overview of current research into low voltage cb

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TheOpenPlasmaPhysicsJournal,2009,2,105-119

OpenAccessOverviewofCurrentResearchintoLow-VoltageCircuitBrea

ers

*,11,2

PierreFretonandJean-JacquesGonzalez

1UniversitdeToulouse;UPS,INPT;LAPLACE(LaboratoirePlasmaetConversiond'Energie);118RoutedeNarbonne,F-31062ToulouseCedex9,France

2CNRS;LAPLACE;F-31062Toulouse,France

Abstract:Thelow-voltagecircuitbrea

erhasbeenusedformanyyearsfornetwor

andpersonsprotection.Thereviewpapersexistingonthesedevicesgenerallydealwithelectricalaspectsormacroscopicinformationonthearcbutfewconcernthefineunderstandingofarcbehaviourfromitsignitionbetweentheopeningcontacttothecurrentlimitationstageduetoitspresenceinthesplitterplates.Inthispaper,wefocusourattentiononthispoint.Wefirstlydescribethe

wor

ingofsuchdevices,theirlimitationsandthedifferentphenomenaoccurringduringbrea

ing.Then,thedifficultiesinvolvedwithunderstandingthebehaviourofthearcareidentifiedanddiscussedintwomainsections:physicalarccharacteristicsandthestudyofarcmovementduringthebrea

ingprocess.Areviewofthepapersdealingwiththesesubjectsisproposed:bothexperimentalandtheoreticalresultsfromtheliteratureareconfrontedanddiscussedandtechnicaldifficultiesidentified.

Keywords:Low-voltagecircuitbrea

er,plasma,arcmotion,voltagedrop,currentlimitation.

I.INTRODUCTIONThelowvoltagecircuitbrea

erhaslongbeenusedfortheprotectionfromdamage,ofpersonsandnetwor

s,causedbyoverloadorshortcircuits.Itsbasicfunctionistodetectafaultconditionand,byinterruptingcontinuity,toimmediatelydiscontinueelectricalflow.Circuitbrea

ersaremadeinvaryingsizes,fromsmalldevicesthatprotectanindividualhouseholdapplianceuptolargeswitchgeardesignedtoprotecthighvoltagecircuitsfeedinganentirecity.Low-voltagetypes(lessthan1000VAC)arecommonindomestic,commercialandindustrialapplications(TableI-1[1,2]).Generalpresentationsofthelow-voltagecircuitbrea

erandofthephenomenaoccurringinthemcanbe

foundintheliteratureforinstanceinthepapersofMcBride

J.W.andWeaverP.M.[3]andLindmayerM.andSpringstubbeM.[4].NeverthelessaphotographispresentedinFig.(I-1)showingthedifferentelementsofcircuitbrea

ergeometry.Fromcontactopeningtothesuccessfulbrea

ingprocess,differentinstantsofarclifecanbeconsideredinthegeometry:


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Contactopening,jumptotherails(immobility):Innormalusecurrentcontinuityexistsbetweentheopeningcontactintheclosedpositionandonerailofthecircuitbrea

er.Duetoanetwor

defaultortoamanualintervention,theopeningcontactmovesleadingtoarcignition.Duringcontactopeningthearciselongatedanddeformedbythemagneticand*AddresscorrespondencetothisauthorattheUniversitdeToulouse;UPS,INPT;LAPLACE(LaboratoirePlasmaetConversiond'Energie);118RoutedeNarbonne,F-31062ToulouseCedex9,France;E-mails:[email protected],[email protected]

pressureforces.Asthearccannotbeelongatedindefinitely,itgenerallyjumpstotherailbeforetotalcontactopening.Aftercontactopening,thearcremainsinthecontactregion(Fig.II-1).

Arcmovementinthechamberundertheeffectofthepressuregradientandoftheexternalmagneticfield:Afterthejumpofthearcfromtheopeningcontactstotherails,thearcissubmittedtodifferentforces,two

ofwhichhavethegreatesteffectonarcmovement.(1)Thefirstispressure:duetothetemperatureincreaseandthustothehighpressureintheopeningcontactregioncomparedtotheambientpressureinthesplittingchamber,thearcispushedawayfromthecontactsandintothechamber.(2)Thesecondforceisduetothecurrentcirculatingontherails.Thecurrent-carryingpathcreatesamagneticfieldwhich,combinedwiththecurrentcirculationinthearc,createsamagneticforcewhichpushesthearcintothesplittingchamber.Somedesignsmayuseblowoutcoilsorairpufferstoaidtheprocess[5].

Arcinthesplitterplates:Undertheinfluenceofthetwopreviousforcesthearcmovestothesplittingchamber.Duetothethic

nessofthesplittersthearcvelocitydecreaseseventhoughthepropertiesoftheferromagneticsplittersacttodrivethearcintothecuttingchamber.Onceithasbeendividedintoseveralsegments,thearcispushedandelongatedgenerallyleadingtoasuccessfulbrea

ing.Restri

ephenomena:Thearcbehaviourinthechamberiscomplexandrestri

ecanoccurbetweentheopeningcontacts.Restri

ecanbebroughtaboutbytheincreaseoftheelectricfieldbetweenthe

contacts,duetothehighvalueofthearcvoltagewhenthearcentersthesplitterplates.Thegas1876-5343/092009BenthamOpen


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106TheOpenPlasmaPhysicsJournal,2009,Volume2FretonandGonzalez

TableI-1.ListofLowVoltageCircuitBrea

ersandtheirCharacteristics.DetailsontheCharacteristicscanbeFoundwithin[1]and[2]

TypeRatedCurrentsACVoltagesInterruptingCapacityUsualUseMiniatureCircuitBrea

er(MCB)


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thevoltagedropbetweenthetworailsthetotalvoltagebeginshigherthantheexistingnetwor

voltageleadingtoacurrentlimitationandsototheextinction.Thestudyofthelaststepnecessitatesacouplingoftheplasmamodelincludingtheelectromagneticeffectswithanetwor

model.Inthisoverviewpaperthislaststagewillnotbepresentedaswefocusthisreviewontheplasma.

Fig.(II-1).TypicalcurrentandvoltageinaLVcircuitbrea

er[3](tcod:contactopeningdelay,ti:arcimmobilitytime,tr:arcrunning,ts:arcinarcstac

).

Inlow-voltagenetwor

s,oneofthemainitemsofprotectionequipment,responsibleforthesafedistributionofenergyisthecircuitbrea

erinanairmedium.Aircircuitbrea

er(ACB)technologyhasremainedrelativelystaticoverthelasttwentyyearsbutthelatestproductsnowcomingontothemar

ethavealteredthesituation,stimulatingattentiontowardsadvancesinACBtechnology.Comparedtotheirpredecessors,modernACBnowoccupylessthanhalfthevolume(sizereduction).Thisisduetothetrendforsmallerareasbeingallocatedforswitchboardsandthe

demandforhigherpac

ingdensities[6].Nevertheless,toachievethissizereduction,majorinnovationswererequiredspecificallyinthecontacttechnology.Thissizereductionchangesthedynamicarcbehaviourinthechamberma

ingimprovementofthe

nowledgeofarcbehaviournecessary.

