电能设备EMC(1)

15Section1EMCOFELECTRICALPOWEREQUIPMENTMUTUALINDUCTANCEBETWEENWIRESINHELICALLYTWISTEDPOWERCABLESBERNDW.JAEKEL,GERMANYSiemensAG,AutomationandDrives,Germany,e-mail:[e-mail]ctorsinamulti-corepowercableleadstoasituationwherevari-ousconductorloopsarebuiltup.Oneorseveralloopsareformedbythephaseandneutralconductorswiththeoperationalcurrentflowingintheseconductors.Afurtherloopisbuiltupbytheprotectiveearthconductorwhichisconnectedtotheequipotentialbondingsystematseverallocations.Theareaofthisloopisessentiallyarrangedoutsideofthepowercable.Theinductivecouplingfromthephaseconductorloopsintothatloopcausescommonmodevoltagesintheprotectiveearthsystemwithconsequentcom-monmodecurrents.Itcanbedemonstratedthatthiseffecteventakesplaceinthecaseofbalancedphasecurrentsinthecable.Numericalsimulationsandparameterstudieswerecarriedoutinordertodescribethiseffectquantitativelyandtoinvestigatetheinfluenceofdifferentcableparametersontotheresultingcommonmodevoltages.IntroductionPowercablesrepresentcomponentsofanentirepowersupplynetworkwhichcanbecarriedoutindif-ferenttypes.Ifanearthedsystemisrequired,i.e.asys-temwhichisconnectedtothelocalreferenceearth,mainlytwotypesofsupplynetworkscanbedistin-guished:TN-CandTN-S.FromanEMCpointofviewaTN-Spowernetworkshoulddefinitelybepreferred[1].Inthistypeofnetworktheneutralandprotectiveearth(PE)conductorsarestrictlyseparatedexceptatonenetpointwherebothconductorsareconnected,normallyatthetransformerortheswitchgear.Thistypeofinstallationpreventsthatanyoperationalcur-rentsflowoutsideofthephaseandneutralconductors.Nocablenetcurrentsshouldexistandthereforetheequipotentialbondingsystemisgenerallyassumedtobefreeofanyoperationalcurrents.Butwhenlookinginmoredetailatthistypeofnetworkandatthephysi-calstructureofpowercablessomephysicalmecha-nismscanbeidentifiedwhichneverthelessleadtothegenerationofcommonmodevoltagesandcommonmodecurrentseveninthecaseofbalancedloadedTN-Spowernetsystems.LowVoltagePowerCablesMulti-corelowvoltagepowercablesconsistofthephaseconductorsand–dependingontheground-ingarrangementofthepowersupplynetwork–ofaneutralconductorand/oraPEconductor.AnexampleforthestructureofapowercableisshowninFig.1foracableoftypeNYY.Eachoftheconductorsaswellastheentireconductorarrangementarecoveredbyaninsulationforwhichamaterialischosendependingonthespecificrequirementsandfieldsofapplications[2].Thenindividualinsulatedconductorsaretwistedtogetherandeachconductorcanberepresentedbyahelicalline.Anappropriatecylindricalcoordinatesys-temfordescribingthespatialarrangementofaconduc-torisshowninFig.2togetherwiththerelevantparam-eterssuchasaastheradiusofthehelicallinewithrespecttothecentrelineofthecableandthepitchdis-tancepasthetwistlengthofthecable,i.e.thelengthofthecableperrotationoftheconductors.Forsimplic-ityreasonsonlyoneconductorisshown.Thefurthern-1conductorscanberepresentedassimilarlinesandtheyarerotatedbyanangle=3600/nwithrespecttothatoneshowninFig.2.Fig.1:Multi-corepowercableoftypeNYYCommonModeVoltagesinPowerCablesThemagneticfluxdensityBcausedbythecur-rentsintheindividualconductorscanbecalculatedbymeansoftheBiot-Savartlaw,aslongasthesituationatthepowerfrequencyrangeisconsidered:Crd30)'('4rrrIB(1)Irepresentsthephasoroftheexcitingalternatingcurrent,rwithitscylindricalcoordinatesr,,zde-notestheobservationpointandr’withitscylindricalcoordinatesr’,’,z’meansavariablepointonthelinecurrent.Thoughthisexpressioncanbeeasilysolvedinthecaseofstraightwires,thesituationisrelativelycomplexinthecaseofpowercableswherethevariousconductorsaretwistedandeachconductorcanberep-resentedbyahelicalsolenoid(seeFig.2).16Inpowercableswhereaprotectiveearthconduc-tor(PE-conductor)istwistedalongwiththephaseconductorsaninductivecouplingexistsbetweenthephaseconductorloopsandaloopbuiltupbythePE-conductoranditsconnectingstructurestotheequipo-tentialbondingsystem.Thiseffectcanbeexplainedbymeansofaschematicsketchofa4-conductorcableasshowninFig.3.Forreasonsofclaritythetwistingoftheconductorsisnotshowninthefigure.Fig.2:Atwistedconductor(helicalline)inacylindri-calcoordinatesystem[3]TheconductorsL1,L2forexampleformaspatialloopinwhichthephasecurrentIL1-L2flows.Corre-spondingloopsarebuiltupbythearrangementofcon-ductorsL1-L3andL2-L3withtheloopcurrentsIL1-L3andIL2-L3,respectively.AfurtherloopresultsfromthePEconductorwhichisconnecttotheequipotentialbondingsystembyconductivestructures.ThisloopisshownasPE-LoopinFig.3.L1L2L3PEPELoopFig.3:MechanismforgenerationofcommonmodevoltagesTheinducedvoltageUPEinthePE-LoopcanbederivedbymeansofthemutualinductancesbetweenthevariousphaseconductorloopsandthePE-Looporaccordinglybythemutualinductancebetweenthecur-rentcarryingphaseconductorsandthePE-Loop:)(332211PELLPELLPELLPEMIMIMIU(2)withthemutualinductancesMLi-PE(i=1,2,3)tobederivedbyiSLiPELiIdMSB(3)BLirepresentsthemagneticfluxdensitycausedbythecurrentIiinconductorLi(i=1,2,3)andStheareaofthePE-Loop[4].Fig.3showsthesituationforafour-conductorca-ble.Fromthecross-sectionoftheentirecableconfigu-rationitcanbeseenthatth