Theblinkingofnonincandescentcitylightsisshowninthismotionblurredlongexposure.TheACnatureofthemainspowerisrevealedbythedashedappearanceofthetracesofmovinglights.

ACpowerFromWikipedia,thefreeencyclopedia

Powerinanelectriccircuitistherateofflowofenergypastagivenpointofthecircuit.Inalternatingcurrentcircuits,energystorageelementssuchasinductorsandcapacitorsmayresultinperiodicreversalsofthedirectionofenergyflow.Theportionofpowerthat,averagedoveracompletecycleoftheACwaveform,resultsinnettransferofenergyinonedirectionisknownasrealpower.Theportionofpowerduetostoredenergy,whichreturnstothesourceineachcycle,isknownasreactivepower.

Contents

1Real,reactive,andapparentpower2Powerfactor3Reactivepower4Reactivepowercontrol5Unbalancedpolyphasesystems6Basiccalculationsusingrealnumbers7Multiplefrequencysystems8Seealso9References

Real,reactive,andapparentpower

Inasimplealternatingcurrent(AC)circuitconsistingofasourceandalinearload,boththecurrentandvoltagearesinusoidal.Iftheloadispurelyresistive,thetwoquantitiesreversetheirpolarityatthesametime.Ateveryinstanttheproductofvoltageandcurrentispositive,indicatingthatthedirectionofenergyflowdoesnotreverse.Inthiscase,onlyrealpoweristransferred.

Iftheloadsarepurelyreactive,thenthevoltageandcurrentare90degreesoutofphase.Forhalfofeachcycle,theproductofvoltageandcurrentispositive,butontheotherhalfofthecycle,theproductisnegative,indicatingthatonaverage,exactlyasmuchenergyflowstowardtheloadasflowsback.Thereisnonetenergyflowoveronecycle.Inthiscase,onlyreactiveenergyflowsthereisnonettransferofenergytotheload.

Practicalloadshaveresistance,inductance,andcapacitance,sobothrealandreactivepowerwillflowtorealloads.Powerengineersmeasureapparentpowerasthemagnitudeofthevectorsumofrealandreactivepower.Apparentpoweristheproductoftherootmeansquareofvoltageandcurrent.

Thecomplexpoweristhevectorsumofrealandreactivepower.Theapparentpoweristhemagnitudeofthecomplexpower.Realpower,PReactivepower,QComplexpower,SApparentpower,|S|Phaseofcurrent,

Engineerscareaboutapparentpower,becauseeventhoughthecurrentassociatedwithreactivepowerdoesnoworkattheload,itheatsthewires,wastingenergy.Conductors,transformersandgeneratorsmustbesizedtocarrythetotalcurrent,notjustthecurrentthatdoesusefulwork.

Anotherconsequenceisthataddingtheapparentpowerfortwoloadswillnotaccuratelygivethetotalapparentpowerunlesstheyhavethesamedisplacementbetweencurrentandvoltage(thesamepowerfactor).

Conventionally,capacitorsareconsideredtogeneratereactivepowerandinductorstoconsumeit.Ifacapacitorandaninductorareplacedinparallel,thenthecurrentsflowingthroughtheinductorandthecapacitortendtocancelratherthanadd.Thisisthefundamentalmechanismforcontrollingthepowerfactorinelectricpowertransmissioncapacitors(orinductors)areinsertedinacircuittopartiallycancelreactivepower'consumed'bytheload.

Engineersusethefollowingtermstodescribeenergyflowinasystem(andassigneachofthemadifferentunittodifferentiatebetweenthem):

Realpower,P,oractivepower:[1]watt(W)Reactivepower,Q:voltamperereactive(var)Complexpower,S:voltampere(VA)Apparentpower,|S|:themagnitudeofcomplexpowerS:voltampere(VA)Phaseofvoltagerelativetocurrent,:theangleofdifference(indegrees)betweencurrentandvoltagecurrentlaggingvoltage(quadrantIvector),currentleadingvoltage(quadrantIVvector)

Inthediagram,Pistherealpower,Qisthereactivepower(inthiscasepositive),SisthecomplexpowerandthelengthofSistheapparentpower.Reactivepowerdoesnotdoanywork,soitisrepresentedastheimaginaryaxisofthevectordiagram.Realpowerdoesdowork,soitistherealaxis.