Theoptimallow-voltagecircuitbrea

erisanapparatusabletocutthecurrentquic

lywithoutanydeteriorationof


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OverviewofCurrentResearchintoLow-VoltageCircuitBrea

ers

itsstructureorofthenetwor

.Thetechnologicalfocusisontheissues:i)Howtodecreasetheinterruptingtimeandii)Howtodiminishapparatusdegradation.Thetwopointsbeingcorrelated.Thecuttingtimerepresentsthelifetimeofthearcfromtheopeningphasetosplittingandcurrentinterruption(Fig.II-1:fromtitotheendofts).Arcmotioninthechamberisdeterminedbythegasproperties(dependentontheamountofwallerosion),bytheelectromagneticforces(dependentonthecurrentintensity)andbywhetherexternalsystemsexisttooptimizetheireffects(pufferormagneticsystem[3]).Thestudiesarethusdevotedtotheinfluenceofthegaspropertiesonarcbehaviour,andtotheoptimizationofthemagneticfieldeffectproducedbythecurrentcarryingpathintheapparatusorbyanexternalsystem.Ofcourse,evenifthearcisquic

toarriveinthecuttingchamberLVCBtechnologyisbasedonthecurrentlimitation.Anincreasingthetotalvoltagebymultiplyingtheanodeandcathodedropsandbyproducinganelongationofarclengthisalsonecessary.Onesolutiontreatingthetwopointssimultaneouslyconsistsofintroducingasymmetricaldoublebrea

(presentedinparagraphIII-1,Fig.III-3).The

doublebrea

contactsystem[6]providestheopportunitytofurtherelongatethearctoensureevenfasterinterruptionoftheshortcircuit.ThetypicaltotalinterruptingtimeofaconventionalACBis70ms.Theuseofthedoublebrea

systemensuresinterruptioninlessthan30msandasthearcenergyissharedbetweenthetwosetsofcontacts,surfaceerosionisreduced.Thedoublebrea

principlewillbepresentedinpartIII1.2relatedtothestudyoftheOpeningofthecontact.

Fig.(II-2).ExampleoftemperaturefieldinaminiLVCBneartheelectrodes[18].Temperaturesgivenfrom1

Kto7

K(Step1

K)

([2004]IEEE)..

Aswecansee,arcpropertiesandarcbehaviourplayaveryimportantroleinbrea

ingsuccess.Nevertheless,reviewpapersgenerallydealwiththeelectricalaspectsofthearcanddonotproposeacompletefinedescriptionofthearcpropertiesandarcbehaviourduringthebrea

ingprocessfromitsignitiontothecurrentlimitationstage.Inthispaperweproposesuchoverviewofthemainresearchconductedbythecommunity.Wewilltry,allalongthepaper,toconfrontanddiscussexperimentalandtheoreticalaspects.

First,wepresentcurrentresearchintoarccharacteristics

andproperties.MacroscopicelectricalcharacteristicsofLVCBarefirstpresented.Then,measurabledatasuchastemperatureandpressurearepresentedandconfrontedwith

TheOpenPlasmaPhysicsJournal,2009,Volume2107

resultsfrommodels.Tofinishthissectionwepresentthewaythearccompositiononthemodels.Inthesecondpart,wefocusonthestudiesofarcmovementinLVCBgeometry:fromtheopeningcontacttothequenching


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chamber.Wefirstdiscussarcbehaviourduringcontactopening.After,wor

sdealingwitharcmovementinthechamberarepresentedandthen,partisdevotedtotheentranceofthearcbetweenthesplitterplates.

Fig.(II-3).Pressuremeasurementinfrontofthearc(uppertrace)andbehindthearc(lowertrace)[21].PhasesI,II,III,IV,VandVIcorrespondtovariouspositionsofthearc:(I)Immobilitytime,startingwithignitionofthearc.(II)Arcmotion.(III)Arcburnsasasmallbandinthechamber.(IV)Plasmaextendstolowerregionsofthearcchamber.(V)Equilibriumofforces,plasmastopsexpanding.(VI)Extinctionofarc([1998]IEEE)..

II.CHARACTERISTICSOFTHEARCCREATEDINTHECHAMBEROFALVCIRCUITBREAKERAfirststepinunderstandingofcircuitbrea

erisprobablyobtainingthearcscharacteristics.Themosteasilyobtaineddataaregenerallymacroscopicvaluessuchthevoltageandtheintensityinthedevice.Nevertheless,onlylittleinformationonthearccanbededucedfromthesevalues.Moresuitableinformationtocharacterizethearcwouldbeitslocaltemperature,itsshapeoritscomposition.Allthesedatacanbeobtainedfromtheoreticaland/or

experimentalwor

s.Inthisparagraph,weproposetodescribethesecharacteristicsandhowtheyaregenerallyobtainedintheliterature.

II-1.MacroscopicData,CharacteristicsofCurrentandVoltageVersusTime

AlotofpapersdealwithLVCBmeasurementsofthecurrentandtensioncharacteristicsversustime(as[3,7-9]).Theseelectricalquantitiesseemtobethemostbasicinformationtobeobtainedinthis

indofdevice.Typicalintensityandvoltagevariationsobtainedduringelectricalbrea

ingareplottedinFig.(II-1).Inthisfigurewecan

observefourzones:Thecontactsopenaftertheperiodtcod,whichcorrespondstoastepinthearcvoltage.Aftercontactopeningthearcremainsinthecontactregionforaperiodti.Theconductorsarearrangedtocreateaselfblastmagneticfieldwhichforcesthearcalongthedivergingarcrunners(periodtr)towardsthesplitterplates.Whenthearcreachesthesplitterplatesitisspitedintomultiplearcsinseries,resultinginahightotalarcvoltagerequiredforeffective


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108TheOpenPlasmaPhysicsJournal,2009,Volume2

currentlimitation.ThevoltagefluctuationsobservedinFig.(II-1)inthelastperiodareduetothearcpresencebetweenthesplitterplatesandtoitssegmentation.Inthisarea,theadditionalvaporscomingfromthesplitterplates,theindividualmovementofeacharcscolumnbetweenthesplittersandtheeventualpresenceofmetaldropletsleadtostrongvoltagefluctuations.Thesephenomenashouldbeta

enintoaccountinthemodeltowellrepresentthevoltagevariations.

Fromtheseelectricaldata,itisdifficulttodeduceinformationonthearcpropertiesorontheLVCBbrea

ingcapacity.Nevertheless,itshouldbementionedthatsomeauthorsli

eOnchiT.etal.[10]proposeelectricalmodelsbasedonthis

indofmeasurementandsimpleconsiderationsonthearcvoltage.TheyobtaininterestingpredictionsontheelectricalbehavioroftheirLVCBconfiguration.Unfortunately,theresultsdependontheLVCBgeometrystudiedandcannotbegeneralized.

II-2.PlasmaCharacteristicsTemperature,Pressure

Inordertohavemoredetailsonarccharacteristicsandarcbehavior,engineersandresearchersgenerallytrytoobtainitslocalfluidpropertiessuchitsenthalpyortemperature,itspressureanditsvelocity.Someofthesepropertiescanbeobtainedbothexperimentallyandfromtheory.Thetemperatureinthecircuitbrea

erchamberisexperimentallydifficulttoestimate.Thesmalldimensionsofthechamberandthelifetimeofthearc(fewtenmilliseconds)ma

emeasurementsdifficult.Tocompletethelistofdifficultiesencounteredinexperimentalsetupswecanquote:theincertitudeonthelocalpressurevalue,onthecompositionandontheplasmadimensions.Allthese

quantitiesareneverthelessnecessarytoexperimentallyestimatetheplasmatemperature.

ToimproveourunderstandingofplasmainLVCB,theoreticalmodelshavebeendeveloped.However,onedifficultyoftheoreticalstudiescomesisthephysicalcomplexityofthephenomenaandthethreedimensionalcharacterofthedevices.Brea

inginaLVCBneedsatemporaldescriptionofthearcandplasmabehaviourthroughouta3Dgeometry.Inordertocompareandtovalidateanytheoreticalmodel,onlyfewquantitiesareavailableeventhoughsomeexperimentalpapersexistonspectroscopicmeasurementsoronarcmotion.Someorders

ofmagnitudeofthetemperaturecanalsobegivenbythemodelbut,toour

nowledge,norealvalidationhasbeenreportedbetweenexperimentalandtheoreticalwor

s.

Weproposeinthefollowingparagraphstosumupthemain

nowledgeofplasmacharacteristicsreportedintheliterature.

