetransformersislimited,loss,etc.Inrecenttimeshowever,there'sbeenacalltoupgradethedistributiongridandmakeitmoresmarterandallowittohandlepowerowintheoppositedirectionsaswell,amongalistofotherimprovementsi.e.allowforgeneratorstobeconnectedatthedistributionlevel(calleddistributedgeneratorsorDGs)andnotjustatthehigh 10

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voltage(HV)level.Thisinitiativehascometobeknownassmartgridandafewsuchinstallationsarealreadyindevelopment[ 2 ].Customerswhousegeneratorsforstand-bypowerorcheap,alternativepowerareembracingtheideaofDGs.Thishasencouragedplannerstoenvisionagridthatcanaccommodategeneratorsontheconsumersidefromwhichtheutilitiescanpurchaseexcessenergyduringshortages.Suchimprovementswouldmakeitunnecessarytobuymorepowerorinvestinexpensivegeneratorstosatisfythegrowingdemands.Whiledistributedgenerationhasmanyadvantagestooffer,itseffectonthegridisstillbeingstudied,especiallyathighpenetrations.InthecurrentstateoflowpenetrationofDGsinthegrid,theireffectisnegligible.However,itisexpectedthatthepenetrationofDGswillincreaseinthefuture.Ambitioustargetsof30%renewablepenetrationintheUSgridby2030havebeenmade.AlthoughnotallofitisintheformofDGs,theyareexpectedtoformasignicantlylargeportionofrenewablesources.EuropeancountriesalreadyhaveasignicantpercentageoftheirgenerationproducedbyDGsandrenewableenergy[ 3 ]anditisestimatedtogrowfurtherinthefuture.WiththegrowingpresenceofDGs,studyingitseffectsathighpenetrationsbecomesnecessarybecausegeneratorswillaffectthedirectionofpowerow;theireffectsneedtobeconsideredmorecarefullywhenmultiplegeneratorsareconnectedatmultiplelocations.Integrationofnewsourcesleadstoproblemswithcontrol,protection,islandingandmaintenance,tolistafew.Multiplenewsourcesembeddedintothegridwouldonlycomplicatethematter.ThisstudyexploresoneaspectofintegrationofDGscalledVoltage/VARControlwhichaimstocontrolthevoltageandpowerowinthedistributiongridthroughVARcompensationusingDGs.Anotheraimofthisstudyistominimizelossduringpowerowinthedistributiongrid-calleddistributionlosses.LossprolecanalsobenetfromtheproperplacementofDGsonthegrid;forexample,athumbruleislinecurrentscanbereducedbyplacingpowersourcesclosetoloadcenters.Sincelossisdirectlyproportionaltothesquareofmagnitudeofline 11

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current,reducingthelinecurrentreduceslosses.Similarly,observationscanbemadeonsizingofDGsinagridandtheeffectofhigherpenetrationofDGsonthelossprole.SensitivityisaconceptassociatedwiththepowerowJacobianandiscalculatedbyinvertingtheJacobianmatrix.Sensitivityofanodedenotesthechangeinvoltageatthatnodeforaunitchangeinpoweratsomenodeonthegrid.IfthepowerchangecanbeaffectedbyaDG,sensitivitycanindicatetheamountofpoweroutputnecessarytoeffectarequiredchange.BasedontheconceptofsensitivityVVC,lossminimization,sitingandsizingofDGsandtheeffectofDGpenetrationonlossesarestudied.Thestudyhasbeenorganizedasfollows:chapter 2 discussesthemotivationforthestudyandgivesanoverviewofdistributionnetworks,distributedgeneration,theVoltage-VARcontrolproblemanddistributionlosses.Chapter 3 formulatesthevoltage/VARcontrolproblemmathematically.Chapter 4 listspaststudiesinVoltage-VARcontrol,useofdistributedgeneratorsforvoltagecontrol,distributionlossandoptimizationandacompensationtechniquebasedonsensitivity.Chapter 5 discussesamodiedalgorithmbasedonsensitivitytoincorporatelossoptimizationintheVolt-VARcontrolproblem.Chapter 6 discussessitingandsizingofDGsandtheeffectofincreasingDGpenetrationindistributionnetworks.Chapter 7 concludesthestudywithanoteontheapplicationsofDGs,VVCandlossminimizationusingDGsandfuturework. 12

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CHAPTER2OVERVIEWThepowerindustryisexperimentingwithchangesinthemannerofpowerdeliveryandnewavenuesofpowergenerationandimprovementindeliveryarebeingsought.Thechangesbringwiththemanewsetofchallengesandproblems.Thisstudyaimstotackleasmallsetofthosechallengespertainingtotheinclusionofdistributedgenerationandcommentontheeffectofincreasedpenetrationofthesegeneratorsinthegridandtheireffectonthedistributionsystemlosses. 2.1MotivationThisstudyaimstoaccomplishafourfoldobjective: 1. VoltagecontrolwithreactivepowercompensationusingDGs 2. Distributionlossminimization 3. SitingandsizingofDGs 4. StudytheeffectofincreasingpenetrationofDGsinthedistributiongridVoltagecontrolisanecessaryoperationrequiredtobeperformedbyadistributioncompanytomaintainpowerquality.TraditionallyDGshaven'tbeenincludedinthecontroloperationsbutwiththeincreasingnumberofDGs[ 4 ],[ 5 ],itmaysoonbecomefeasibletousethemforcontroloperations.DGs,especiallytheinverterinterfacedDGshavequickresponseratesandcanrespondquicklytochangingconditions.Lossesareabigconcerninelectricitytransmissionanddistribution.TheU.S.isamongthebiggestconsumersofelectricpowerbutitlosesover260billionkWheveryyear-thehighestintheworld,despitehavinganefcientsystemthatlosesonly6%[ 6 ],[ 7 ].Thelostenergytranslatestoacostofabout$20billion[ 5 ],[ 7 ].China,withcomparablepowerconsumptiontotheU.S.loseslesspowerintransmissionanddistribution.Europeancountrieshaveasimilarlyefcientsystem.Smallerlandareaalsolimitsthelossesinthesenations.ButlargercountrieslikeIndiaandBrazilwithmuchlowerconsumptionsthantheU.S.losenearlyaquarterandasixthofitsenergyrespectivelyintransmissionanddistribution.IndiaisinfactsecondonlytotheU.S.in 13

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theabsoluteamountofpowerlost(nearly220billionkWh).Thereisthusaneedtoimproveefciencyinbothtransmissionanddistributionforeconomicreasons.Increasingdistributionefciencywouldalsoreducetheenergylossinthetransmissionsystemduetothereductioninpowertransmittedoverlonglines.DGswiththeirlocalsitingofferthepossibilityofreducingenergytransmissionoverlongranges.Technologicalimprovementsintheeldofrenewableenergygenerationalsooffersthepossibilitythatfurtherexpansioningenerationdistributedorotherwiseandpowerconsumptioncanbefromcleanenergywithasmallercarbonfootprint.Howeveraframeworkfortheiruseandcontrolneedstobedeveloped.Thisstudyisastepinthatdirectionwithcontrolandcompensationachievedusingsensitivitycoefcients.ChapterdevelopsthemathematicalformulationofthevoltagecontrolproblembutabriefoverviewofthepopularDGtechnologies,distributionsystemsandvoltageandlosscontrolinsections 2.2 2.4 2.2DistributedGenerationDistributedgenerationisablankettermusedtodescribesmallscalepowergeneratorsthatareconnectedatthedistributionleveloronthecustomersideofpowermeter[ 8 ].Whilethere'snoconsensusonthepoweroutputofDGs,moststudiesconsideroutputsrangingfromkilowatts(KW)toafewmegawatts(MW)asdistributedgeneration.DGshavebeenclassiedinsomestudies[ 4 ]intomicro:upto5KW;small:5KW-5MW;medium:5MW-50MW;andlarge:50MW-300MW.Despitethegrowinginterestandthereducingcostsofrenewableelectricitysuchaswindandsolar,fossilfuelbasedgeneratorsarestillthemosteconomicalandreliableformsofgenerationandmicroturbinesareamongthecleanestofcombustionbasedgeneratorsandwhenusedasacogenerationunititcanhaveefcienciesof80%andabove.Microturbinesburnfuelathightemperatureandpressureandtheresultingfumescauserotationofturbinesbladesathighspeeds.Whencoupledwithanalternator,thisproduceselectricity.Microturbinescanbedesignedforawidevarietyof 14

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fuelssuchasfueloil,naturalgas,etc.Microturbinesaresmallinsize,cleanandcanoperateforlongperiodsoftimewithlowmaintenance[ 8 ].Fuelcells[ 8 ]generateelectricitythroughelectronsgeneratedbyanelectrochemicalreaction.Theelectronstravelthroughtheelectricalcircuitconnectedtothecellproducingdirectcurrent.Fuelcellsrequireaconstantsupplyoffuel-forexample,hydrogentooperate.Fuelcellscanhaveanefciencyofover50%evenwithoutCHPandover80%withcogeneration.Unlikefuelbasedgenerators,renewablesharnessthenaturalsourcesofenergywhichalsomakesthemintermittentsources;forexample:solarcellscannotworkefcientlyonacloudyday,awindturbinecannotgenerateelectricitywhenthereisnowindanddroughtswillhaltproductioninahydroelectricpowerstation.Themostpopularformsofrenewableenergyaresolar-thermalpower,solarphoto-voltaiccellsbutthemostpopularisprobablywindenergy.Windenergyhasbeenusedtodoworkforalongtimeandthey'rebeingusedtogenerateelectricityaswell.Windturbinesaredesignedtointerceptthepathofthewindwhichcausesrotationoftheturbineblades.Theyaretypicallyconnectedtoaninductiongeneratortoproduceelectricitybutsynchronousgeneratorsareinuseaswell[ 9 ].Toproduceusableelectricity,steadywindsarenecessary.Wideopenspacesarethereforeidealtosetupwindturbinesandwindfarms;forexample,MidwestUSAiswellsuitedforlargewindfarms.Butsomeofthestrongestwindsareobservedovertheseaanditisestimatedthatwindenergyismoreabundantoff-shorethanon-shore[ 10 ].Despitehavingoneofthelargestinstalledwindcapacitiesintheworld,USAdoesnothavemanyoff-shorefarms.Off-shorefarmsareabundantinmanyEuropeancountrieswherewindpowerisalreadyasignicantportionofthegeneratedpower;example:20%inDenmarkor10%inIrelandandSpain[ 11 ].Solarpowerisutilizedintwoways-directlyconvertingtoelectricitywithaphotovoltaiccellorindirectlywithaconcentratedsolarpowerwherethesunlightis 15

