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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