ExperimentalInformationontheArc


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Variousexperimentalmethodstoobtainpropertiesofthermalplasmascanbefoundintheliterature.Themostcommonpropertiesmeasuredinplasmasaretemperatureandpressure.Thegasvelocityisthemostdifficulttoobtain.Inaplasmatorchortransferredarcforexample,thetemperatureisgenerallyobtainedbyspectroscopicemissionorabsorptionmethods[11].Thesetechniquesarebasedontheintegratedlightemittedorabsorbedbytheplasma.Fromthespectrallyresolvedmeasurementofthesequantitiesandthe

FretonandGonzalez

nowledgeoftheplasmacomposition,itispossibletodeducetheintegratedarcemissivity(orabsorption)versusthewavelength.Then,localdatamustbereconstructedfromtheintegrateddata.ThereconstructionisperformedbytheAbelinversionmethod[12]insymmetricalcasesortomographymethods[12]in3Dcases.Finally,thetemperatureisobtainedfromtheemissivity/absorptiondatausingtheassumptionofLocalThermodynamicEquilibrium

(L.T.E)[13]andmethodssuchBoltzman'sdiagramorabsolutelineintensity[11].InLVCBdevices,suchmeasurementsarequitedifficulttoobtainduetothe

transientbehaviorofthearcandtoits3Dshape.Moreover,theplasmacompositionisdifficulttodetermine.Indeed,beforecontactopeningtheLVCBareairfilled,butduetotheinteractionofthearcwiththeelectrodes,theplasticwallsandthesplitters,theplasmaisactuallycomposedofamixtureofair,organicvaporsandmetalvapors.Thedifficultiesthusencounteredprobablyexplainthelac

ofpapersonarctemperaturemeasurementsinLVCB.Wecanquotetwomaingroupswor

ingonthistopic.AFrenchgroupfromOrleanswhoarema

ingemissionandabsorptionmeasurementsonthearc[9,14]andaJapanesegroupwhoproposedanoriginalmethodbasedonspectralfilterstoobtainlocalmeasurementsofthearctemperature

[15-18].Initially,theFrenchgroupperformedemissionspectroscopicmeasurementsinaLVCB[9]wherethepresumedcurrentwas3

A.Morerecentlytheysetupaspecialauxiliarysourceproducinganintenselightthatenablesabsorptionstudies[14].Theythusestimatedtheintegratedabsorptionofthecopperatomiclinespresentinthearcduetoerosionofthecontacts.Thegreatadvantageofsuchmetallinesisthattheygenerallyhaveverydifferentenergylevelsbutveryclosewavelengths.Theycanthusbemeasuredbyamonochromatorinoneshotwhichisveryconvenienttostudytransientphenomena.Fromtheseintegratedlines,theauthorssimulatedtheabsorptionspectrum.Then,withoutreconstruction,theyuseda

Boltzmannsdiagramtodeducethemeantemperatureofthearc.Theyobtainedavalueequalto0.77eVthatistosay8800K.Itshouldbenotedthatthistemperatureislowcomparedtousualtemperaturesinthermalplasmas(1520

K).Nevertheless,itcorrespondstothemeantemperatureobtainedfromatomiccopperlineslocatedonthesideofthearc.Asnoreconstruction(suchastomography)isused,thismeasurementonlyrepresentsameantemperatureofthehotgasaroundthearc.TheJapanesegroupproposesanothermethod,basedonplasmaemission,toestimatethearc


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temperatureinacommercialLVCB((ratedcurrent12Ainnormalusewithoutshortcircuit)andawor

ingvoltageofabout380VAC).Novalueforthecurrentintensityduringshortcircuitisgivenbytheauthors.Intheirdevice,silverispresentintheelectrodessotheyusedsilveremissionsfortheirmeasurements.Intheirexperiment[17,18],theydonotuseamonochromatorbuttwoCCDcolorcamerasandtwocolorfilterscenteredonvariouswavelengthranges[18].Fromtheratiobetweenthelightcollectedthroughthetwofilters,theauthorsestimateameanarctemperature[16].TheadvantageoftheirmethodisthattheuseofCCDprovidesa2Dpictureofthewholearcintermsofsilveremission.Inanotherpaper,theseauthors[17]appliedatomographicmethodtoacommercialmini-circuitbrea

erCJX1-12/22(HailiElectrical).Theauthorsusetheset-upofpaper[16]


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ers

whichisimprovedtoobtainthreedifferentimagesofthearcwitheachfilter.Fromtheseimages,applyingthetomographicmethod,theauthorsestimatethelocalarctemperaturesforallplanes.AnexampleisgivenforaplaneneartheelectrodesinFig.(II-2).WecanobservefromFig.(II-2)thatthetemperaturededucedbythismethodwasnotveryhighintheplasmacoreasitdidnotexceed8000K.Generally,inthermalplasmasclosetotheelectrodesonecanexpecttemperaturesintherange10to20

K[19].Thisdifferencecanbeexplainedbythemethodusedforthemeasurements.ItisbasedontheemissionofAgatomiclineswhichpresentanemissionmaximumbetween7000and9000K.Itisthereforeexpectedtomeasuresuchlowtemperatures.

Inordertoconcludeontemperaturemeasurements,fromthesetwoapproachesfoundintheliterature,wecanseethatonlytemperaturesinthefringesoftheplasmahavebeenexperimentallyobtained.AsnoticedbyFretonP.etal.[20],careneedstobeta

enontemperaturemeasurementsnottoconfusethistemperaturewiththatofthearccore.The

plasmacoretemperature,inLVCBisdifficulttoobtainduetothecomplexityofachievingspectroscopicmeasurementsonasmalltransientarc.

Otherquantitiesthathavebeenexperimentallyobtainedintheliteratureconcernthevariationofpressureinthechamberduringthearcmovement[21,22].Inthewor

ofLindmayerM.andPaul

eJ.[21],thestudyismadeinasimplifiedLVCBgeometry,withoutsplitterplates,wor

inginair(under240V,50Hz,8

ARMS).Themeasurementsweremadeusingtwopiezoresistivepressuretransducerslocatedatthefrontandthebottomofthechamber.Withthesetwosensors,theauthorsmeasuredthepressure

evolutionbehindandinfrontofthearcforthreedifferentchambergeometries.AnexampleofrelativepressuremeasurementforoneconfigurationisgiveninFig.(II-3).Duringthearcmovementthereisanincreaseofpressureinthechamberwhichreaches3bars(startingfromatmosphericpressure).Thepressureincreaseinfrontofthearcisessentiallyduetotwoeffects:theheatingofsurroundinggasbythearcandtheablationofelectrodesandwallmaterial.Theauthorsconcludethattheincreaseofpressureinthebac

ofthearcalsodependsonthecrosssectiondimensionsofthechamber.Thewiderthechamber,thelowerthepressureincreases.Theauthorsnoticedthattheriseinpressureatthebac

ofthearccouldplaya

eyroleon

restri

esinthechamber.ThesameresultswerefoundbyDomjeanE.etal.[22].

Anotherwaytoobtaininformationonthearccouldbetomodelitsbehavior.Thisapproachispresentedinthenextparagraph.

TheoreticalInformationontheArc

Beforetheincreaseofcomputercapacities,modelswere


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generally2Dandsimplified(li

ein[22]or[23]).Thesemodelsaregenerallyquestionable:howcana3DobjectsuchthearccreatedinaLVCBberepresentedin2D?Nevertheless,sincetheendofthenineties,alotofpaperspropose3DtransientmodelsforLVCB[21,24-28].Forthearcdescription,thesemodelsgenerallyconsidertheplasmaasanelectricalNewtonianfluidwhichcanbedescribedbyNavierSto esfluidequationsandpotentialscalarand


vectorequations.InaCartesiansystem(Ox,Oy,Oz),theplasmaisdescribedintermsoftemperatureT,pressureP,velocitiescomponents(vx,vy,vz),potentialscalarV,potentialvectorcomponents(Ax,Ay,Az)andotherdeducedvariablessuchtheself-inducedmagneticfield(Bx,By,Bz)orthecurrentdensities(jx,jy,jz).Ifmixturesofgasesareta

enintoaccount,amassfractionequationmustalsobesolved[24].Alltheseequationsarewrittenintheformofthegeneralizedequation(II-1)

....