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focusedtoasmallregionusinglensesandmirrorstogeneratesteamtorotateturbines.PhotovoltaiccellsconvertsolarenergytoelectricityusingthephotovoltaiceffectwhereavoltagedifferenceisinducedacrossP-Njunctionbyshiningradiation(solarradiation)ononeofthesurfaces[ 12 ].PhotovoltaiccellsgenerateDCvoltageandadditionalelectronics(calledinverters)areneededtoconvertittoACforinterconnectionwiththegrid.Whilethecostofsolargeneratormodulesisreducing,itisstillmoreexpensivetoproduceaunitofenergyusingsolarthatthemoretraditionalgenerators.WiththeemphasisonrevampingthegridintoasmartgridwhichseekstosupportplugandplayusagecapabilityforDGs,itcanbeassumedthatDGsaregoingtobecomeanintegralpartoftheelectricgridbecauseDGscanbeusedtoexpandthepowercapacityofadistributionsystemwithoutpurchasingadditionalpowerorbuildexpensive,newgeneratorstations.Anotheradvantageofdistributedgenerationisthatthegeneratorsaremuchsmallerthanthecentralizedgenerationresourcesandthereforecheaper.Thereforenewtechnologicalimprovementscaneasilybedeployedintheformofdistributedgenerators.Distributedgeneratorsdonotcurrentlyhaveanactiveroleinprovidingancillaryservicestothegrid;theyareinsteadexpectedtoproducepowerataconstantrateataconstantpowerfactor.Duringlowvoltagesituationstheyarerequiredtoridethroughordisconnectfromthegridinseverecases.Tworeasons[ 13 ],[ 14 ]fortheirpassiveconnectionare1>DGsdonothavesufcientgenerationcapabilitytohaveasignicanteffectand2>acontrolalgorithmoperatinginparallelwiththeutilitycontroloperationsmightaggravatethesituation.Howeverwithmodern,fastacting,electroniccontrolsystemsandcommunicationnetworks,DGscanbeincludedinacoordinatedcontrolplantoprovidevoltageandpowersupport.Thisstudyisanattempttodevisesuchacoordinatedcontroltechnique. 16

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2.3DistributionNetworksDuetoeconomiesofscale,generationofpowerwastraditionallydoneatremotelocationsclosetothefuelsourceandawayfromtheconsumers.Distributionnetworksaredeliverysystemstobringpowerfromthegeneratorsthoughthetransmissiongridtotheconsumer.Thetransmissionsystemwhichbeginsatthegeneratorandendsatthedistributionsubstationisameshednetworkforincreasedreliabilityandpowersharing.Butthedistributionsystem(beginningatthedistributionsubstationandendingatthecustomer'spremises)ismainlyradiali.e.linesstartingfromthesubstationrarelyformloops. Figure2-1. SchematicofaPowergrid.Source:USDepartmentofEnergy[ 15 ] Mostnodesofadistributionsystemarerarelyconnectedtomorethantwoothernodes.Theseriesofbranchesformingachainareknownasfeederlinesandthefeeder(s)connectedtothesubstationbusareknownasthemainfeeder.Theothersareknownaslateralsorsub-feeders.Nodesareanypointsofinterestinthenetwork,generallypointswithaconnectedload,alateral,atransformer,DG,regulator,etc.Anotherdifferencebetweendistributionandtransmissionsystemsisthatseriesresistanceofdistributionlinesasafractionoftheseriesreactance(typicallyreferencedbyR/Xratio)ismuchhigherfordistributionlineswhereasintransmissionlinesthereactanceisdominant.Aconsequenceofthispropertyisrealpowercanalsobedispatchedforvoltageregulationwhereasintransmissionsystems,reactivepowerproducesabiggervoltagechangeforthesameamountofdispatch.Althoughthis 17

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studyislimitedtotheconventionalreactivepower(VAR)support,fromavoltageregulationstand-point,realpowerdispatchcanproduceasimilarresultassumingthelinereactanceandresistancearecomparable.Adistributionsystemmayalsobeunbalancedi.e.allthreephasesofthepowersystemmaynotbeequallyloaded;oneormorephasesmaynotevenbeused.Thisisoneofthereasonsthattraditionalpowerowalgorithmsusedfortransmissionsystemscannotbeusedfordistributionsystems.Duetotheunbalancednature,thehighR/Xratiosandtheradialnatureofthegrid,Newton-Raphsontypemethodsmayfailtoconverge.Thereforeothermethodsbettersuitedforradialdistributionsystemconditionshavebeendeveloped.Theforward-backwardmethodsweepbasedonladdertheory[ 16 ]isusedinthisstudyforallpowerowoperations.ThepowerowalgorithmtreatsthesubstationbusastheslacknodeandtheremainingnodesasPQnodes.IncludingPVnodesinthefeedercomplicatespowerowbecausekeepingaconstantvoltageataparticularnoderequiresaVVCoperation.Therefore,forsimplicityevenDGsareconsideredasPQnodeswithanegativeloadvaluetoindicatethattheyfeedpowerintothenetworkinsteadofconsumingit.Asevidencedbytheradialtopology,thedistributiongridwasnotoriginallydesignedforabidirectionalowofpower.Althoughthecablescanhandlethereverseowofcurrent,protectiondevicessuchasdistancerelaysassumeaunidirectionalowofcurrent.Abidirectionalowwillcauseareductioninlinecurrentswhichcanadverselyaffectthedetectioncapacitiesoftherelay.Itisalsoaconcernforservicepersonneloperatingonafaultyline-inaradialstructureitiseasytode-energizealinebycuttingoffthemainsupplytotheline.ButwithDGsconnected,thelinemaybeislanded-whichimpliesthatthelineiscarryingcurrentfromtheDGsbutnotthemainsupply.Linevoltageregulatorsoperationisalsoaffectedsincetheyestimatevoltageatadownstreamnodebasedonthecurrentthroughitslinecompensationcircuitandasecondarysourcelocateddownstreamdisruptsthisrelation.Thereforeacontrol 18

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procedurethatdoesnotdependheavilyonlinecurrentstoestimatevoltagemustbemadeavailableforusewithDGs. 2.4VoltageandReactivePowerControlTheANSIstandard[ 1 ]requiresthevoltagesduringsteadystateoperationtobeasfollows:onanominalvoltageof120V,theservicevoltageisallowedaleewayofVoltage-VARcontrolorVVCreferstoregulatingthevoltagebyfeedingorconsumingreactivepowerasnecessary.Whilerealandreactivepowersandnodevoltageandphaseareallintricatelylinked,there'sastrongerrelationbetweenreactivepowerandvoltagemagnitude;betweenrealpowerandvoltageangle.Thisphenomenonexistsbecauseofthedecouplingofrealandreactivepowerthatoccursifthelineresistanceismuchsmallerthanthereactanceandvoltagemagnitudeatallnodesismaintainedataround1pu.Lineimpedanceisaxedparameterandhastobechosenduringsystemdesignbutthesecondconditionisvalidwhenthegridisadequatelycontrolledandmaintained.Forthecaseoftransmissionlines,linereactiveimpedanceisindeedmorethanresistance,butfordistributionlinesitisnotnecessarilytrue.Dependingontheratioofreactanceandresistanceofalinebothactiveandreactivepowermayhaveequaleffectonthevoltageofthegridbutbyconvention,reactivepowerischosenforcompensation.Incaseofreactivepower(VAR)compensation,theruleofthumbis:injectingVARintothegridincreasesthevoltagewhileabsorbingitreducesthevoltage.Traditionallyvoltagecontrolhasbeendoneusingswitchingcircuits,transformers,linedropcompensators,stepvoltageregulators,loadshedding,reactivepowercompensationusingcapacitorbanks,etc.Withthegrowingpopularityofdistributedgenerationordispersegenerationotheravenuesofcompensationhaveopenedup.ThisstudyisconcernedwithVVCbutonethatisbasedonsensitivityofvoltagetoreactivepowerinjectionsfromDGs.ThestudyalsoexploresthepossibilityofusingvoltagesensitivityandVVCtoreducedistributionpowerloss. 19

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Reducinglossesinvolvesreducinglinecurrentsallalongthefeeder.Thiscanalsoberestatedasreducingthevoltagedifferencebetweenadjacentnodes.Itiseasytoprovethatdistributingpowersourcesacrossthefeederreducesthelinecurrentandtherebylosses.ForexampleinFigure 2-2 ,asingleDGisconnectedatthelastnodeofanN+1nodefeeder.Assumingallthenodeshaveanequalsizedloadconnectedtoitandtheydrawthesameamountofcurrentirrespectiveofthevoltageatthenode,thecurrentatthesourcebusisNIloadwithouttheDG.IftheDGassumesanequalload,thecurrentdrawnfromeachsourcewouldbeNIload=2.Table1comparesthelowestvoltage,maximumcurrentandlossesforthecasewithandwithoutDG.Withoutanyformofvoltagecontrolorcompensation,voltagemagnitudedecreasessteadilyalongthelengthofthefeederbeginningatthesubstation(node0). Figure2-2. N+1loadfeederwithadistributedgeneratorconnectedatthelastnode WiththeDGhowever,thedecreaseinvoltageislowerbecausethenetcurrentfromasinglesourceissmallerthanthecurrentdrawnfromthesubstationwithoutanyDG.Therefore,thevoltagereducesmovingfromeitherendofthefeedertowardsthecenter.ForsimplicityNistakentobeeven. Table2-1. Comparisonofvoltage,currentandlosswithandwithoutDG WithoutDGWithDG LowestvoltageV0)]TJ /F5 11.955 Tf 11.95 0 Td[(ZlineNIloadV0)]TJ /F5 11.955 Tf 11.96 0 Td[(ZlineNIload=2MaximumcurrentNIload1 2NIloadTotalpowerloss1 6N(N+1)(2N+1)I2loadRline1 12N(N+1)(N+2)I2loadRline 20

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Itcanbeinferredthatincreasingthenumberofpowersourcesreducesthemaximumlinecurrent.Sincelossisproportionatetothesquareofthelinecurrent,reducingthemaximumcurrentmagnitudehasahugeimpactonthetotaldistributionlossinafeeder.Intheexample,reductionisbyalmostafactorof4.IntheexampleofFigure 2-2 thetypeofloadusedisconstantcurrentload-wherethecurrentdrawnisindependentofthevoltage.PowerconsumedbyaloadisgivenbyVI*,thereforeifaconstantcurrentloadisconnectedatahighervoltageitconsumesmorepower.Theothercommonlyusedtypesofloadareconstantpowerandconstantimpedance.Constantpowerloadsdrawthesameamountofpowerirrespectiveofthevoltagebutcurrentdrawnreduceswithincreasingvoltage.Constantimpedanceloadshaveconstantimpedanceregardlessofthevoltagebutpowerincreasesasthesquareofvoltageandcurrentincreaseslinearlywithvoltage. Figure2-3. Currentdrawnatdifferentvoltagesfordifferentloadtypes Ifallloadsonagridwereofthesametype,lossminimizationwouldbeasimpleproblem.Foraconstantpowerloadahighervoltageloadispreferredthereforelettingthenodewiththehighestvoltagetobeat1.05pu.(maximumallowedvoltageaccordingtoANSIstandards)wouldbesufcient.Forconstantimpedancelettingthelowestvoltagebe0.95pu.wouldsolvethecontrolproblem.Forconstantcurrentloadsaslongasthenodalvoltagesarewithinallowablelimits,nocontrolisnecessary.Fora 21

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homogeneousloadtypecontrolissimpleirrespectiveoftheloadsizesbutactualloadsarenothomogeneousandoptimizationisrequiredtodeterminethebestcongurationanddispatch.Chapter 3 listssomeofthetechniquesusedinpreviousstudies. 22

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CHAPTER3PROBLEMDESCRIPTIONAnelectricalsystemisgovernedbypowerowequationswhicharearesultofKirchhoff'scurrentlawandOhm'slaw.Theseequationsdenetherelationshipbetweenthevoltageateachnodeinthegridandtheloadsorgeneratorsconnectedtothem.Knowingthevoltageateachnode,itispossibletoknowthecurrentinallthelines;theexactpowerconsumedorinjectedateachnodeandothermetricssuchasstabilityofthegridetc.Thevoltagesatallnodes(denedbyavoltagephasormagnitudeandangle)areknownasthestateofthesystem.ThesetpowerowequationscanberepresentedasF(x,u)=0wherexisthestatevectoranduisthevectorofallcontrolvariablessuchastappositionorvoltageregulator,onloadtapchangingtransformer,generatorpoweroutput,etc.andtheloadsatdifferentnodes.FistherelationbetweenxandudenedbyKirchhoff'scurrentlawandOhm'slaw.Foreaseofcalculationallvariablesarerepresentedintheperunitsystem.VoltagecontrolaccordingtoANSIstandardsrequiresthattheutilityvoltagenotvarymorethan5%fromthenominalvoltageof1pu.Ifxcanbeseparatedasx=264jVj375wherejVjisthevectorofnodevoltagemagnitudesandisthebusangle,thenvoltagecontrolimplies0.95jVij1.05forallnodesi=1,2,...NifVigoesoutofbounds,ucontrolcanbeadjustedsothatViiswithinlimitsagain.Inu=264ucontroluload375 23