Theunitforallformsofpoweristhewatt(symbol:W),butthisunitisgenerallyreservedforrealpower.Apparentpowerisconventionallyexpressedinvoltamperes(VA)sinceitistheproductofrmsvoltageandrmscurrent.Theunitforreactivepowerisexpressedasvar,whichstandsforvoltamperereactive.Sincereactivepowertransfersnonetenergytotheload,itissometimescalled"wattless"power.Itdoes,however,serveanimportantfunctioninelectricalgridsanditslackhasbeencitedasasignificantfactorintheNortheastBlackoutof2003.[2]

Understandingtherelationshipamongthesethreequantitiesliesattheheartofunderstandingpowerengineering.Themathematicalrelationshipamongthemcanberepresentedbyvectorsorexpressedusingcomplexnumbers,S=P+jQ(wherejistheimaginaryunit).

Powerfactor

Theratiobetweenrealpowerandapparentpowerinacircuitiscalledthepowerfactor.It'sapracticalmeasureoftheefficiencyofapowerdistributionsystem.Fortwosystemstransmittingthesameamountofrealpower,thesystemwiththelowerpowerfactorwillhavehighercirculatingcurrentsduetoenergythatreturnstothesourcefromenergystorageintheload.Thesehighercurrentsproducehigherlossesandreduceoveralltransmissionefficiency.Alowerpowerfactorcircuitwillhaveahigherapparentpowerandhigherlossesforthesameamountofrealpower.

Thepowerfactorisunity(one)whenthevoltageandcurrentareinphase.Itiszerowhenthecurrentleadsorlagsthevoltageby90degrees.Powerfactorsareusuallystatedas"leading"or"lagging"toshowthesignofthephaseangleofcurrentwithrespecttovoltage.

Purelycapacitivecircuitssupplyreactivepowerwiththecurrentwaveformleadingthevoltagewaveformby90degrees,whilepurelyinductivecircuitsabsorbreactivepowerwiththecurrentwaveformlaggingthevoltagewaveformby90degrees.Theresultofthisisthatcapacitiveandinductivecircuitelementstendtocanceleachotherout.

Wherethewaveformsarepurelysinusoidal,thepowerfactoristhecosineofthephaseangle()betweenthecurrentandvoltagesinusoidwaveforms.Equipmentdatasheetsandnameplatesoftenwillabbreviatepowerfactoras" "forthisreason.

Example:Therealpoweris700Wandthephaseanglebetweenvoltageandcurrentis45.6.Thepowerfactoriscos(45.6)=0.700.Theapparentpoweristhen:700W/cos(45.6)=1000VA.[3]

Reactivepower

Fundamentally,electricalpowerisdeveloped,deliveredandconsumedasvoltageandcurrent.Inasimpledirectcurrent(DC)device(likeaflashlight)thepower(thebrightnessofthebulb)isthevoltagetimesthecurrentandismeasuredinWatts.Wattsareameasureoftheabilityofadevicetoperformusefulwork.Thisiswhatiscalledrealpowerbecauseitcanproduceuseful(real)work.

Inalternatingcurrent(AC)systemslikeallmodernpowersystemsthingsbecomeabitmorecomplicated.Commoncustomerloaddevicesespeciallymotorscausetherelationshipbetweencurrentandvoltagetoshift.Sincemostoftheelectricpowersystemloadisfrommotorsusedinfactories,businessesandhomes,thisbecomesasignificantissueforutilities.

ThisshiftintherelationshipofvoltageandcurrentinACsystemsreducestheabilityofthesystemtodeliverpowertoperformusefulwork.Inextremecases,thevoltageandcurrentcanshiftsomuchthatalmostnousefulworkcanbedelivered.(Therearealsootherundesirableeffectsonthepowersystemwhenthisshiftgetslargelikelowvoltages,andincreasedequipmentheatingandsystemlosses.)

Thisshiftiswhatcausesaneedforreactivepower.Itismeasuredinvars(fromtheFrenchtermVoltAmperereactive).Whilereactivepowerdoesnotprovideusefulwork,itisessentialformotorsandtransformerstowork.Reactivepowerrequiredbycustomerloadmustbesuppliedinsomeway.