..

....

..

+(..v)=(....

)+S(II-1)

..t

Inthisequation,isthevariabletobesolved,themassdensity,....thediffusioncoefficientandS..thesourceterm.Forexample,fortheenergyequation,canbe:hthestatic

enthalpyofthegas,....is../Cpwhere..isthethermalconductivityandCpthespecificheatandS..correspondstoadditionaltermsinordertota

eintoaccounttherareofwor

duetopressureforces,therateofwor

duetoviscousstresses,jouleeffectandradiativelosses.Moredetailsforotherequationscanbefoundin[29].

ForallthemodelsofLVCBintheliterature,thecommonhypothesesarethefollowing:


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1-TheplasmaisalaminarNewtonianfluid

2-TheplasmaisassumedtobeinLocalThermodynamicEquilibrium(LTE)

3-Thesystemisgenerallythreedimensional(3D)anddescribedinCartesiangeometry(Ox,Oy,Oz)

Withtheseequationsandassumptionsitispossibletoobtainthearccharacteristicsinthechamber.AtypicaltemperaturefieldobtainedbysimulationofaLVCBinair(I=100A)ispresentedinFig.(II-4).InFig.(II-4)wecanseethatamaximumof19

KisobtainedinatypicalLVCBsimulation.Thisvalueismoreusualforthermalplasmamediumthanthetypicalonesobtainedexperimentallyinthesame

indofdevices.Neverthelessasexplainedbefore,thetheoreticaltemperaturesofthearccorecannotreallybecomparedwithexperimentaltemperaturesofthefringesandtodate,itseemsthatexperimentaltemperaturesofthearccorehavenotbeenobtained.Obviously,temperatureisnottheonlydatathatcanbeobtainedfrommodels.Pressure,velocitiesandcurrentdensitydistributionscanalsobe

calculated.Nevertheless,authorsgenerallyfocustheirreportsontemperaturefields.However,eventhoughcomputationalfluiddynamicsCFDmodelsseemtogiveinterestinginformationonarcproperties,attentionshouldbepaidtovariousdifficulties:1)which

indoftransportandthermodynamicpropertiescanbeusedinmodels?2)Howcantheexternalmagneticfieldinthechamberandthedisplacementofthearcbeta

enintoaccount?3)Howcantheinitialinstantofcontactopeningbestudied?4)What

indsofvalidationareavailableforthemodels?Thefirstpointcorrespondstothearcpropertiesandisdiscussedinthenextparagraph.Points2and3willbediscussedattheendofthispaper;point4iscoveredallalongthepaper.

Onemorepointcommontoexperimentalandtheoreticalresultsis5)howresultsobtainedgenerallyinsimplifiedgeometrycanbeappliedtorealbrea

ingdevices?IndeedduetothecomplexityoftheLVCBdevice,extrapolationon


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arcbehaviourinrealdeviceshouldbeta

enwithalotofcare.Theobtainedresultsinsimplifiedgeometryaregenerallycorrelatedtoparametricstudiesandshouldbeseenasindicatorsfortheunderstandingofarcbehaviour.

Fig.(II-5).Equilibriumcompositionof10%PA690%Airplasma[26].

Fig.(II-4).ExampleofmodelingtemperaturefieldsforLVCBwor

inginair(I=100A)[26].

II-3.CompositionoftheArc

Thearcinthechambermovesandalongitsdisplacementinteractswiththerails(electrodes),thesidewalls(PA66walls)andatthefinalstageofthebrea

ingprocesswiththesplitterplatesleadingfromanairmediumtoamediumcomposedofairwithmetalandorganicvapours.Twoapproachesaredevelopedinthemodels:thefirstconsistsofstudyingarcbehaviourassumingahomogeneousgas

composedofairorairwithorganicvapours[30],thesecondconsistsoftheimplementationinthemodelsofanerosioncodeabletogeneratevapourdependingontheenergytransferredtothewall[26].Thetypesofvapourthatcanbeablated:iron,silver,carbon,hydrogen,oxygen,nitrogenorcopperaresonumerousthat,toour

nowledge,nomodelsseparatelyconsiderandtraceeachvapour.

Experimentaldiagnosticsbasedonimagerycanpredicttheexistenceofmetallicvapoursbychec

ingtheassociatedwavelength,neverthelessthequantificationremainsproblematic.Below,wepresentsomestudiesonthissubjectfoundintheliterature.

TheoreticalInformationonthePlasmaComposition

Variouspapersdealwithcalculationofcomposition,thermodynamicpropertiesandtransportcoefficientsforCHONmixtures[26,31].ThecalculationsarebasedonLTEassumptionsandgivethecomposition,thedensity,thespecificheat,thesoundvelocity,thethermalconductivity,theviscosityandtheelectricalconductivityversustemperatureandpressure.AnexampleofL.T.Eplasmacomposedof10%PA-6and90%airfor1atmisproposedinFig.(II-5).Withthepresenceoftheorganicvaporintheair,thecreationofabundantC-H-O-Ncompoundsisseento

occuratlowtemperature.Thesecompoundshaveagreatinfluenceontheproperties,aspresentedinFig.(II-6)wherethethermalconductivitiesofpureairplasmaand90%air10%PA6areplottedversustemperature:thedifferencesbetweenthetwoplasmasareclear.Additionalpea

sappearatlowtemperaturesandamplitudeschangeathightemperatures.

Fig.(II-6).Thermalconductivitiesfor100%airand90%air0%


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PA6mixtures.

Inordertostudytheinfluenceofgaspropertiesonarcbehaviortwoapproacheshavebeenpursued.Asimplifiedapproximationshouldbetoconsiderhomogeneousvaporproportioninthewholecircuitbrea

ergeometry[26].Theplasmacompositionversustemperatureiscalculatedforagivenproportionandincludedinthemodeldataban

s.Inthiscase,thereisnoneedofanadditionalmassfractionequationandaqualitativeinfluenceofsuchplasticvaporscanbeseenonthearcbehavior.In[26]forexample,itwasfoundthatthepresenceofplasticvaporledtoanincreaseofthearcvoltageandadecreaseofitssize.In[26]restri

eoccurrencealsoseemstobeinfluencedbytheproportionofPA66.Inreality,themixtureofplasticvaporswithairisnothomogeneous.Indeed,plasticvaporscomefromtheerosionofthewallsanddiffusethroughtheplasmaovertime.Inordertota

eintoaccountthepresenceofvaporsinamodel,anerosionmodelshouldbedeveloped.Moreover,asplasticvaporsandairarereactivegasesspecialtreatmentoftheequationsisneeded.Murphyproposedageneralizedsolutionforsuchgases[32]byaseparationofeachspeciesofthemixtureintotwomaincomponentsAandB.Forthesetwoartificialcomponentshecalculatesnewpropertiesand

diffusioncoefficient.Inthisapproach,amassfractionequationforgasAorBmustbesolvedandadditionaltermsmustbeaddedtotheenergyequation.Thegaspropertiesdependlocallyontheplasmatemperature,pressureandmassfraction.Thisapproachhasalreadybeenusedforhigh


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ers

voltagecircuitbrea

ersimulation[33]butnotyetforLVCB.Thedifficultyinsuchanapproachistoseparatethespeciesintotwogases.Inrealcircuitbrea

erthevaporscanbeexperimentallyobserved.Neverthelesstheirquantificationinthemediumduetothedifficulties(Timescaleand3Dproblem)

eepsdifficult.Duetothefactthatthemodelcurrentlyusesimplifiedgeometryandthatitexistsadifficultytorepresentsodifferentvaporsdistributions(Fe,Ag,Cu,PA66)nodirectcomparisonarepossible.NeverthelessevenifdirectcomparisonisnotpossibleitisexperimentallyandtheoreticallyobservedthatthePA66vaporspresencetendstoacceleratethearcvelocitydisplacementinthechamber[26].