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ucontrolisavectorofallcontrolvariablesanduloadisthevectorofloadvalues.Thevectorofcontrolsignals,ucontrol,canbechosenindifferentwaystoachievetherequiredresult.Henceanobjectivefunctionisnecessarytochoosebestvectorbasedonsomecriteria.Iftapchangingtransformersareused,thenumberoftapchangesisoftenacriterion.Ifcompensationmethodsarebeingusedanditcoststheutilitydifferentratesfordifferenttypesofcompensationthenthemosteconomicaldispatchissought.Linelossesarealsooftenconsideredforoptimizationsincelossescanbecontrolledbyvaryingthevoltageatthedifferentnodes.Thepowerlostasheatonasinglelinebetweennodesi,j,isgivenasPilossj=Ii2jRij=(Vi)]TJ /F5 11.955 Tf 11.95 0 Td[(Vj)2=RijwhereV=jVjejandRijistheresistanceofthelinebetweennodesiandj.Powersystemshowever,arenotsinglelinesbuthavethreephases,whichincaseofadistributionnetworkmaybeunbalanced.Thereforethetotallossiscalculatedasaproductofvectorsandmatricesas:Pilossj=RealfVIg=Real(Vi)]TJ /F5 11.955 Tf 11.96 0 Td[(Vj)Zij)]TJ /F9 7.97 Tf 6.59 0 Td[(1(Vi)]TJ /F5 11.955 Tf 11.96 0 Td[(Vj)Ifthesystemisthreephase,Viisa31complexvectorofvoltagesofthethreephasesofeachnodeandZijisa33complexmatrix.Thetotalsystemlossisobtainedbyaddingthelossoverallthelines Plosstotal=Xi,jReal(Vi)]TJ /F5 11.955 Tf 11.95 0 Td[(Vj)Zij)]TJ /F9 7.97 Tf 6.58 0 Td[(1(Vi)]TJ /F5 11.955 Tf 11.95 0 Td[(Vj)(3)Fortwonodesi,jnotconnectedtoeachother,Zi)]TJ /F9 7.97 Tf 6.59 0 Td[(1jisazeromatrixanddoesn'tcontributetotheloss.ThereforethegeneralVVCwithlossoptimizationproblemcanbewrittenas 24

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MinimizePlosstotal=Xi,jReal(Vi)]TJ /F5 11.955 Tf 11.95 0 Td[(Vj)Zi)]TJ /F9 7.97 Tf 6.58 0 Td[(1jVi)]TJ /F5 11.955 Tf 11.95 0 Td[(Vj (3)SuchthatF(x,u)=00.95pujVij1.05puanduminiuiumaxi8i=1,2,...Mwhereuiarethecontrolvariables.InthisstudythecontrolvariablesusedarethereactivepowerproducedbyDGsconnectedatdifferentnodesinthedistributiongrid.Adjustingthepowerproductionmaynotalwaysbesufcientcontrolmechanismandvoltageregulatorsmayneedtobeadjustedaswell.Thetapchangingoperationisnotincludedintheoptimizationbutperformedifoptimizationfailstoproduceafeasibleresult.Theoptimizationandresultsarediscussedindepthinchapter5.Chapter 4 discussesthepaststudiesdoneintheeldofvoltageVARcontrol,sitingandsizingofreactivepowersourcesanduseofvoltagesensitivityforcontrol.InadditiontoVARoptimization,placementofDGsonthefeedercanalsobeusedtoadjustlosses-somepositionsarebettersuitedforlossreductionthanothers.SimilarlythecapacityoftheDGscanalsobeoptimizedforabetterperformance.TheoptimalsitingandsizingofDGsisdiscussedinchapter 6 .AlsodiscussedinthechapteristheeffectofincreasingpenetrationofDGsondistributionlosses. 25

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CHAPTER4LITERATUREREVIEWVoltageandreactivepowercontrol(Volt/VARcontrolorVVC)isanimportanttaskthathasbeenstudiedmanytimesforboththetransmissiongridanddistributiongrid.Whilenewinnovativetechniquesarebeingsoughtforvoltagecontrol,themostcommonlyusedmethodsarestillthetimetestedonessuchasfeederreconguration[ 17 ],[ 18 ]tominimizelinecurrents.Theradialstructureofthedistributionsystemalsosupportsregulationthroughstepvoltageregulatorwithlinedropcompensator[ 16 ].InjectingreactivepowerusingcompensationdevicessuchasstaticVARcompensators(SVCs),staticsynchronouscompensators(STATCOMs)andotherexiblealternatingcurrenttransmissionsystem(FACTS)devicescanbeusedtoboostvoltageaswellascontrolthephaseangle[ 19 ].Thesimplestandmostcommonlyusedformofcompensationthoughiscapacitorbankswhichmaybelocatedatthesubstationoralongthefeederline.Traditionalcontroltechniqueshavedealtwithoptimizingthepositionsofthetapsinthetransformersorcontrollingtheoutputofthecompensationdevices[ 20 ]orbothwhileoptimizingforeconomicorothersystemconstraints.Duetothenon-linearityofthecontrolproblem,evolutionaryalgorithmssuchasparticleswarmoptimization[ 21 ],[ 22 ]orgeneticalgorithm[ 23 ],[ 24 ]havebeenextensivelyusedforoptimization.RecenttechnologicalimprovementshavemadeDGspopularasaparallelsourceofpowerforimportantorsensitiveloads.Theircapacitytoinjectexcesspowerintothegridhasmadethemaviableoptionforcompensation.AlthoughDGsarebeingconnectedtothegrid,theirinvolvementinprovidingancillaryservicesisnegligible.ThereisstillconcernregardingintegrationandcontrolofnewgeneratorsinthedistributiongridalthoughextensiveliteratureisavailableonvariousaspectsofDGintegrationandutilizationfromthevarioustechnologiesitentails[ 4 ],[ 5 ],[ 8 ],[ 25 ],theirimpact-botheconomic[ 26 ]andonthevoltageprole[ 27 ],[ 28 ];andincentivestopromotetheiruse 26

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[ 29 ];totheconcernsandchallengesofusingDGs[ 25 ],[ 30 ].AlotofresearchworkhasalsobeendoneoncontrolinvolvingDGs[ 13 ],[ 27 ],[ 31 ],[ 32 ]andmoreimportantlysizingandsitingtheDGsonthegrid[ 28 ],[ 33 ],[ 34 ].Withthecurrentfocusonupgradingtheelectricgridtoasmartgridwithsupportfordecentralizedcontrol,differentmethodsofdecentralizedcontrolarebeingresearched.Multiagentsystems(MAS)[ 35 ],[ 36 ]areamongtheideasbeingexplored.ThealgorithmdevelopedbyBaranandMarkabi[ 37 ]todeterminetheoptimumreactivepowerdispatchofDGsusinglinearprogramming,isanexample.Asimilaralgorithmthatdispatchesbothrealandreactiveisdiscussedin[ 38 ].SensitivityofdifferenttypeshavealsobeenusedtodeterminethelocationofDGsonthegrid[ 39 ],[ 40 ]aswell.ButGozelandHocaoglu[ 41 ]withanintentiontoavoidJacobianandadmittancematrix,developedananalyticalmethodtolocateandsizeDGsonaradialsystemusingalosssensitivityfactorbasedonthecurrentinjectionmatrix.Thegoalwastodeterminetheamountofinjectionrequiredtoreducethelossestoaminimum.Butwithalossfunctionthatcanbederivedfrommeasuredvoltagesensitivities,itmaybeeasiertocalculatethelosssensitivitycoefcients. VoltageandReactivePowercontrolusingSensitivity.ThealgorithmdevelopedbyMarkabiandBaran[ 37 ]implementedasimplemulti-agentdistributedVVCalgorithmbasedonsensitivitycoefcients.TheyusedsensitivitycoefcientsderivedfromthepowerowJacobiantodeterminedispatchusinglinearprogramming.However,tomakethealgorithmdecentralizedandindependentofthegridarchitecture,sensitivitycoefcientsofnodeswithoutaDGwereeliminatedthroughKronreduction.ButthenewcoefcientsarenotmeasurablequantitiessincetheyhavebeenadjustedbyKronreductionandmadesystemdependent.Nevertheless,theconceptofusingsensitivitytodeterminedispatchisausefulresult.Dispatchiscanstillbecalculatedusingthemeasuredsensitivityvalueswhicharethetrueinstantaneoussensitivityvalues. 27

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AsinglefeederlinewithmultipleDGsconnectedalongthelengthofitwiththeDGscarryingmostoftheloadwasconsideredinthestudy.EachDGisassumedtobeanagentwithintelligence.Theremainingnodesarepassivewithnointelligence.Alltheagentscancommunicateamongthemselvestoshareanynecessaryinformation.Eachagentperformsthreeimportanttasksmonitoring,moderatinganddispatch.Monitoringreferstocheckingthenodevoltageandverifyingthatitisalwayswithinthespeciedrange(within5%ofthenominal).Whenthevoltageisnolongerwithinlimits,theagentcorrespondingtothe(most)affectednodeactsasthemoderator.TheynotethatthevoltagesofthedownstreamnodesareusuallythemostseverelyaffectedanditmightbenecessarytohaveadummyDGwithnooutputconnectedatthesenodestomonitorthevoltageatthethesepoints.ItessentiallytranslatestohavingameasuringdevicelikeaPMUconnectedattheendnodeandextendingthecommunicationnetworkstilltheendofthefeeder.IfthatmaynotbepossiblethensomemethodofestimatingthevoltageattheendisnecessaryforexamplebyassumingaconstantvoltagedifferencebetweentheendofthefeederanditsnearestDGunit.Whenanodalvoltageviolatestheoperatinglimits,theclosestDGsensesitandcommunicateswiththeotherDGsandrequestsforreactivesupportandreceivestheirbids.ThebidsarethemaximumsupporteachDGcanlendandthesensitivitycoefcientfortheparticularnode.ThemoderatorthendecidestheoptimaldispatchschemeforDGs.TheDGsonreceivingthedispatchchangetheoutputpowertosuitrequirements.Thisisthedispatchmode.Ingeneral,feedingreactivepowerintothegridincreasesthevoltagewhileconsumingitreducesthevoltagemagnitude.Thisbehavioriscapturedbythesensitivitycoefcientsandsimplelinearprogrammingcancalculatethedispatchscheme.TheproblemisformulatedasMinimizeXiQi (4) 28