Reactivepowerflowisneededinanalternatingcurrenttransmissionsystemtosupportthetransferofrealpoweroverthenetwork.Inalternatingcurrentcircuits,energyisstoredtemporarilyininductiveandcapacitiveelements.ACconnecteddevicesthatstoreenergyintheformofamagneticfieldincludeinductors(alarge

coilofwire).Whenavoltageisinitiallyplacedacrossthecoil,amagneticfieldbuildsup,andittakesaperiodoftimeforthecurrenttoreachfullvalue.Thiscausesthecurrenttolagbehindthevoltageinphasehence,thesedevicesaresaidtobesourcesoflaggingreactivepower.

AcapacitorisanACdevicethatstoresenergyintheformofanelectricfield.Whencurrentisdriventhroughthecapacitor,ittakesaperiodoftimeforachargetobuilduptoproducethefullvoltagedifference.OnanACnetwork,thevoltageacrossacapacitorisconstantlychangingthecapacitorwillopposethischange,causingthevoltagetolagbehindthecurrent.Inotherwords,thecurrentleadsthevoltageinphasehence,thesedevicesaresaidtobesourcesofleadingreactivepower.

Thepowersystemrequiresbothtypesofpowerrealandreactiveinordertofunctionproperly.Electricgeneratorssupplyreactivepower(inadditiontorealpower)thatisconsumedbycustomerload.

Theshiftingeffectofmotorscanalsobeoffsetusingdevicesthatcounteractthisshiftthemostcommonarecapacitors.Suchcapacitorsarethelargestsourceofthisoffsettingreactivepowerandarecommonlyusedthroughoutthepowersystem.

Anothersourceofreactivepowerisasynchronouscondenserakindofelectricgeneratorthatdoesnotproducerealpower,onlyreactivepower.Therearealsootherdevicesthatusehighpowerelectronicstorapidlycontrolreactivepowerfromlargebanksofcapacitors.

Energystoredincapacitiveorinductiveelementsofthenetworkgiverisetoreactivepowerflow.Reactivepowerflowstronglyinfluencesthevoltagelevelsacrossthenetwork.Voltagelevelsandreactivepowerflowmustbecarefullycontrolledtoallowapowersystemtobeoperatedwithinacceptablelimits.

Reactivepowercontrol

Transmissionconnectedgeneratorsaregenerallyrequiredtosupportreactivepowerflow.ForexampleontheUnitedKingdomtransmissionsystemgeneratorsarerequiredbytheGridCodeRequirementstosupplytheirratedpowerbetweenthelimitsof0.85powerfactorlaggingand0.90powerfactorleadingatthedesignatedterminals.Thesystemoperatorwillperformswitchingactionstomaintainasecureandeconomicalvoltageprofilewhilemaintainingareactivepowerbalanceequation:

Generator_MVARs+System_gain+Shunt_capacitors=MVAR_Demand+Reactive_losses+Shunt_reactors

TheSystemgainisanimportantsourceofreactivepowerintheabovepowerbalanceequation,whichisgeneratedbythecapacitivenatureofthetransmissionnetworkitself.Bymakingdecisiveswitchingactionsintheearlymorningbeforethedemandincreases,thesystemgaincanbemaximizedearlyon,helpingtosecurethesystemforthewholeday.

Tobalancetheequationsomeprefaultreactivegeneratorusewillberequired.Othersourcesofreactivepowerthatwillalsobeusedincludeshuntcapacitors,shuntreactors,StaticVARCompensatorsandvoltagecontrolcircuits.MrSiyabongaakaSoloMdlalosecameupwiththeideaofreactivepower.

Unbalancedpolyphasesystems

Whilerealpowerandreactivepowerarewelldefinedinanysystem,thedefinitionofapparentpowerforunbalancedpolyphasesystemsisconsideredtobeoneofthemostcontroversialtopicsinpowerengineering.Originally,apparentpowerarosemerelyasafigureofmerit.MajordelineationsoftheconceptareattributedtoStanley'sPhenomenaofRetardationintheInductionCoil(1888)andSteinmetz'sTheoreticalElementsofEngineering(1915).However,withthedevelopmentofthreephasepowerdistribution,itbecameclearthatthedefinitionofapparentpowerandthepowerfactorcouldnotbeappliedtounbalancedpolyphasesystems.In1920,a"SpecialJointCommitteeoftheAIEEandtheNationalElectricLightAssociation"mettoresolvetheissue.Theyconsideredtwodefinitions:

thatis,thequotientofthesumsoftherealpowersforeachphaseoverthesumoftheapparentpowerforeachphase.

thatis,thequotientofthesumsoftherealpowersforeachphaseoverthemagnitudeofthesumofthecomplexpowersforeachphase.