Anotherapproachtotreatcomplexmixturesofgasesconsistsinthedevelopmentofa

ineticmodelandtheresolutionofaconservationequationforeachspeciesoftheplasma.Thisapproachta

esintoaccountdeparturesfromchemicalequilibrium.Thethermodynamicandtransportpropertiescalculationprogramneedstobeincludedintheplasmadescriptionproblemandcalculateddirectlyforthe

geometryforeachpointduringconvergence.Duetothetimecalculation,thetransportandthermodynamicpropertiesusedassumeL.T.Eandonlydeparturesfromtheequilibriumofthespeciesdensitiesareestimated.AnexampleofsuchanapproachisproposedbyMercadoCabreraA.etal.ina1Dtransientmodel[30]inair-plastic-metalmixtures.Intheirmodel,theauthorsdeveloped138chemicalreactionsandconsidered36speciesintheplasma.Theyshowthatawea

departurefromchemicalequilibriumexists.However,suchamodelheavyoncomputertimeandsocanhardlybeenadaptedforcomplex3Dmodels.

Allthestudiespresentedabovedealwithplasticvapors

intheplasma.Nevertheless,metalvaporsalsocomefromtheelectrodes(noplasticvaporsareconsidered).ArecentpaperofMaQetal.[24]reportsthestudyofLVCB(wor

ingatatmosphericpressurewithI=150A)inthepresenceofcoppervaporscomingfromitselectrodes.Toachievethisstudy,theauthorscalculatethemassfractionofcopperintheairplasma.Airandcoppervaporsareconsideredtoactastwonon-reactinggases.TypicalfieldsofvaporsobtainedbytheseauthorsforvarioustimesarepresentedinFig.(II-7).Inthisfigure,wecanseetheincreasewithtimeofcoppervaporconcentrationinthedomain.Themodelshowsthatthisleadstodecreasesinarctemperature,arcmotionandarcpressure.Unfortunately,

theirresultswerenotconfirmedwithexperimentaldata.

ExperimentalInformationonArcComposition

Experimentally,thepresenceofmetalvaporsisconfirmedbythetemperaturemeasurementmethodsdescribedbefore.Theyarebasedontheemissionlinesofcopperorsilvercomingfromtheelectrodes.However,theablationofplasticwallshasalsobeenstudiedbysomeauthors.ForexampleDomjeanE.etal.[22]reportedthe


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measurementofwallablationbyweighingthesidewallsbeforeandafterbrea

ing.AsshowninFig.(II-8),theauthorsfoundthattheablatedquantitiesofplasticaredirectlyproportionaltotheJouleenergyabsorbed.

Inadditiontothesemeasurements,theauthorsproposeanablationmodelwhichta

esintoaccounttheenergyreceivedbythewallfromradiationandthermalconduction.


Agoodagreementbetweentheoreticalandexperimentaldatawasfoundandtheauthorsconcludethatmorethan90%oftheenergyneededtoablatethewallisprovidedbytheabsorptionofradiationfromthearc.Thisresultsupporteddatafoundpreviouslybyotherauthors[34].

Fig.(II-7).CoppervaporconcentrationforvarioustimesinaLVCBsimulation[24].

Fig.(II-8).AblatedmassofplasticwallsversusJouleheating[22].

Asmentionedbefore,anotherimportantpointforagoodunderstandingofthebrea

ingprocessconcernsthedisplacementofthearc,duringcontactopening,inthechamberandinthesplitters.

III.ARCMOVEMENTINLVCBA

eyelementinthebrea

ingprocessisthestudyofarcdisplacement.Indeed,thebrea

ingefficiencydependsonthetimenecessarytocutthecurrent,andthusonthetimeitta

esthearctomovebetweenthecontactsandthesplitters.Thismovementcanbedescribedinthreesteps:

Openingofthecontacts,thearcformsandstaysbetweenthecontacts

Thearcispushedbyseveralforcesandmovesinto

thechamber.Onceinthechamberitispushed

towardsthesplitterplates

Thearcentersthesplitters.

Eachstephasbeenstudiedexperimentallyandtheoreticallyintheliterature.Thefirsttwopoints,are


17/36


coveredjustbelow.Thelastchapterofthispaperisdevotedtothethirdpoint.

III-1.OpeningoftheContacts

Thefirststepinthebrea

ingprocessiscontactsopeningandthecreationofanarc.Thisfirststepisofprimaryimportance,as,inthebrea

ingprocess,thearcshouldremainforaslittletimepossibleonthecontacts.Thistimeisgenerallycalledtheimmobilitytime.Theliterature[8,35,36]identifiesthevariousparametersthatcanplayaroleintheimmobilitytime:

Theopeningspeedofthecontacts

Thematerialthecontactsaremadeof

Ventingofthegeometry

Polarityofthecontacts.

Arccurrent

Variouspapersstudytheinfluenceofthesepointsexperimentally[8,35,36]ortheoretically[37,38].Wepresentsomeofthesepapersabove.

ExperimentalWor

onOpeningContacts

ExperimentallyaquitedetailedstudyofthesubjectwasdonebybyMcBrideJ.W.andPechrachK.[35].Intheirpapertheyreportedvariousexperimentsondifferentcontactmaterials(seeTableIII-1),contactvelocities(4,5.5and10m/s),pea

currents(50A,1.4

Aand2

A)andventingarrangementsofthegeometry(open,cho

edoffclosedventsatthebottomofthegeometry).Inseveralcasestheyalsomeasuredcurrentandvoltageandusedanimagingsystembasedonopticalfiberstoobtainpicturesofthearc(1000images/ms).

TableIII-1.ContactMaterialsUsedin[35]

MaterialCompositionCM-3Silvercadmiumtinindiumoxides(15%metaloxides)CM-4Silvercadmiumtinindiumoxides(18%metaloxides)AgNiSilverNic

el(10%)HGHSilverNic

el(0.15%)M2-1Silvertinindiumoxides(11%tinindiumoxides)Ag\CSilvergraphitecontactsM2Silvertinindiumoxides(15%tinindiumoxides)

Theauthorsinvestigatedcontactmovementtimefor


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differentmaterials.Intheirgeometriesonecontactwasmobilecontactandonefixed.Forthemobilecontact,theauthorsdeterminedtwotimes:tcmandtcf.tcmisthetimedifferencebetweenthestartofthearcandapointwheretherootreaches10mmdisplacementandtcfthetimebetweenthestartofthearcandthetimewhenthearcbeginstomoveawayfromthecontact.ThesetimesarereportedinFig.(III1)forallthematerialstested.Intheirconditions,movementofthearcawayfromthecontactdidnotdependcloselyoncontactmaterials:thedurationsinvolvedwerebetween300and400s.Theyconcludedthatthecontactmaterialhada

FretonandGonzalez

wea

influenceonthemotionofthearcrootawayfromthecontactregion.AnotherstudyproposedbyBelbelE.M.andLauraireM.[8]showsinfactthatthematerialdoesnotreallyplayasignificantrolewhenthecontactspeedexceeds5m/s.Intheirpaper,BelbelE.M.andLauraireM.didnotstudyexactlythesamematerialasin[35]buttheyfoundthatforlowervaluesoftheopeningvelocity,theimmobilitytimecanbemultipliedbytwo,dependingonthematerial[8].

Fig.(III-1).Influenceofcontactmaterialsoncontacttimeforapea

currentof2

A,10m/scontactspeed[35]([2001]IEEE)..

Theinfluenceofpolarityonthemovementofthearcfordifferentgeometrieswasalsostudied[35].Fromthisexperiment,itwasfoundthattheventingoftheLVCBhasagreatinfluenceonarcmovement.Forthefixedcontact,polarityseemstoplaynorole.Thisisnotthecaseforthemovingcontactwherepolaritycombinedwithdifferentventingplaysanimportantrole.ThiseffectisreportedinFig.(III-2)wherethetimetcmisplottedversusventareaforthetwopolarities.

Fig.(III-2).Influenceofventareaonmovingcontacts[35].