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SuchthatVk=Vmin)]TJ /F5 11.955 Tf 11.95 0 Td[(V0kandQminiQ0i+QiQmaxiwhereQiisthechangeinreactivepoweroutputofithDG,V0kisthecurrentvoltageatnodekandQ0iisthecurrentreactivepoweroutputofithDG.TheDGcausingthehighestsensitivitytotheaffectednodeischosenanditsupportsthenodetowhateverextentitcan.IfthereactivepowersupportofthatDGdoesnotsufce,theDGwiththenexthighestsensitivityhelpsandsoonuntilthevoltageexcessordeciencyhasbeencompensatedandallthevoltagesarewithinthespeciedlimits.IftherearennodesinthedistributionsystemandV1,V2...Vnarethenodevoltagemagnitudes(assumingabalancedfeeder,butthetheorycaneasilybeexpandedtounbalancedsystems)andtherearem(mn)DGswithreactivepowerQ1,Q2...Qm,thevoltagesensitivityisdenedas ij=@Vi @Qj8i=1,2,...nand8j=1,2...m(4)ThepartialderivativesformtheJacobianmatrixusedinNewton-RaphsonpowerowanditdenestherelationbetweenVARsupportoftheDGsandvoltageatthenodes.TheeffectofthemDGsonitsnodevoltagecanbemoreaccuratelyexpressedbyconsideringthatthenetreactivepowerinjectionatmostnodesiszero.HencenvoltageequationscanbereducedtoonlymequationsbyKronreduction.Thecoefcientsofthevariablesobtainedthusaretherequiredsensitivities.ItiseasytodeterminetheVARsupportfromequations( 4 )and( 4 ).IfHistheJacobianmatrix,Pisthevectorofrealpowerinjectionsareeachnode,Qisthereactivepowerinjected,xisthevectorofvoltagemagnitudesandisthevectorofnodevoltageangles,thenf=264PQ375andx=264V375 29

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f=Hx H=264HPHPVHQHQV375(4)HQVisthepartialofreactivepowerwithrespecttovoltagemagnitude.Reactivesupportcanbeobtainedusingrealandreactivepowerdecoupling,whichisbasedonthefactthatthevoltagemagnitudeatanodeaffectsthereactivepowerinjectedatthatnoderatherthantherealpowerwhichisaffectedbythevoltageangle.Hence Q=V=HQVV(4)Qisdividedbythenodevoltage,V,tolinearizethepowerowequations.SinceQiszerofortheloadnodes,therowsandcolumnsofHQVcanberearrangedtoHQV=264B11B12B21B22375whereB11=partialderivativeofreactivepowerinjectionattheloadnodeswithrespecttovoltagesattheDGnodesB12=partialderivativeofreactivepowerinjectionattheloadnodeswithrespecttovoltagesattheDGnodesB21=partialderivativeofreactivepowerinjectionattheDGnodeswithrespecttovoltagesattheloadnodesB22=partialderivativeofreactivepowerinjectionattheDGnodeswithrespecttovoltagesatthesenodes. 2640Q=V375=264B11B12B21B22375264VLVDG375(4)VListhevectorofvoltagesattheloadnodes. 30

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Therefore,VDG=(B22)]TJ /F5 11.955 Tf 11.95 0 Td[(B21B1)]TJ /F9 7.97 Tf 6.59 0 Td[(11B12))]TJ /F9 7.97 Tf 6.58 0 Td[(1QDG=Vor (4)VDG=QDG (4)isthesensitivitymatrix.TheelementsofdeterminethereactivesupportthateachDGprovides.Thereforeequation( 4 )changestoMinimizeXiQi (4)SuchthatVk=mXi=1kiQi=Vmin)]TJ /F5 11.955 Tf 11.96 0 Td[(V0k0Q0i+QiQmaxiEquation( 4 )indicatesthatthebestsolutiontothisproblemistohavemaximumdispatchfortheDGwiththehighestsensitivityuntilgeneratorcapacityisreached.Ifthatisnotsufcient,DGwiththenextlargestsensitivityadjustsitsoutputandsoforthuntilthevoltagedrophasbeencompensated.Adrawbackofthisalgorithmisthatitadjuststhevoltagetobringitwithinacceptableoperatingrangebutonlybarely.Soifvoltageexceeds1.05puitisloweredto1.05pu,ifitfallsbelow0.95puitisraisedto0.95pu.Thismaynotbethebestvoltageproleforadistributionfeedersincetheloadisalwayschanging;evensmallvariationsinloadorDGoutputcancausethevoltagestogooutofrangeagain.Tomaintainitatavoltageslightlyhigherthanacceptablelevelmightseemlikeagoodoptionbutthatonlyinvitesthequestion,'howhigh?'.Theanswerliesnotinraisingorloweringthevoltagetoaxedlevel,buttooptimizethevoltageforotherparameters.Lossistheobjectivechoseninthisstudybecauseitnotonlyreducesthewastageofenergylinesbutalsofreesupthelinecapacityformoreusefulpowerow.Anewsetofconstraintsandoptimizationfunctioncanthereforebedevisedtoaccountforthese.Afewmodicationstothealgorithmaresuggestedwhichemployaquadraticoptimizationfunctionratherthanalinearone.Thisisdiscussedinchapter 31

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5 .Chapter 5 alsodiscussesvoltagesensitivityanditsbehaviortochangesinloadandpowergeneration. 32

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CHAPTER5VOLTAGE-VARCONTROLANDLOSSMINIMIZATIONTheobjectiveofvoltage-VARcontrolcanbeexpandedfromjustmaintainingthevoltageattheendofeachfeedernodewithinthespeciedvoltagerangetoalsoprotectthevoltageagainstvariationsinthesystemconditionssuchasloading,faults,lossofpower,etc.Withaccesstopowergenerationsourcesatdifferentlocationsinthegriditbecomespossibletonotonlymaintainvoltageswithinoperableregionsbutmanipulatethepowerowsothatotherobjectivescanbeachieved.Themostimportantadvantageofusingvoltagesensitivityforthispurposeisitallowsfortheestimationofthenewstate-andsubsequentlyotherparametersthatareafunctionofnodalvoltage-withoutperformingloadowanalysis.Acomplexsetofnonlinearequationscanbeapproximatedtoalinearcombinationofsensitivitycoefcients,savingpreciouscomputationresourceandtime. 5.1VoltageSensitivitySensitivityhasbeendenedinchapter 4 (equation( 4 ))astheinverseofthepowerowJacobian.Voltagesensitivitywithrespecttochangeinreactivepowerinjectionatanode(herebyreferredtoasvoltagesensitivityorjustsensitivity;thisstudydealsexclusivelywithreactivepowerandvoltagechangeunlessotherwisespecied)isannnblockinthe2n2nJacobianmatrix.SensitivityisaneasywayofestimatingthenewstateofthegridwhentheDGoutputsarechangedsinceitistheobserved,steadystatevoltagechangeforaunitchangeinpowerproduction.Figure 5-1 showsthesensitivityofphaseAforallnodesofa34nodefeederfor1KVARchangeinoutputpowerofaDGwhenconnectedatfourdifferentlocations.Themissingsensitivityvaluesareaconsequenceofanunbalancedfeeder-notallnodesutilizeallthreephases.Usingsensitivity,forsomechangeinpowerproduction,thevoltagechangeinthefeedernodescanbeestimatedbyscalingthesensitivityatthesenodestheappropriateamount.Therelationisdescribedbyequation( 4 ).However,theexpressionfor, 33

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thesensitivityismodiedfromequation( 4 );insteadofusingsensitivityofonlysmallsubsetofnodesfromareducedsetofpowerowequations,thesensitivityofallnodesrepresentedbythecolumnsofHQ)]TJ /F9 7.97 Tf 6.58 0 Td[(1Vareused.Equation( 4 )exploitsthefactthatpowerinjectionatnon-DGnodesiszero.HencethesensitivitycalculatedfromonlyDGconnectednodesdoesnotrepresentthethemeasurablechangeinvoltageattheparticularnodes;itisacalculatedquantity,althoughitmaystillbenumericallysimilartothemeasurablesensitivity.Sincethemagnitudeofvoltagechangeisquitesmall(oftheorderof10)]TJ /F6 11.955 Tf 7.09 -4.34 Td[(4p.u.=KVARchangeinpowerinjection),themismatchbetweenthecalculatedandtheobservedvaluemaygounnoticed.Patternsandtrends[ 42 ]similartothoseofthecalculatedsensitivityofequation( 4 )arealsoobservablefortheactualmeasuredsensitivitycoefcients. Figure5-1. Sensitivityof34nodefeederforfourdifferentDGpositions Foraperfectlydecoupledsystem,thesensitivityparametersareaconstantwithHQVgivenbytheadmittancematrix.Butevenforalosslesslineitisnotpossibletohaveaperfectlydecoupledsystemandthesensitivityvarieswithvoltage.Overlargevoltagerangessensitivityisnon-linearbutoversmallerranges-suchasinLVorMVcompensationschemesitcanbeapproximatedtoalineartrend(gure 5-2 ).Mathematicallythisobservationcanbemadebynotapproximatingthenodalvoltageto 34

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1pu.Thisisalsotheexpressionusedinthisstudy.ButthemostaccuratevaluecanbeobtainedbyinvertingtheJacobianH=264HPHPVHQHQV375withnoassumptionsorapproximations.Thecolumnsrepresentthesensitivitycoefcientsforallthenodes-exceptthesubstationbus-forallpossibleDGlocations.Thesensitivityofthesubstationbusis0duetothecontrolactionofthesubstationcontrolsystem.IntheJacobianofdimension2n2n(whennumberofnodesinthefeederisn+1;sensitivityofthesubstationbusiszero)andthevoltagesensitivitytoreactivepowerisannblockinthebiggermatrix.Figure 5-2 istheplotofsensitivityofaparticularnodewithDGxedatadifferentnodeandthereactivepoweroutputoftheDGisvariedfromfrom-100KVARto+100KVARinstepsof1KVAR.PlotAistheresultofrepeatingtheprocessfordifferentvaluesofrealpoweroutput.WhileplotAisforallthreephases,plotBdisplaysthesensitivityforasinglephase(phaseA)withrespecttothenodevoltageinsteadofthereactivepoweroutput.Figure 5-2 istypicalofmostnodes.Itisobservedthatwhilesensitivityisnotaconstant,itcanbeapproximatedasalinearfunctionformostcases.Thecentralizedvoltagecontroloptimizationfunctionisderivedassumingaconstantsensitivityandtheconsequencesofassuminglinearlyvaryingsensitivityareexplained. 5.2CentralizedVoltageControlandLossOptimizationIfthesensitivityisfairlyconstant,asinglecoefcientcanbeselectedforeachnodeandphaseforcontrol.Butduetothevaryingvoltageandloadingandinjectionconditions,sensitivityalsovaries.Hencetherearefewerapproximations.Thecentralizedcontrolapproachusesallthevoltageandapproximatesensitivityvaluesforvoltageandlossestimation.Thedecentralizedalgorithmwhichisgiventoacoordinated 35

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AVariationwithchangeinreactivedispatch BVariationwithnodevoltageFigure5-2. Variationofsensitivity controlstructurebasedonlocalinformationisdiscussedinsection 5.3 butbothofthemoptimizethesamequantity-loss.Thedecentralizedversionisanextensionofthecentralizedversion. 36