The1920committeefoundnoconsensusandthetopiccontinuedtodominatediscussions.In1930anothercommitteeformedandonceagainfailedtoresolvethequestion.ThetranscriptsoftheirdiscussionsarethelengthiestandmostcontroversialeverpublishedbytheAIEE(Emanuel,1993).Furtherresolutionofthisdebatedidnotcomeuntilthelate1990s.

Basiccalculationsusingrealnumbers

Aperfectresistorstoresnoenergy,socurrentandvoltageareinphase.Thereforethereisnoreactivepowerand .Thereforeforaperfectresistor

Foraperfectcapacitororinductorthereisnonetpowertransfer,soallpowerisreactive.Thereforeforaperfectcapacitororinductor:

WhereXisthereactanceofthecapacitororinductor.

IfXisdefinedasbeingpositiveforaninductorandnegativeforacapacitorthenwecanremovethemodulussignsfromSandXandget

Instantaneouspowerisdefinedas:

wherev(t)andi(t)arethetimevaryingvoltageandcurrentwaveforms.

Thisdefinitionisusefulbecauseitappliestoallwaveforms,whethertheyaresinusoidalornot.Thisisparticularlyusefulinpowerelectronics,wherenonsinusoidalwaveformsarecommon.

Ingeneral,weareinterestedintherealpoweraveragedoveraperiodoftime,whetheritisalowfrequencylinecycleorahighfrequencypowerconverterswitchingperiod.Thesimplestwaytogetthatresultistotaketheintegraloftheinstantaneouscalculationoverthedesiredperiod.

Thismethodofcalculatingtheaveragepowergivestherealpowerregardlessofharmoniccontentofthewaveform.Inpracticalapplications,thiswouldbedoneinthedigitaldomain,wherethecalculationbecomestrivialwhencomparedtotheuseofrmsandphasetodeterminerealpower.

Multiplefrequencysystems

SinceanRMSvaluecanbecalculatedforanywaveform,apparentpowercanbecalculatedfromthis.

Forrealpoweritwouldatfirstappearthatwewouldhavetocalculateloadsofproducttermsandaverageallofthem.Howeverifwelookatoneoftheseproducttermsinmoredetailwecometoaveryinterestingresult.

howeverthetimeaverageofafunctionoftheformcos(t+k)iszeroprovidedthatisnonzero.Thereforetheonlyproducttermsthathaveanonzeroaveragearethosewherethefrequencyofvoltageandcurrentmatch.Inotherwordsitispossibletocalculatereal(average)powerbysimplytreatingeachfrequencyseparatelyandaddinguptheanswers.

Furthermore,ifweassumethevoltageofthemainssupplyisasinglefrequency(whichitusuallyis),thisshowsthatharmoniccurrentsareabadthing.Theywillincreasethermscurrent(sincetherewillbenonzerotermsadded)andthereforeapparentpower,buttheywillhavenoeffectontherealpowertransferred.Hence,harmoniccurrentswillreducethepowerfactor.

Harmoniccurrentscanbereducedbyafilterplacedattheinputofthedevice.Typicallythiswillconsistofeitherjustacapacitor(relyingonparasiticresistanceandinductanceinthesupply)oracapacitorinductornetwork.Anactivepowerfactorcorrectioncircuitattheinputwouldgenerallyreducetheharmoniccurrentsfurtherandmaintainthepowerfactorclosertounity.

Seealso

WarofCurrentsElectricpowertransmissionTransformerMainselectricity

References

1. ^IEEE100:theauthoritativedictionaryofIEEEstandardsterms.7thed.ISBN0738126012,page232. ^"August14,2003OutageSequenceofEvents"

(http://web.archive.org/web/20071020070028/http://www.ferc.gov/industries/electric/indusact/blackout/091203blackoutsum.pdf).FERC.20030912.Archivedfromtheoriginal(http://www.ferc.gov/industries/electric/indusact/blackout/091203blackoutsum.pdf)on20071020.Retrieved20080218.

3. ^"ACpowercalculation"(http://web.archive.org/web/20120618165213/http://encon.fke.utm.my/courses/see1023/AC_CircuitAnaysis2.ppt).091123encon.fke.utm.my(googlecache)

"ACPowerJavaApplet"(http://www.circuitmagic.com/acpower.htm)

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