19/36


ers

Whentheventsareopen,thearcmovesfasterinthecathodicpolarity.Theauthorsexplainthissituationinpartbythefactthatthereisagreaterenergytransferbetweenthearcandthecontactswhenthepolarityiscathodic.Thisgrowthofenergytransferincreasestheproductionofmetalvaporswhichareblownwhentheventsareopen.Thevaporfacilitatesthedisplacementofthearcawayfromthemovingcontact.Nevertheless,forthisfirstanalysis,McBrideJ.W.andPechrachK.[35]consideredthattheflowisthermallydrivenanddoesnotta

eintoaccounttheeffectofmagneticforceswhichcanbestrong,asmentionedbyPetrachK.etal.[39].

AfinalexperimentproposedbyMcBrideJ.W.andPechrachK.[35]showsthatthehigherthecontactspeed,thelowertheimmobilitytime.ThesameresultwasfoundbyBelbelE.M.andLauraireM.[8].

Theseexperimentalresultssuggestthattheincreaseofthecontactspeedandthechoiceoftheventareawilldecreasetheimmobilitytimeonthecontact.Anotherwayto

achievethisconsistsofadoublearcingchamberdesignasproposedbyAbriA.etal.[40].Inthis

indofchamber,twoarcsarecreatedfrommovingcontacts(Fig.III-3).Thetwoarcspresentoppositepolaritiesandrepeleachother.Thiseffectdiminishestheimmobilitytimeofthearconthecontacts.

Fig.(III-3).Doublearcingchamber[40]([1991]IEEE)..

TheoreticalStudiesonOpeningContacts

Fortheoreticalstudiesaboutarcbehaviorduringcontact

opening,wecanonlyindicateonegroupwhohaswor

edonthesubject.WuY.etal.[37,41]proposeda3DCFDmodelofanarcinsimplifiedcircuitbrea

ergeometry.These


authorsdescribedtwophases:theopeningofthecontact(byamovinggrid)andthemovementofthearcinthechamber.Thesimulationwasdoneforaconstantcurrent(1.5

A)andaconstantexternalmagneticfield(5.5mT)pushesthearcawayfromthecontacttothechamber.TheplasmaisairinLTEandnovaporfromelectrodesorwallsisconsidered.Aswewillseelaterinthissection,animportantpointforthe

modelsisthedescriptionofthearcdisplacementontheelectrodes.ThispointisnotclearlydescribedbytheauthorsandseemstobebasedonapreviouspaperfromKarettaF.andLindmayerM.[28].AnexampleofresultsintermsoftemperaturefieldisproposedinFig.(III-4).Themovingcontactistheanodeandwecanseethearcjumpfromthemovingcontacttotheelectrodesenabledbyhotgasflow.Itcanbeseenthattheexternalmagneticfieldstronglyinfluencesarcshapeasthearcispushedawayfromthecontacts.


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Inadditiontothemodel,theauthorsphotographedthearcandmeasuredthearcmovement.AcomparisonbetweenexperimentandmodelisproposedinFig.(III-5).Dashedlineswithsymbolsareexperimentalcurvesandplainlinestheoretical.Thecomparisonofcurves1and3relatedtothemovingcontactshowsthatthearcvelocitypredictedbythemodelisoverestimatedcomparedwiththeexperimentalone.Ananalysisofcurves2and4forthefixedcontactsleadstothesameconclusions.Notethatintheorythearcrootvelocitywasthesame,butthiswasnotobservedexperimentally.

III-2.MovementoftheArcintheChamber

Inthisparagraph,wedescribethebehaviorofthearcinthechamber,onceitleavesthecontacts.Inthechamber,thearcisgenerallypushedtowardsthesplittersbythemagneticfieldcreatedbytheconductorsinthechambercombinedwiththermalflowandoverpressureeffects.Duringthisdisplacement,unwantedrestri

esofthearccanoccur.Wepresentaboveexperimentalandtheoreticalwor

sonthistopic.

ExperimentalWor

sontheBehavioroftheArcinChamber

Experimentally,arcbehaviorinthechambercanbestudiedbyanalyzingtheevolutionofcurrentandvoltagevariations.Themeanresidencetimeofthearcinthechamberisthusestimated,andrestri

ephenomenaareobserved.FievetC.etal.[23]reportastudyonre-stri

esinLVCBwheretheypresentsuchelectricalmeasurements.Thecurvesobtainedinasimplifiedcircuitbrea

ergeometrycoupledwithasourcewhichdeliversa5

Apea

value50Hzsine-shapedcurrent,areplottedinFig.(III-6).Theauthorsstudiedresidualcurrentthroughoutthearcing

contactregionafterthearchadleftit.Itisplottedonthetopofthefigurealongwithmeasurementsfrompressuresensors.Restri

ephenomenacanbeobservedonthepotentialcurve.There-stri

esaresystematicallycorrelatedwithanincreaseinresidualcurrent.Stepsshouldbeta

entopreventthemastheydelaythebrea

ingprocess.TheauthorscoupledthesemeasurementswithdiagnosticspectroscopyonC2band.Theyshowedthatre-stri

esgenerallyoccurinareaswherethegasisattemperaturesofover4000K.Theirmeasurementsarelin

edwitha2Dmodel.


21/36


Fig.(III-4).Three-dimensionaltemperatureevolutionoftheairarcplasmaduringtheopeningofthemovingcontact.Onlytemperatureshigherthan3000Kareshownforclarity[41]([2008]IEEE)..

Fig.(III-6).Oscillogramtracesandmainphasesduringatypical

Fig.(III-5).Arcpositionversustime[37].

circuit-brea

ingoperation[23].


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ersTheOpenPlasmaPhysicsJournal,2009,Volume2115

Fig.(III-7).Comparisonbetweenimagingtechniqueandmagnetictechniqueforpredictingthearclocationinthechamber[45].

Tostudythebehaviorofthearcinthechamber,moreprecisemethodsconsistinmeasuringitsdisplacementbyimaging(opticalfiberorCCD)ormagneticsensors.Suchmeasurementshaveregularlybeenreported[21,42-44].AveryoriginalsolutionwasdevelopedbyaFrenchgroupwhomeasuredarcdisplacementinaLVCB(withapea

ofcurrentof4

Aandatotalvoltageof360V)usingprobesbasedonHalleffectcoupledwithaninversemethod.Theirsensorsmeasurewithafrequencyof1MHzandarenotdependentonthetransparencyoftheLVCBwalls.Byconsideringthearcasasegmentofcurrent,theinversemethodprovidestheexactarclocationinthechamber.Tovalidatethetechnique,theycomparedthedataobtainedbytheinversemethodwithimagesofthearcobtainedbyaCCDcamerainasimplifiedgeometry.AnexampleoftheirresultsisplottedinFig.(III-7)[45].

Thesamegroupofauthorsusedthesamemethodinanotherpaper[46]andestimatedthevelocityofarcdisplacementontheconductorrails.ItdependsonthemaximumvalueofthecurrentasshowninFig.(III-8).Thevalueobtainedisconsistentwithotherresultsbasedonclassicalimagingsystems[44].

Fig.(III-8).Theaveragespeedofthearcversusthepea

valueoftheswitchedoffcurrent[46].

TheoreticalStudiesoftheBehavioroftheArc

ObtainingtheoreticalresultsintheLVCBchamberisarealchallengeduetothedifficultytota

eintoaccountthearcmovementandtheforcesactingonthearc.Onedifficultyistoreachagooddescriptionoftheexternalforcesactingonthearcandespeciallytheexternalmagneticfieldcreatedby

theconductorsintheLVCB.Afirstsolutionconsistsofcalculatingthecurrentdensityoverthewholedomain(conductorsandplasma)andofsolvingtheBiot-Savartformulationtodeducethemagneticfield.Thismethodwasproposedin[27,28].Nevertheless,itisverytimeconsumingandnotveryconvenient.Anothermethod,suitedfor

rectilinearconductorswasproposedin[26].Itconsistsofcalculatingtheexternalmagneticfieldbyusingasimplifiedformulationofasinglewireanddeducingtheinducedmagneticfieldbyusingthepotentialvectorapproach.Finally,someauthorsproposedtota

etheexternalmagneticfieldintoaccount,onlybyaconstantvalue[37].Thislastapproachisnotreallysatisfactory.Theproblembecomesquitecomplicatedinthepresenceofferromagneticmaterialsli

eiron,inwhichcaseavectorpotentialapproachisproposedthatta

esintoaccountthematerialpermeability[4,


23/36

47].