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5.2.1ObjectiveFunctionTheexpressionfordistributionlossonasinglebranchwasderivedinequation( 3 )asMinimizePlosstotal=Xi,jReal(Vi)]TJ /F5 11.955 Tf 11.95 0 Td[(Vj)Zi)]TJ /F9 7.97 Tf 6.58 0 Td[(1j(Vi)]TJ /F5 11.955 Tf 11.95 0 Td[(Vj)SuchthatF(x,u)=00.95pujVij1.05puanduminiuiumaxi8i=1,2,...MwhereZijistheimpedancebetweentwonodesiandj.Consideringthetotallossandnotonlytherealpowerloss,lossij=(V2)]TJ /F5 11.955 Tf 11.95 0 Td[(V1)Z)]TJ /F9 7.97 Tf 10.82 0 Td[(112(V2)]TJ /F5 11.955 Tf 11.96 0 Td[(V1)IfthevoltagesafteroptimizationareV01andV02thenlossij=(V02)]TJ /F5 11.955 Tf 11.95 0 Td[(V01)Z)]TJ /F9 7.97 Tf 10.82 0 Td[(112(V02)]TJ /F5 11.955 Tf 11.96 0 Td[(V01)butV0=V+VandVcanbeestimatedusingvoltagesensitivityaslossi0j=(V2+V2)]TJ /F5 11.955 Tf 11.96 0 Td[(V1)]TJ /F6 11.955 Tf 11.95 0 Td[(V1)Z)]TJ /F9 7.97 Tf 10.82 0 Td[(112(V2+V2)]TJ /F5 11.955 Tf 11.96 0 Td[(V1)]TJ /F6 11.955 Tf 11.95 0 Td[(V1)Simplifying,lossi0j=(V2)]TJ /F5 11.955 Tf 11.95 0 Td[(V1)Z)]TJ /F9 7.97 Tf 10.82 0 Td[(112(V2)]TJ /F5 11.955 Tf 11.96 0 Td[(V1)+(V2)]TJ /F6 11.955 Tf 11.96 0 Td[(V1)Z)]TJ /F9 7.97 Tf 10.82 0 Td[(112(V2)]TJ /F6 11.955 Tf 11.95 0 Td[(V1)+(V2)]TJ /F5 11.955 Tf 11.95 0 Td[(V1)Z)]TJ /F9 7.97 Tf 10.82 0 Td[(112(V2)]TJ /F6 11.955 Tf 11.96 0 Td[(V1)+(V2)]TJ /F6 11.955 Tf 11.96 0 Td[(V1)Z)]TJ /F9 7.97 Tf 10.82 0 Td[(112(V2)]TJ /F5 11.955 Tf 11.95 0 Td[(V1)Thersttermontherightoftheequationislossijhencelossi0j)]TJ /F5 11.955 Tf 11.96 0 Td[(lossij=(V2)]TJ /F6 11.955 Tf 11.95 0 Td[(V1)Z)]TJ /F9 7.97 Tf 10.82 0 Td[(112(V2)]TJ /F6 11.955 Tf 11.95 0 Td[(V1)+(V2)]TJ /F5 11.955 Tf 11.95 0 Td[(V1)Z)]TJ /F9 7.97 Tf 10.82 0 Td[(112(V2)]TJ /F6 11.955 Tf 11.96 0 Td[(V1)+(V2)]TJ /F6 11.955 Tf 11.96 0 Td[(V1)Z)]TJ /F9 7.97 Tf 10.82 0 Td[(112(V2)]TJ /F5 11.955 Tf 11.95 0 Td[(V1) (5) 37

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Sincelossijdenotestheinitial(orcurrent)stateoflossintheline,itisaconstantwithrespecttooptimizationandcanbeneglected.Thiscorrespondstooptimizingforchangeintotallossratherthanthetotallossitself.Thusthenewvalueoffisf0f0=Xi,j(Vi)]TJ /F5 11.955 Tf 11.96 0 Td[(Vj)Zi)]TJ /F9 7.97 Tf 10.82 0 Td[(1j(Vi)]TJ /F6 11.955 Tf 11.96 0 Td[(Vj)+(Vi)]TJ /F6 11.955 Tf 11.95 0 Td[(Vj)Zi)]TJ /F9 7.97 Tf 10.82 0 Td[(1j(Vi)]TJ /F5 11.955 Tf 11.95 0 Td[(Vj)+Xi,j(Vi)]TJ /F6 11.955 Tf 11.96 0 Td[(Vj)Zi)]TJ /F9 7.97 Tf 10.82 0 Td[(1j(Vi)]TJ /F6 11.955 Tf 11.96 0 Td[(Vj) (5)ThechangeinvoltageatkthnodeVk,canberepresentedasVk=XiikQiDGOr,invectorform:Vk=QTDG (5)Substitutinginequation( 5 )andsimplifying,f0=Xi,j(Vi)]TJ /F5 11.955 Tf 11.96 0 Td[(Vj)Zi)]TJ /F9 7.97 Tf 10.82 0 Td[(1j(ijQDG)+(QTDGij)Zi)]TJ /F9 7.97 Tf 10.82 0 Td[(1j(Vi)]TJ /F5 11.955 Tf 11.95 0 Td[(Vj)+Xi,j(QTDGij)Zi)]TJ /F9 7.97 Tf 10.82 0 Td[(1j(ijQDG)whereij=i)]TJ /F8 11.955 Tf 12.06 0 Td[(jisa3mmatrixcontainingthesensitivitycoefcientsofeachofthethreephasesofaparticularnodewithrespecttoalltheconnectedDGs.Therefore,f0=Xi,j((Vi)]TJ /F5 11.955 Tf 11.96 0 Td[(Vj)Z)]TJ /F9 7.97 Tf 10.82 0 Td[(1ij)QDG+QDG(ijZ)]TJ /F9 7.97 Tf 10.82 0 Td[(1(Vi)]TJ /F5 11.955 Tf 11.95 0 Td[(Vj))+Xi,jQDG(ijZ)]TJ /F9 7.97 Tf 10.82 0 Td[(1ij)QDGThiscanbefurthersimpliedtoaquadraticequationinvectorformasf0=AQDG+QTDGB+QTDGCQDG 38

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Consideringonlytherealpowerloss,thenalobjectivefunctionis f0=PQDG+QTDGQQDG(5)whereP=RealfA+BgandQ=RealfCgAsecondvoltageregulatorcontrollevelexistsabovethisDGdispatchcontroltoutilizethecontroloptionsalreadyincorporatedinthefeeder.DuetotheexistenceofDGs,tappositionscannotbeaccuratelyselectedbythelinecompensatorcircuitanddownstreamvoltagehastobecommunicatedtotheregulatorcontrollerorthetapcanbeshiftedbyonepositionatatime.Foreachchangeintapsettings,theoptimizationalgorithmfortheDGsisexecuted.Thecombinationofboththeseoperationsdeterminestheidealsettings.UnlikethecompensationalgorithmofMarkabiandBaran,thismethodoflosscontrolisnotgiventodispersivecontrol;thisisacentralizedpowerowandlosscontrolalgorithmbecausetodeveloptheobjectivefunctionallthenodevoltagesarenecessary.Anagentbaseddecentralizedvariantofthisalgorithmcanalsobedevised;discussedinsection 5.3 .Howeverwiththeincreasingincorporationofcommunicationchannelsbetweentheagentsofapowergrid,itbecomespossibletolocatethecontrolcenteratanylocation,includinganodeonthefeederline.Itisthroughthecommunicationnetworkthatadispersedcontrolofthegridcanbeachieved.AnotherimportantnoteregardingthecentralizedalgorithmisthatVusedinthederivationisacomplexquantitywhereasvoltagesensitivityintheJacobianisthechangeinvoltagemagnitudewithrespecttoDGoutput,whichisarealnumber.Usingangularsensitivityandvoltagesensitivitytoreactivepowerandthevoltageprole,thecomplexVcanbecalculated.Inthesimulationshowever,thecomplexvoltagechangeismeasured.Bychoosingasmallenoughchangeinreactivepowerinjectionandusingthatforsensitivitythemagnitudeofthecomplexvalueandtheactualchangeinvoltage 39

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magnitudecanbemadecomparable.FortheIEEE13nodeand34nodefeeders,1KVARwasfoundtoservethepurpose. 5.2.2ConstraintsandOptimizationProblemThegeneralconstraintsofthesystemarethevoltageconstraintsgiveninequation( 3 )are:0.95pujVij+jVij1.05puandcapacityconstraintsoftheDGs QminiQi+QiQmaxi8i.(5)Usingtherelation( 5 )inequations( 5 )and( 5 ) 0.95)-222(jVijjVij=QTDGi1.05)-222(jVij(5)And Qmini)]TJ /F5 11.955 Tf 11.96 0 Td[(QiQiQmaxi)]TJ /F5 11.955 Tf 11.96 0 Td[(Qi(5)Thecompleteoptimizationproblemcan,therefore,bedenedasMinimizef0=PQDG+QTDGQQDG (5)Suchthat:VminiQDGTiVmiaxandQmini)]TJ /F5 11.955 Tf 11.96 0 Td[(QiQiQmaxi)]TJ /F5 11.955 Tf 11.95 0 Td[(QiAnevolutionarytechniquecalledparticleswarmoptimization(PSO)isusedtosolvetheoptimizationproblem. 5.3DecentralizedVoltageControlandLossOptimizationDecentralizedvoltagecontrolisimplementedusingdataavailablelocallytothecontroller.Unlikethecaseofcentralizedcontrolwheredatafromallthesensorsinthenetworkaretobecollectedatanaggregatorsitebeforedecisionsaretaken,decentralizedcontrollerreactstolocalphenomena.Thisisparticularlyusefulwhen 40

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communicationsystemsareexperiencingproblemsduetoweatherorotherreasons.Implementingasystemwithmultipledecisionmakingbodiesalsomakesthesystemrobusttoothercontingenciesandintentionalattacks.Inthisstudyhowever,themyriadcontrollersdonotactindividually,rathereachonemonitorsthelocalconditionsandcoordinateswithothersuchcontrollerscalledagentstoachievetherequiredgoal.Thisisknownasamultiagentsystem.Thecontrolstructureissimilartotheonedescribedinsection 4 withchangesintheinformationbeingexchanged,andtheoptimizationalgorithmusedtodecidedispatch.TheagentscontrolDGinstallationsandvoltageregulatorsandperformmonitoring(ofvoltageititspointofcontact),moderation(negotiatewithotheragents)anddispatch(executeoptimizationalgorithmandcommunicatedispatchschemetootheragents)operations.Duetotheabsenceofallnodevoltages,equation( 5 )cannotbeused.Asmallmodicationtotheobjectivefunctionofequation( 5 )canbeusedforlocaloptimization.Thecentralcontrolschemegeneratesanewobjectivefunctionbeforeoptimizationtoreectthevoltageproleofthefeederwhichisanoperationthecontrolagentcannotperform.Ifareferencevoltageproleofthefeedercouldbeusedinstead,voltagedatacollectionwouldbeunnecessarytodeterminetheobjectivefunction.Forexample,equation( 5 )determinesthechangeinthelosswithrespecttotheinitialcondition-thevoltageconditionontheentirefeederbeforeoptimization.Similarlyiftheinitialconditioncanbemeasuredagainstaxedreference,anewfunctiondoesnothavetobecalculatedbeforeeachexecution.Abasecasevoltageprole-forexample,whennoneoftheDGswereconnected-canbeusedasareference,.IfthevoltagesforthiscasearerepresentedasVrefk,changeinlosscanbecalculatedaslossi0j=(Vrefi+Vrefi+Vi)]TJ /F5 11.955 Tf 9.63 0 Td[(Vrefj)]TJ /F8 11.955 Tf 9.63 0 Td[(Vrefj)]TJ /F6 11.955 Tf 9.63 0 Td[(Vj)Zi)]TJ /F9 7.97 Tf 10.82 0 Td[(1j(Vrefi+Vi+Vrefi)]TJ /F5 11.955 Tf 9.63 0 Td[(Vrefj)]TJ /F6 11.955 Tf 9.63 0 Td[(Vj)]TJ /F8 11.955 Tf 9.63 0 Td[(Vrefj) 41

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whereVrefi+Vrefi+Vi=V0i,thenewvoltagetobeestimatedandVrefi+Vrefi=Viisthevoltagebeforecontrol.lossi0j=)]TJ /F6 11.955 Tf 5.48 -9.69 Td[((Vrefi+Vrefi)]TJ /F5 11.955 Tf 11.96 0 Td[(Vrefj)]TJ /F8 11.955 Tf 11.95 0 Td[(Vrefj)+(Vi)]TJ /F6 11.955 Tf 11.95 0 Td[(Vj)Zi)]TJ /F9 7.97 Tf 10.82 0 Td[(1j)]TJ /F6 11.955 Tf 5.48 -9.68 Td[((Vrefi+Vrefi)]TJ /F5 11.955 Tf 11.96 0 Td[(Vrefj)]TJ /F8 11.955 Tf 11.96 0 Td[(Vrefj)+(Vi)]TJ /F6 11.955 Tf 11.95 0 Td[(Vj)lossi0j=(Vrefi+Vrefi)]TJ /F5 11.955 Tf 11.96 0 Td[(Vrefj)]TJ /F8 11.955 Tf 11.95 0 Td[(Vrefj)Z)]TJ /F9 7.97 Tf 10.82 0 Td[(1(Vrefi+Vrefi)]TJ /F5 11.955 Tf 11.96 0 Td[(Vrefj)]TJ /F8 11.955 Tf 11.96 0 Td[(Vrefj)+(Vi)]TJ /F6 11.955 Tf 11.95 0 Td[(Vj)Z)]TJ /F9 7.97 Tf 10.82 0 Td[(1(Vrefi+Vrefi)]TJ /F5 11.955 Tf 11.96 0 Td[(Vrefj)]TJ /F8 11.955 Tf 11.96 0 Td[(Vrefj)+(Vrefi+Vrefi)]TJ /F5 11.955 Tf 11.95 0 Td[(Vrefj)]TJ /F8 11.955 Tf 11.96 0 Td[(Vrefj)Z)]TJ /F9 7.97 Tf 10.82 0 Td[(1(Vi)]TJ /F6 11.955 Tf 11.95 0 Td[(Vj)+(Vi)]TJ /F6 11.955 Tf 11.95 0 Td[(Vj)Z)]TJ /F9 7.97 Tf 10.82 0 Td[(1(Vi)]TJ /F6 11.955 Tf 11.95 0 Td[(Vj)Thersttermoflossi0jislossij,linelossforthecurrentvoltageprole.Therefore,lossi0j)]TJ /F5 11.955 Tf 11.95 0 Td[(lossij=(Vi)]TJ /F6 11.955 Tf 11.96 0 Td[(Vj)Z)]TJ /F9 7.97 Tf 10.82 0 Td[(1(Vrefi)]TJ /F5 11.955 Tf 11.96 0 Td[(Vrefj+Virefj)+(Vrefi)]TJ /F5 11.955 Tf 11.96 0 Td[(Vrefj+Virefj)Z)]TJ /F9 7.97 Tf 10.82 0 Td[(1(Vi)]TJ /F6 11.955 Tf 11.96 0 Td[(Vj)+(Vi)]TJ /F6 11.955 Tf 11.96 0 Td[(Vj)Z)]TJ /F9 7.97 Tf 10.82 0 Td[(1(Vi)]TJ /F6 11.955 Tf 11.96 0 Td[(Vj) (5)Thersttermoflossi0jcanbeignoredasitisaconstantwithrespecttotheoptimizationproblem.Theremainingthreetermsformtheoptimizationfunction.Vrefkisknownsinceitisthereferenceprole;anapproximatevalueforVrefkwillbecalculatedusinglocalvoltageinformation.Theprecisevalueisnotnecessarysincethevaluerequiredforestimatingthelossis(Vrefi)]TJ /F8 11.955 Tf 12.73 0 Td[(Vrefj)thechangeinvoltagedifferencebetweentwoadjacentnodes.Similartoequations( 5 )to( 5 ),bysubstituting( 5 )in( 5 )andsimplifying,f=Xi,jlossi0j)]TJ /F5 11.955 Tf 11.95 0 Td[(lossij=AQDG+BQDG+QTDGCQDG (5)Suchthat:VminkQTDGiVmaxkandQmini)]TJ /F5 11.955 Tf 11.95 0 Td[(QiQiQmaxi)]TJ /F5 11.955 Tf 11.95 0 Td[(Qi8i=1,2,...m 42

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WhereA=Xi,j((Vrefi)]TJ /F5 11.955 Tf 11.96 0 Td[(Vrefj)Zi)]TJ /F9 7.97 Tf 10.82 0 Td[(1jij+(Vrefi)]TJ /F5 11.955 Tf 11.96 0 Td[(Vrefj)0Zi)]TJ /F9 7.97 Tf 10.82 0 Td[(1jTij)andB=Xi,j(VirefjZ)]TJ /F9 7.97 Tf 10.82 0 Td[(1ij+VirefjTZ)]TJ /F9 7.97 Tf 10.82 0 Td[(1Tij)andC=Xi,j(iTjZi)]TJ /F9 7.97 Tf 10.82 0 Td[(1jTij)Virefj=(Vrefi)]TJ /F8 11.955 Tf 12.36 0 Td[(Vrefj)isestimatedusingthelocalvoltagevalue.Sincealocaleventsuchasavoltageviolationtriggerstheoptimization,itisassumedthatthevoltageatthespecicnodeisknown.Thereferencevoltageatthatnodeisalsoknown.Usingthedifferencebetweenthetwoknownvoltages,somecompensationdispatchthatwillbridgethedifferenceiscalculatedi.e.(QDG)suchthat(QDG)k=Vrefkaterrantnodekiscalculated.ThedispatchschemedoesnotnecessarilyhavetobefeasiblesinceitisatheoreticalvalueusedtoestimateVirefj.Itispossibletoallocatetheentiredispatchtoonegeneratorbutitispreferredtouseasmanygeneratorsaspossible.With(QDG)known,Vrefi=(QDG)icanbecalculatedforallnodes;subsequently,Bcanalsobecalculated. 5.4OptimizationAlgorithm 5.4.1QuadraticProgrammingThebasicquadraticoptimizationproblemisdenedbytheobjectivefunctionGwherexisthevectortobeoptimized,Hisasymmetricmatrixandfisavector:MinimizeG=1 2xTHx+fTx (5)SuchthatAxbAeqx=beqlbxub 43

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Inthelossminimizationproblemhowever,theHmatrixisnotsymmetricduetothecomplexnatureofvoltage,sensitivityandlineseriesimpedance;alsoduetotheuseofcomplexconjugatestocalculatetheHmatrix.ThereforeHismadesymmetricwiththerelationH=(H+HT)=2However,despiteconvertingtheHessiantoasymmetricmatrix,theMatlabfunctionquadprogforquadraticprogrammingfailedtoproducefeasibleresults. 5.4.2ParticleSwarmOptimizationDuetothefailureofconstrainedquadraticoptimization,aswarmbasedtechniquecalledParticleSwarmOptimization(PSO)[ 21 ],derivinginspirationfromtheockingbehaviorofbirdswaschosen.PSOemploysalargeswarmofagentseachofwhichcansaveinformationaboutitselfandtheswarmandalsochangeitscourseofmotionaccordingtothisinformation.Theagentsareinitiatedatrandomlocationsinthesearchspacewhichdenotestherangeofvalueseachvariableintheoptimizationproblemcantake.Thevariablestobedeterminedformthelocationvectoroftheagent.Eachlocationinthesearchspacehasanassociatedtnessvaluewhichisthevalueoftheobjectivefunctionfortheparticularsequenceofvariablevalues.Duringaniterationofthealgorithm,eachagentupdatesitslocationvaluebyadjustingitvelocityaccordingtoequations( 5 )and( 5 ).Duringthisexplorationeachstoresitspersonal(pbest)andtheswarm'sglobal(gbest)bestvalues.Theseindicatethebestlocationwheretheparticularagentexperiencedthebestobjectivevaluefunctionandthebestvalueforthewholeswarmrespectively.Eachagenthasitsownpersonalbestbuttheswarmsharesacommonglobalbestlocationandvalue.Byupdatingitsownlocationbasedonpbestandgbest,everyagentconvergestotheoptimallocation.vi=wvi+c1rand(pbesti)]TJ /F5 11.955 Tf 11.96 0 Td[(xi)+c2rand(gbest)]TJ /F5 11.955 Tf 11.96 0 Td[(xi) (5) 44

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xi=xi+vi (5)wherexiisthepositionvectorofagenti,pbestiisthebestlocationithasbeento,gbestisthebestpositionfortheentireswarm.c1andc2areconstantsandwistheinertialconstant. 5.5ResultsandObservationsTheperformanceofthreealgorithms: 1. Dispatchlinearlyproportionaltothesensitivityoftheaffectednode(Linear) 2. CentralizedcompensationusingPSO(PSO) 3. DecentralizedcompensationusingPSO(Dispersed)aretestedfor3differentcases:case1>optimizingwhenreactiveoutputofallDGsiszero;case2>alltheloadsarescaleddownto80%and;case3>alltheloadsarescaledupto130%.Intherstcase,alltheDGsareconnectedtothegridbuttheDGsareworkingatpowerfactor=1.ByadjustingthereactivepoweroutputofeachDG,totalsystemlossisoptimized.Whilethetestfeedersassumeastaticload,realloadsarechangingconstantly.Assumingthatthetheloadsdonotgenerallychangesteeply,20%reductioninallloadsor30%increaseinallvaluesfromthebaseloadisconsideredtheworstcasescenarioandtheperformanceismeasuredforboththeseconditions.Animplicationoflowsensitivityvaluesisthatlargedispatchesarenecessarytobeabletoeffectasignicantchangeonthevoltage.AveryoptimisticcasewheretheDGsbearmostoftheloadisconsidered.Butaconsequenceofthisisthatpowerproduction(bothrealandreactive)needstobesteppeddownwhentheloadsarescaleddownorthesubstationwillbehavelikealoadandabsorbpowerinsteadoffeedingittothegrid.Therefore,theDGsarescaleddownbyafactorof30%.TheDGsarenotscaledupwhentheloadincreasesthough.ThethreealgorithmsforthethreecasesaretestedontheIEEE13and34nodefeeders(Appendix).Forboththefeeders,thecapacitorbanksareignoredandall 45

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reactivesupportisassumedbytheDGs.WhilethecapacitorcanalsobemodeledasaDGwithdiscreteoutputvaluesandzerorealpower,itissimplertoignorethecapacitors.Additionally,forthecaseofthe34nodefeeder,theloadonnode27isnotscaledsinceitisaverylargeloadanditisconnectedafterastepdowntransformer.Hencevoltageisverysensitivetoevenminorchangesinthesizeofthisload(gure 5-1 ).Itisassumedtobeaconstantload.Thetablesbelowtabulatetheresultsforthethreecasesforthetwofeedercongurations.BothLinearandDispersedvarietiesoptimizethereactivepowersonlyifanodeisviolatingthevoltagelimits.PSOvarietyontheotherhand,attemptstoreducelossinanysituation.Ifnodevoltageisoutsidelimits,eventhatisadjusted.ThereforeinTables 5-1 and 5-2 thegaininlosssavingsiszeroforLinearandDispersedfor13nodefeeder.Incaseofthe34nodefeeder,becausethevoltageregulatortapscannotbecalculatedaccurately,notallthevoltagesarewithinacceptablelimits,thereforetheDGoutputsarevaried.Ahugegaininlosssavingsisobservedforthe34nodefeederwiththemaximumbeingachievedbytheDispersedmethod.Butthemethodalsorequiredthechangingoftaps.SincetapsarechangedonlywhenDGoptimizationfails,itcanbeinferredthatPSOperformsbetterintermsofoptimizationeveniftheresultsarenotasgood.Forthe13nodefeeder,amodest5%savingswasobserved. Table5-1. Comparisonofoptimizationperformanceforcase1 FeederOptimizationOptimizedSavingEstimationTapPowerReductiontypeAlgorithmLoss(KW)(%)Error(KW)changes(KVA) Linear0000013PSO61.045.730.03067.45Dispersed00000 Linear62.0634.301.26082.1534PSO55.1041.670.39053.46Dispersed47.2649.980.50382.53 The34nodefeederseemstobemoreamenabletooptimization.Signicantsavingscanbeobservedthroughoptimization.DispersedandPSOappeartobe 46