Oncetheexternalmagneticfieldhasbeenestimated,anotherproblemistota

eintoaccountthedisplacementofthearcunderthefield.Toachievethis,twomain

indsofmodelexistintheliterature.Oneisbasedontheelectrodetemperatures;itcanbecalledthethermallydrivenmodel(TDM)andwasproposedbyKarettaF.andLindmayerM.[28].Thismodelwasthenusedinseveralpaperssuchas[32].AsecondmodelwasproposedbySwierczins

yB.etal.[26]andvalidatedbyYangQ.etal.[44].Itcanbecalledtheelectricalconductivitydrivenmodel(ECDM).Thebasisofthesetwomodelsisasfollows.

TDMwasproposedthefirsttimein1998byKarettaF.andLindmayerM.[28].TheseauthorsproposedtosatisfythefollowingconditionforthecurrentdensitydistributionJn,iatthecathode:

N

I=Jn,i

Ai(III-1)i=1

where:Iisthecurrentintensity,AitheareaoftheboundaryelementI,NthetotalnumberofelementaryelementJn,imustsatisfyequation(III-2)


24/36


Ci

Jn,i=IN(III-2)

..C

,NA

=1

andthecoefficientsCihavethefollowingform:

....W

Ci=Ti2exp

....i,N(III-3)

..

bTi

WecanseethatthecoefficientsCidependonthetemperatureaccordingtotheRichardsonslawwhichdescribesthethermoemissionofthecathode.Wisthewor

functionoftheelectrodematerial,Tithetemperatureoftheithelementand..i,Nistheelectricalconductivityinthecelladjacenttoelementi.Withthismodel,theauthorspredictedthepositionofthearcanditsdisplacement[28].Theyfoundanarcvelocitycloseto90m/sforacurrentintensityof

1000A.ThisvaluewasinagreementwiththeexperimentalvaluespresentedinFig.(III-8).Thismodelseemstobesupportedbyphysicaldata(Richardsonslaw)butisdebatable.Indeed,thetemperatureusedinequation(III-3)isonlydeducedfromaheatfluxbalance,withoutconsideringanysheathorphenomenonbetweentheplasmaandtheelectrodes.Moreover,theauthorsusedthesamemodelforthecathodeandtheanodewhereasthethermalbehaviorofthesetwo

indsofelectrodesistotallydifferent.

ThesecondmodelwasdevelopedbySwierczins

yB.etal.[26].Itisbasedontheassumptionthatthemostprobablelocationofthearcrootiscorrelatedwiththeelectrical

conductivitiesoftheplasma.Inordertoestimatethislocation,theauthorsdividedthegeometryundertheelectrodesintounitaryvolumesaspresentedinFig.(III-9).

Fig.(III-9).Descriptionoftheseparationofthegeometryinvariousslicestoenableaself-coherentdisplacementofthearc[26].

Foreachunitaryvolume,ameanelectricalconductivityiscalculatedandtheauthorsassumedthatthelocationofthe


25/36

arcrootcorrespondstotheelementaryvolumepresentingthehighestvalueofconductivity.Foracurrentintensityof100A,theauthorsfoundaspeedofthearccloseto10m/s,whichiscoherentwiththeexperimentaldatapresentedinFig.(III-8).Moreover,thismodelwasreusedbyYangQ.etal.[44],whocomparedtheresultsofa3DmodelandexperimentalmeasurementsofthearcrootpositioninasimplifiedLVCBgeometry.ThiscomparisonisplottedinFig.(III-10)andwecanseeagoodagreementbetweenthepredictionsofthemodelandthemeasurements.

FretonandGonzalez

Fig.(III-10).Comparisonofarcrootpositionsbysimulationandexperimentundertheinfluenceofanexternalmagneticfieldof4mT[44].

Fromtheseresults,wecanconcludethatthetwomodels(TDMandECDM)giveagoodestimationofthearcrootmovementinthechamber.TDMisneverthelessquestionableasitisbasedonthermaleffects,whereas,atthesametime,theboundaryconditionforthetemperaturedoesnotta

ewellintoaccounttheinteractionbetweenthearcandthe

electrodes.Itshouldbenotedthatthebestwaytota

eintoaccountthedisplacementofthearcshouldbetodevelopmodelsforthecathodeandtheanodesuchthoseproposedin[48,49]forsimplifiedgeometries.Thereasonthatthiswor

hasnotalreadybeendoneisprobablyexplainedbythedifficultiesofusingthesemodelsincomplexsituations(transient,inair,inmovement...).

III-2.TheArcintheSplitterPlates

Theinterruptionofashortcircuitofseveral

iloAmpsisperformedbythedisplacementoftheelectricalarcfromanignitionareacorrespondingtothepositionoftheopening

contacttoaquenchingchamber.Thequenchingchamberconsistsofparallelsteelplates.Thebrea

ingtechniqueisbasedoncurrentlimitationwhichmeansthattheeffectivepea

valueofthearccurrentisfarbelowtheprospectivecurrentvalue.Thistechniquerequiresanextremelyrapidriseofthearcvoltageobtainedbysqueezingandsplittingthearc.Duringthisphaseanewarcmayre-appearundercertainconditionsatthebac

intheignitionareaandthearcinthechamberthenextinguishes.Thisphenomenoniscalledarcre-stri

ing,arcbac

commutationorarcre-ignition.Duringthecurrenttransferbac

wardsfromthesplittingplatestotheignitionregion,analysiswithanultrafastelectronicimagerytechniquehasshownthattwoarcsstandinparallelduring

thisphase[23],atthesametimesimulationshaveshownthatthegasevaporatedfromthesidewallplaysasignificantroleinthere-stri

eprocess[23].

TheoreticalWor

swithanArcintheSplitterPlates

Thecut-offcurrentoccurswhenthearcislocatedinthesplitterplates.Modelingofarcsegmentationisalwaysdifficult.Indeedthedistancebetweentwosplitterplatesisverysmallandinrealitythearccolumnbetweentwo


26/36

splittersisreducedtotheanodeandcathodesheaths.This


27/36


ers

meansthatadescriptionofnonequilibriumplasmaisnecessarytomodelarcbehaviorsatisfactorily.Toour

nowledgenowor

shavebeenreportedthatta

eintoaccountsuchphysicsandthedescriptionconsistsofthearcexistencebyacontinuityofthecurrentdensity.Somewor

s,suchas[47],dealwiththeinfluenceoftheferromagneticplatesonarccolumnmovement.Otherauthors[43]haveshownthewea

influenceofthenatureofthesplittingplates(copperorsteel)onarcbehaviourandonrestri

ing.

Asapreliminarysteptomodelarcbehavioraroundsplitterplates,LindmayerM.etal.[50]presentintheirgeometryaninsulatingbarrierofvaryinglengthbetweentwoparallelcopperarcrunners.Neverthelesstheauthorsconcludethatfurtherwor

isnecessarytoaddaphenomenologicalarcrootmodelintothecompletesimulationprocess.Inrealitythemodelpresentedbytheauthorsincludespoorrepresentationofphysicalphenomenaandthesidewallsaremodeledbystationaryheatboundaryconditionswithafixedtemperatureof2000K.Itseemsdifficultwithsuchanapproachtota

eintoaccountthe

vaporscomingfromthesplitterplates.Themethodoftheauthorsconsistsinconsideringathinlayerequalto0.1mmwithanonlinearresistancecompletelysurroundingthesplitterplate.Thelocalvalueofthenonlinearresistanceischosenaccordingtoanarbitraryvoltage-currentdensitycharacteristic[51].Thisvoltagevariationfollowingthecurrentdensitycorrespondstoanignitionvoltage.Theauthorsconclude[51]thatthevalueoftheignitionvoltagehastobechosenonthebasisofmeasurementresults.Howeverthearcmotionpresentedbytheauthorsfromtheirmodelseemstopresentbehaviorsimilartotheexperimentalone.