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workingequallywellalthoughPSOgaveslightlybetterresultsoverallforcase2(table 5-2 ).BecauseLinearlimitsitselftoadjustingthevoltagetotheANSIstandard,itslossoptimizationperformanceisnotonparwiththeothers. Table5-2. Comparisonofoptimizationperformanceforcase2 FeederOptimizationOptimizedSavingEstimationTapPowerReductiontypeAlgorithmLoss(KW)(%)Error(KW)changes(KVA) Linear0000013PSO40.265.800.03080.31Dispersed00000 Linear64.0022.471.220119.734PSO48.3141.471.29084.83Dispersed49.7139.791.28072.71 Intable 5-3 ,'NA'impliesthatasteadystateconditionwithnovoltageviolationswasnotachievedthroughoptimization.Fig 5-3 depictsthecauseforthis.ItcanbeseeningraphofphaseCthatafteroptimization,theminimumvoltageisjustabove0.95puwhereasthemaximumvoltageisfarabove1.05pu.Thereactivepowerdispatchnecessarytoreducethepeakvoltagewillalsopushthelowervoltagebelowthe0.95range.Inthenextiteration,theminimumvalueisraisedbutthemaximumvaluealsobreakstheupperlimit.Thecyclerepeatsandasolutioncannotbefound.ItneedsaconcertedeffortoftheregulatorsandDGstosolveit.HencePSOandDispersedconvergedtoasolutionbutLineardidnot.Incaseofthe34nodefeeder,node5justbeforetherstregulatorexperiencesalowvoltagewhichisfurtheraggravatedbytheincreaseinload.TheDGatthenodedoesnothavesufcientcapacitytoraisethevoltage.ThevoltagemayinfacthavebeenmadeworsebythepresenceoftheDGbecausethecurrentowfromtheDGmayhaveincreasedthevoltagedropintheregion.Thereforenoneofthemethodshaveapositiveinuenceonthevoltageandlossproblem.Itcanbeseenthatallthemethodshadapositivelosssavingdespitethemagnitudeinsomecases.Optimizationalsoledtoanoverallreductioninpowerconsumptionin 47

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Table5-3. Comparisonofoptimizationperformanceforcase3 FeederOptimizationOptimizedSavingEstimationTapPowerReductionnodesAlgorithmLoss(KW)(%)Error(KW)changes(KVA) LinearNANANANANA13PSO108.0217.494.565187.13Dispersed108.3317.265.32597.61 LinearNANANANANA34PSONANANANANADispersedNANANANANA APhaseA BPhaseB CPhaseCFigure5-3. Noresultconditionofthe13nodefeeder 48

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allcases.Thereforeoptimizationiseconomicalfornotonlyreducingthelinelossesbutalsothetotalpowerconsumption.Thusifpowerhasanassociatedgenerationanddistributioncost,expensescanbereducedwiththeuseofDGs.Itisobservedthatthelossestimationerrorisalsoquitesmall.Withincreasingscalingoftheloadsthough,theerrorincreasesduetotheapproximationsinvolvedinthesensitivityparameter,suchasapproximatingthesensitivitycurvetoalinearrelationship,theminorinuenceofincreasingreactivedispatchonsensitivityofDGsconnectedatotherlocations,etc.Therefore,itmightbeusefultocontinuouslymonitorvoltageanddispatchreactivepowerratherthanperformoptimizationwhenavoltageviolationoccurssothatvoltagedifferenceandsensitivityvariationcanbecontained.Itwasobservedingure 5-2 thatsensitivityisnotaconstantbutcanbeapproximatedtoalinearlyvaryingquantity.Thenthesensitivitycanbewrittenas=Q+0whereistheslopeoftheline.ThereforeV=Q=(Q)2+0QIfvoltageisaquadraticfunction,losswouldbeaquarticfunction.Buttheobservedimprovementinestimationduetoaquarticlossfunctionwasnotsignicantenoughtoaccountforahigherorderlossfunction. 49

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CHAPTER6GENERATORSITINGANDSIZINGChapter5discussedoptimizationofDGoutputforoptimallossperformancewheretheDGswerealreadyconnectedatcertainlocationsonthegrid.However,lookingatthevoltagesensitivityvalues,itisapparentthatconnectingDGsatsomepositionsyieldbettersensitivitythanothernodesi.e.thesameamountofpowerproducesahighervoltagedifferenceforsomeDGlocationsthanothers.InthischaptersensitivityasappliedtodeterminingthepositionoftheDGanditssizearediscussed.TheeffectofhavingtoomanyortoofewDGsarealsoconsidered. 6.1GeneratorSitingThelocationoftheDGonthefeederisanimportantfactorindeterminingtheeffectithasonvoltagesatothernodes,powerowinthegridandconsequentlypowerloss.Forexample,DGsconnectedlowerdownthefeedercausesagreaterchangeinvoltageforthesamepowerthanaDGconnectedupstreamtoit.Generally,fartherawayfromthesubstationaDGislocated,higherarethesensitivitycoefcientscorrespondingtoit.Figure 6-1 plotssensitivitiesforphaseAofthe34nodefeederfor6differentDGlocations.SensitivityishigherforalmostallnodeswhentheDGislocatedatthelastnodeofthemainfeeder.ThesixthscenariohastheDGlocatedonalateralbranchratherthanthemainfeederunliketherst5cases.EvenwhenanodehasaDGconnectedtoit,ithadalowersensitivitywhencomparedtoaDGlocatedlowerdownstream.Itshouldbenotedthatthisrelationisvalidforageneraldecreasingtrendinthevoltages.Forothertypesofproles,thesensitivitypatternsaredifferent.Example,gure 6-2 showsthesensitivityforauniformlydecreasingvoltageproleona21nodefeederfordifferentDGlocations;gure 6-3 showssensitivityforanincreasingtrend.Similarlybasedonthetruevoltageconditions,thesensitivitypatternforanyfeedercongurationmaybecalculated.In 50

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Figure6-1. Sensitivityof34nodefeederforsixdifferentDGpositions generalthevoltageproleonmostfeedersisofthedecreasingtype,thereforesensitivityofbecomesmorenegativemovingdownthefeeder. Figure6-2. SensitivityforadecreasingvoltageprolefordifferentDGlocations Forvoltagecontroloperations,achievingalargevoltagechangewithasmallamountofdispatchisdesirableforeconomicreasons.Basedonthesensitivityvalueswecaninferthattoconservepower,itisidealtolocatetheDGonthenodewiththehighestimpactonvoltage-typicallythenodesattheendoffeederlinesandlaterals.Butforlossoptimization,itisnotonlynecessarytousetheleastamountofpowerfor 51

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Figure6-3. SensitivityforanincreasingvoltageprolefordifferentDGlocations compensation,itisalsoessentialthatlinescarrytheleastamountofcurrent.Currentandpowersensitivitycoefcientsareusefulincomparingtheseperformances.Boththeseindiceshowever,canbederivedfromvoltagesensitivity.Powersensitivityisthetotalchangeinpowerthataunitamountofreactivepowergenerationcausesi.e.equation( 5 )forasingleDGandQDG=1unit.Comparingthepowersensitivityatdifferentnodesandchoosingthenodewiththesmallestnumericalvaluecandecidethebestlocation.Currentsensitivitybydenition,istherateofchangeoflinecurrentswithchangeinDGinjectionpower.Butcurrentinalinecanberepresentedusingthevoltageatthenodesattheendofthelineas:Iij=(Vi)]TJ /F5 11.955 Tf 11.96 0 Td[(Vj)=ZijorIij+Iij=(Vi+Vi)]TJ /F5 11.955 Tf 11.96 0 Td[(Vj)]TJ /F6 11.955 Tf 11.95 0 Td[(Vj)=ZijButVk=k1,thereforeIij=ij=Zij (6) 52

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BycomparingtheIijvaluesforallpairsi,jandallDGlocations,DGsitescanbeidentied.Figure 6-4 plotsthecurrentsensitivityvaluesforallthenodesforallpossibleDGlocationsonanexample20nodefeeder(Appendix).Sincetheaimistoreducelossbyreducingcurrent,theDGsiteshouldbechosensothatthereductionincurrentismaximum.Fortherstfewcandidatesites,currentsensitivityisnearlyatdownstreamoftheDGnodeanddropsfornodesupstreamtoit.Forthelastfewnodes,currentsensitivitydropsfromaroundnode10butincreasesdownstreamtoit.Thisisnotpreferable.Hencethebestcandidateisnode10andthenodesimmediatelyadjacenttoit. Figure6-4. SensitivityofcurrenttoDGlocation Theselectionprocedurecanbemadeevensimplerconsideringlosssensitivity.Losssensitivityhasalreadybeendenedinequations( 5 )and( 5 ).BysettingVk=k1unit,losssensitivityforaDGlocationcanbeobtained.Figure 6-5 plotsthevariationoflosswithdifferentDGlocations.Locatingitatnode10reduceslossthemaximum,henceitistheidealcandidate.IfmultipleDGsaretobeinstalledthenitisbettertochooseonepositionatatime.WhenanotherDGlocationisbeingcited,allthepreviouslyselectedDGsareconnectedtotheirrespectivenodes,thenthelosssensitivitiesarecalculatedforallthecandidatenodestodecidethenewDGlocation. 53

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Figure6-5. SensitivityofpowerlosstoDGlocation UsingpowerlosssensitivityalsoaccountsforloaddistributioninthegridandpositioningtheDGclosetotheloadcentersothatcurrentowisreduced.Theexamplefeederhadmostoftheloadconcentratedbetweennode4andnode10ofthefeeder.Theoptimalnode,asselectedbypowerlosssensitivityandcurrentsensitivityisthenodeattheendoftheloadconcentration,whichalsoimpliesthatofthe7nodeswiththehighestloads,node10hasthehighestvoltagesensitivity.Thereforepowerlosssensitivitycombinestheadvantageofbothvoltageandcurrentsensitivitiesintoasinglequantity. 6.2GeneratorSizingGeneratorsizingandgeneratorsitingaretwointerdependentoperationswiththelocationoftheDGsiteinuencingtheamountgenerationnecessaryataparticularpositionandthesizeofalreadyinstalledDGsinuencinghowmanymoregeneratorsarenecessaryandwhere.Generatorsizingcanbedoneinmanyways:generationcapacitycanbeaddedinmultiplesofsomebasequantityasneededthroughoptimizationbutusuallysizingandsitingisperformedasacombinedoperation.SomeDGcongurationsareconsideredforinstallationinthesystemandoptimizationiscarriedouttodeterminethebestcandidatesfromtheavailablechoicesandtheoptimalsitefortheirinstallation. 54

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In[ 41 ]sizingoperationwasdoneusinglosssensitivityparameterstooptimizethelosscharacteristicsofthegrid.Ananalyticalexpressionforlosswasderivedfromthecurrentequationsandbusincidencematrix.Bydifferentiatingthisexpressionandequatingittozero,thesizeoftheDGwascalculatedsothatnetlossinthecircuitisminimum.Withthelossexpressionofequation( 5 )and( 5 ),theproblemcanbesolvedasasimplequadraticequation.Ifthenewcongurationdoesnotleadtooutofrangevoltages,theDGisretained.Forexample,forthe34nodefeedera-80KVARDGwasindicatedasnecessarytominimizeloss.ButinlinewiththeaimofcompensationduringfaultsandexpansionofgenerationcapabilityusingDGs,theintentistocalculatetheminimumsizeofDG.IntheIEEE34nodefeeder,node27oftensuffersfromlowvoltage,reachingdowntolessthan0.9puinsomecases.ADGwhichcanprovideforsuchasituationisrequired.Ifsensitivityisassumedtobeaconstant,theamountofreactivepowernecessarycanbecalculatedasQDG=V=.ThevalueofQDGmightturnouttobetoohigh.AworkaroundforthisistosharethenecessarypowerovermultipleDGs.Orsomeportionofthereactivepowercanberelegatedtorealpower.Dependingonthegridconditions,therealandreactivepowersensitivityvaluesmaybecomparable.Insuchacaseitmaybeusefultoprovidetheminimumvoltagesupportusingrealpowerinjectionandprotectionagainstchangesusingreactivepowerdispatch.Forexample:ifthelowestvoltageis0.88pu,sensitivityis610)]TJ /F9 7.97 Tf 6.59 0 Td[(4pu=KVARandsupportcapabilityupto1puisnecessary,thenQ=0.12=610)]TJ /F6 11.955 Tf 7.08 -4.34 Td[(4=200KVAR.Iftherealpowersensitivityisequaltothereactivepowersensitivity,foraDGoperatingat0.85powerfactor,theratioofreactiveandrealpowerisroughly0.6.Therefore,P=125KWandQ=75KVAR.Ifthere'smorethanonenodetoaccountfor,alinearprogrammingwithinequalityconstraintsmaybesetuptosimultaneouslysolveformultipleDGsizesas: nXj=1iqjQj+irjRjVi8i=1,...m,j=1,...n(6) 55

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wheremisthenumberofnodesandnarethenumberofDGsand Qj=Rjtan)]TJ /F6 11.955 Tf 7.47 -9.69 Td[(cos)]TJ /F9 7.97 Tf 6.59 0 Td[(1(j)(6)jisthepowerfactoroftheDG. 6.3ImpactofDGPenetrationonLossTostudyDGimpact,the34nodefeederwaschosen.Upto10DGswerefreetobeplaced.DGswereaddedoneatatimeandeachonewasplacedatanodesothatthetotallosswasaminimum.ThesizeoftheDGswasvarieddependingonthenumberofgenerators.TheDGsizewasxcalculatedasLoadtotal=3P=100=NwhereLoadtotalisthetotalloadonallthe3phasesofthesystem,PisthepenetrationinpercentandNisthenumberofDGs.Penetrationwasvariedinstepsof5%from0to80%andnumberofDGswasvariedfrom1to10instepsof1.LosseswereplottedafunctionofthenumberofDGsandpenetration(gure 6-6 ). Figure6-6. VariationoflossesfordifferentpenetrationlevelsandnumberofDGs TheobserveddatasuggeststhatlossreduceswithincreasingDGpenetrationbutthereductionwithincreasingnumberofDGsisnotveryapparent.Atlargerpenetrationlevels,havingmoreDGsdoesseemtobehelpfulbutinthecaseofthe34nodefeeder,10werenotnecessary.Similarlosslevelswereobservedevenwith5or6DGs.ItwasalsoobservedthatwhilemultipleDGswerelocatedatthesamenodeatlower 56

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penetrations,theywerescatteredacrossafewnodesathigherpenetrationandDGcount;clusteringofDGsattheanodeindicatesthatabiggersizedgeneratorisnecessaryatthatlocationandthetotalnumberofDGsnecessaryisnotreally10butthenumberofuniqueDGlocations.ThisalsosuggeststhatlossmayincreaseifNuniquelocationsaredesiredanddifferentsizeDGsarenotpreferred.Sitingandsizingthereforeplaysanimportantroleinlossminimization. 57

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CHAPTER7CONCLUSIONIntegrationofdistributedgenerationintothegridisahotresearchtopicanditpromisesmanybenets.Butitalsobringswithitmanyproblemsrelatedtocontrol,protection,islanding,etc.Inthisthesisoneaspectofthatproblem,namelydistributionlineloss,wastackledusingsensitivitycoefcients.Analgorithmwasdevisedtomitigatethelossesandimprovepowerow.Itwasfoundthatincludingdistributedgenerationinthedistributiongridcanhelpreducethelinelossesbyreducingthemaximumcurrentowinginaline.Sincelossisproportionaltothesquareofthecurrent,evensmallreductionincurrentcanimprovethevoltageandlossprolesignicantly.InclusionofDGsandproperdispatchofreactivepoweralsoledtoareductioninthetotalpowerconsumedinthefeeder.ThereforeDGscanplayanimportantroleinpeakshavingoperations.ItiseconomicallyadvantageoustointegrateDGsintothegrid.DGsalsocontributetothecapacityexpansionoftheutilitygridandpreventthepurchaseofexpensivepowerfromtheenergymarket.However,DGsinlargenumberscanplayhavocwithexistingcontroloperationssuchasvoltageregulation.Alinevoltageregulatorestimatesthevoltageconditionatadownstreamnodeandadjustsitstapstocontrolthevoltageatthetargetnode.Theestimationisbasedonthecurrentowingthroughitslinedropcompensatorcircuit.Bychangingthecurrentowpattern,DGscausetheregulatorstounderestimatetheseverityofvoltageproblemsandcauseinadequatecontrol.Therefore,whenDGsareincludedinthegridinsufcientquantityitisessentialforvoltagestobemeasuredratherthanestimated.AnditmayalsobecomenecessaryforDGsthemselvestoparticipateinthecontroloperation.Optimizinglossinthegridrequirescompleteknowledgeofthesystemconditionsforefcientoperation.Itisbetterperformedasacentralizedcontroltechnique.However,itisstillpossibletoobtainsatisfactoryresultsthroughlocalizedcontrolwithcoordination 58

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oftheotherDGs.Suchatechniquewasimplementedusingamultiagentcontroloperation.LossoptimizationcangreatlybenetfromtheproperlocationofDGsinthedistributionsystem.FromsimulationsonanexamplesystemitwasobservedthatplacingDGsclosetotheloadconcentrationisbenecialeventhoughvoltagesensitivitywouldindicateplacementneartheendofthefeederlinebecausethesameamountofpowerdispatchcaneffectalargerchangeinvoltage.LosssensitivityisabetterparametertodecidethesitingofDGs.IthasalsobeenfoundpossibletodecidethesizeoftheDGusingvoltagesensitivity.SimulationsonthepenetrationofDGsinthegridandtoanextent,increasingthenumberofDGswerefoundtofavorminimizationofloss.Allresultsregardinglossseemtofavortheinclusionofdistributedgeneratorsintothegrid.Howeversomeobservationsduringthestudydocallforfurtherresearchsuchas:thesmallvalueofsensitivity.Itimplieslargedispatchforasignicantchangeinvoltage,whichfurtherimplieslargeDGs.Thatmaycausethesubstationtoabsorbpowerinsteadofsupplyingit.Therefore,caremustbetakenduringDGsizingtoensurethatcurrentowisnotreversedatthesubstationbus.AxedDGsizewouldinterferewiththiswhentheloadisvarying.ThereforerealpoweroutputoftheDGsmustalsobevariedalongwiththereactivepower,especiallyinsmallsystems.Simulationsinthisstudywereimplementedonsmallsizedsystemswithveryfewnodes.Simulationsonbiggerandmorecomplicatednetworksneedtobeperformedandstudied,particularlythebehaviorofsensitivityandtheeffectofpenetrationandnumberofDGonthesystem.Futurestudiesincludingthemodelofthedistributedgeneratoranditsresponsetothethedynamicbehaviorofthegridarenecessary.Theresponsetoincreasingpenetrationofthedistributedgenerators,thevaryingloadconditionsandtheabilityofthegeneratorstotrackloadchangesandcontroloperationswithoutinterferingwitheachotherevenathighpenetrationsneedtobestudied. 59

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APPENDIX:FEEDERCONFIGURATIONS StandardIEEEtestfeederswerechosenforallvoltagecontrolandpoweroptimizationsimulations[ 43 ].Thefeederschosenwereof13nodesand34nodesrespectively.TheonelinediagramsofthetwofeedersareshowninFigure 7 and 7 .Anexample20nodefeederwasusedtotestDGlocationusingthevarioussensitivitycoefcients. IEEE13NodeFeeder.The13nodefeederisasmall,highlyloaded,wye-connected,unbalancedtestfeeder[ 44 ]withcapacitorcompensationaswellasavoltageregulator.ThenodeshavebeenrenumberedaccordingtoFigure 7 forconvenience.Forvoltagecontrolsimulations,twoDGsatnodes2and8areconsidered.BoththeDGsareofthesamecapacity-500KWandamaximumof300KVAR.TheDGsareconsideredtohaveaconstantrealpoweroutputbutthereactivepowerisvariedaccordingtonecessity. FigureA-1. SchematicofIEEE13nodetestfeeder.Source:IEEE13NodeFeeder[ 43 ] 60

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IEEE34NodeFeeder.The34nodefeederisalong,lightlyloaded,wye-connected,unbalancedtestfeeder[ 44 ]basedananactualfeederinArizona.Ithastwocapacitorbanksandtwolnevoltageregulatorsforvoltagecontrol.ThenodeshavebeenrenumberedaccordingtoFigure 7 forconvenience.Forvoltagecontrolsimulations,veDGsarelocatedatnodes5,9,15,19and27.AttemptingtosizealltheDGsequallyresultedinvoltgeviolationssotheyaresizedateither100KWor120KWandamaximumof60KVAR. FigureA-2. SchematicofIEEE34nodetestfeeder.Source:IEEE34NodeFeeder[ 43 ] Example20nodeFeeder.The20nodefeederisanoverloadedfeederwithamajorloadconcentrationatthebeginningofthefeederwithabout75%ofthetotalloadconnectedequallytothenodes4through10.Itwasdesignedprimarilytocheckiftheloadcentercanbedetectedbythedifferentsensitivitycoefcients.ThefeederisabalancedsystemwithnodeslocatedatuniformdistancesandthelineshavingR=1,X=1andnoimpedancebetweenthephases.Likethe34nodestandardfeederitoperatesat24.9KV. 61

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BIOGRAPHICALSKETCH AnuragR.KatticompletedhisBachelorofEngineeringinelectronicsandcommunicationengineeringfromVisvesvarayaTechnologicalUniversity,Belgaumin2008.HeworkedattheIndianInstituteofScience,Bangaloreaftergraduationonswarmbasedoptimization,patternrecognition,roboticsandcontrol.In2009hedecidedtopursuegraduatestudiesandhewasadmittedtotheUniversityofFloridafortheMasterofScienceprograminelectricalengineeringwithafocusoncontrolsystems.Hesoonrealizedhisinterestingreenenergyandpowersystems.Hiscurrentresearchinterestsincludepowersystemsandcontrol,smartgrids,distributionsystems,greenenergyandoptimization.ThisthesisistheculminationofhisworkintheeldandcompletestheMasterofSciencethesisrequirements. 66