ExperimentalWor

swithanArcintheSplittersPlates

Thestudyofarcbehaviourinthesplitterplateisdifficulttoperform.Neverthelesswecanquotetwooriginalstudiesfromtheliterature[51]and[43].Oneisrelatedtotheobservationbyhighspeedmoviecamerashooting38500framespersecond.Foropticalobservation,onesideconsistsofaglassplatepressedagainstthesidewallsbyanacrylicplate.Theauthorsobtaininformationonarcbehaviourduringthedisplacementincludinginthesplittersplatearea.Thepictureswerethencomparedwiththetheoreticalresults.Thesecondstudyisrelatedtothewor

proposedbyDebellut

E.etal.[43].Theauthorsproposeamagneticcamera.Theprincipleconsistsoftheuseonehundredprobestomeasurethemagneticinductionoutsidethebrea

ingdevice.Thensoftwarebasedonareconstructionmethoddeterminestheaveragelineofcurrentrepresentingthearc.Testshavebeencarriedoutinaquenchingchambercomposedofacopperorsteelsplittingplate.Than

stothemagneticcamera,thearcpositionsandtheirrespectiveintensitiesarebothdetermined.Eventhoughnodifferencesinarcbehaviourhavebeennoticedbetweenacopperandasteelsplittingplate,the


28/36

methoddescribesthearcmotioninthequenchingchamber.IV.CONCLUSIONInthispaperwepresentedanoverviewofcurrentresearchintoLow-VoltageCircuitBrea

ers.AgeneralpresentationoftheLVCBprocessispresentedgivingthedifferentbrea

ingstages.Wefocusourattentionon


experimentalandtheoreticalexistingstudiesandonthedifficultytocharacterizesuchbrea

ingprocessduetoitscomplexity.Thecomplexityisduetonumerousphysicalaspects,tothesmallthreedimensionalsizeofthegeometryandtothetemporalbehavior.Thesepointsarepresentedintwomainchapters.

I)TheFirstChapterisRelatedtoPlasmaCharacteristics

Wepresenttheexperimentalquantitieswhichcanbeobtainedsuchasvoltageandcurrentintensityvariations,butalsotemperatures,speciesdensity,thevelocityofthearcdisplacement.Duetoarcmovementandto3Dbehavioronlymeanquantitiescanbeobtainedbyexperimentaldevices.

Indeedmostofexperimentalmethodsneedtoassumethe

nowledgeofthepressureandcomposition,toconsiderhomogeneousplasma,orthatsymmetryexists.

Inparallelmodelsaredeveloped.Assumingtheplasmaasafluid,theNavierSto

esequationsaresolved.TheequationsarecompletedbyadditionalsourcestermsasJouleseffectandLorentzforcesandequationsfortheelectricarcrepresentationanditseffects.Numerousphysicalmechanismsareta

enintoaccountforthearcandplasmadescriptionsinthecolumnandclosetothearcrootattachments.

Wecansoconsiderthatthedevelopedmodelsareabletowelldescribetheplasmacharacteristicsinthemediumta

ingintoaccountalltheeffectsduetomagneticorconvectiveforces.Neverthelesstheplasmacharacteristicsarecorrelatedtotheplasmapropertiesdependingonthevaporspresence.Thevaporscomefromthecontacterosion,therail,thesplittersandthePA66walls.Evenifpapersexistpresentingtheinfluenceofvaporsonarccharacteristicsandthatthetransport,thermodynamicandradiationpropertiesareavailableforthemodelsdataban

,duetothedifferentnaturesofthevapors(Forexample:Cu,Fe,PA66,Ag,..),tothecomplexitytodevelopanerosionmodelta

ingintoaccountallthequotedvapors,tota

eintoaccountallthe

differentvaporspresenceintheequations(suchastheenergyequation),tocalculatethediffusioncoefficientofeachspeciesinthemedium,andtothedifficultytovalidatethepredictingvaporsfieldswithexperimentalvalues,the

nowledgeoftheplasmacompositioninthegeometryduringtime

eepsthemaindifficultyforimprovingtheLVCB

nowledge.Oneeffortofthecommunityissocurrentlyorientedon(i)Experimentalmethodstowellcharacterizethearcin3D.(ii)Modelserosion.(iii)Diffusioncoefficientcalculationforseveralcomponentsandadditional


29/36

termsintheenergyequationincaseofreactinggases.

II)TheSecondChapterConcernstheArcMovement

Severalstagesneedtobeconsidered:fromthecontactsopening,thecommutationononerailduringtheopening,thearcmovementontherailsduetoforcesasmagneticorconvective,thearcsegmentationandrestri

estothefinalstepwherethevoltagedropincreases.Theincreaseofthevoltagedropleadstoacurrentlimitationandtothecutoffcurrent.

Themostinterestingpointonexperimentalstudiesonarcmovementismadebetheuseofsensorsallowingmeasuring


30/36


thearcpresence.Numerouscaptorsareplacedonthegeometrypermittingtodeducethegeneralshapeofthearcanditsmeanvelocityinthechamber.Themethodallowsdemonstratingeffectsofthesplitteronthearcmovement,ortheinfluenceoftheplasmapropertiesonitsvelocity.Measurementsareperformedandgiveresultsduringallthebrea

ingprocessfromthecontactopeningtothebrea

ingstage.Themethodallowsalsostudyingtherestri

ephenomenon.

Theoreticalstudiesexistonthearcmovementdescription.Neverthelessthedescriptionsarepoorandfarfromthe

nowledgelevelgivenbyexperimentalresults.Toour

nowledge,amodelabletodescribethearccommutationfromtheopeningcontacttotheraildoesnotexist.Aspresentedinthepaper,two

indsofdescriptionexisttorepresentthearcmovementontherails:onebasedonthermalaspect,thesecondonthemeanelectricalconductivityclosetotherail.Forthemodeling,eveniftwoapproachesallowrepresentingonemovementwhichcomparedwithexperimentalresultsissatisfactory,thetwo

methodsneedtobeimproved.Indeedthetwomethodsallowobtainingresultscomparablewithexperimentalresultsbutonlyaftertheadjustmentofparameterscomingfromexperimentalresults.

Theexperimentalcharacteristicsonthearcmovementallowobtainingthemeanarcvelocityandtocharacterizetheinfluenceofsomeparameterssuchtheinfluenceofthenatureoftherailorofthenumberofsplittersinthebrea

ingchamber.Animprovementonthemodelneedstobemadefortherepresentationofthedifferencestagesofthearcfromtheopeningtothebrea

ingprocess.Indeedcurrentlyparametricstudiesgiveinformationontheinfluenceofsome

parametersonthearcdisplacementbutwearefarfromapredictivemodelabletooptimizethedesignofaLVCBforareductionsizeoradoublechamberdefinition.Oneeffortofthecommunityissocurrentlyorientedonthedescriptionofallstagesofthebrea

ingprocess.Thedifficultiesareencounteredon(i)thearcrootattachmentrepresentationwiththeelectrodevoltagedrop,(ii)thedefinitionofcriteriaforarcdisplacementontherails,(iii)thedescriptionofthearcsegmentationonthesplitterplates.

ThecharacteristicsoftheplasmaandtheanalyzeoftheelectricarcinaLVCB

eepcomplexevenifeffortsaremadebythecommunityonexperimentalortheoretical

wor

s.Throughtwochaptersoneontheplasmacharacteristicstheotheronthearcdisplacement,wehaveanalyzetheexistingpapers.Thisstudyallowsdrawingoutthepointsofinterestsofthenextyears.Theeffortontheexperimentalwor

sshouldbeonthearccharacteristicsasforthemodelsitshouldbeonthearcrootattachmentdescriptionandarcmovement.

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