Section1EMCOFELECTRICALPOWEREQUIPMENTMUTUALINDUCTANCEBETWEENWIRESINHELICALLYTWISTEDPOWERCABLESBERNDW.JAEKEL,GERMANYSiemensAG,AutomationandDrives,Germany,e-mail:bernd.jaekel@siemens.comAbstract.Thearrangementoftheconductorsinamulti-corepowercableleadstoasituationwherevariousconductorloopsarebuiltup.Oneorseveralloopsareformedbythephaseandneutralconductorswiththeoperationalcurrentflowingintheseconductors.Afurtherloopisbuiltupbytheprotectiveearthconductorwhichisconnectedtotheequipotentialbondingsystematseverallocations.Theareaofthisloopisessentiallyarrangedoutsideofthepowercable.Theinductivecouplingfromthephaseconductorloopsintothatloopcausescommonmodevoltagesintheprotectiveearthsystemwithconsequentcommonmodecurrents.Itcanbedemonstratedthatthiseffecteventakesplaceinthecaseofbalancedphasecurrentsinthecable.Numericalsimulationsandparameterstudieswerecarriedoutinordertodescribethiseffectquantitativelyandtoinvestigatetheinfluenceofdifferentcableparametersontotheresultingcommonmodevoltages.IntroductionPowercablesrepresentcomponentsofanentirepowersupplynetworkwhichcanbecarriedoutindifferenttypes.Ifanearthedsystemisrequired,i.e.asystemwhichisconnectedtothelocalreferenceearth,mainlytwotypesofsupplynetworkscanbedistinguished:TN-CandTN-S.FromanEMCpointofviewaTN-Spowernetworkshoulddefinitelybepreferred[1].Inthistypeofnetworktheneutralandprotectiveearth(PE)conductorsarestrictlyseparatedexceptatonenetpointwherebothconductorsareconnected,normallyatthetransformerortheswitchgear.Thistypeofinstallationpreventsthatanyoperationalcurrentsflowoutsideofthephaseandneutralconductors.Nocablenetcurrentsshouldexistandthereforetheequipotentialbondingsystemisgenerallyassumedtobefreeofanyoperationalcurrents.ButwhenlookinginmoredetailatthistypeofnetworkandatthephysicalstructureofpowercablessomephysicalmechanismscanbeidentifiedwhichneverthelessleadtothegenerationofcommonmodevoltagesandcommonmodecurrentseveninthecaseofbalancedloadedTN-Spowernetsystems.LowVoltagePowerCablesMulti-corelowvoltagepowercablesconsistofthephaseconductorsand–dependingonthegroundingarrangementofthepowersupplynetwork–ofaneutralconductorand/oraPEconductor.AnexampleforthestructureofapowercableisshowninFig.1foracableoftypeNYY.Eachoftheconductorsaswellastheentireconductorarrangementarecoveredbyaninsulationforwhichamaterialischosendependingonthespecificrequirementsandfieldsofapplications[2].Thenindividualinsulatedconductorsaretwistedtogetherandeachconductorcanberepresentedbyahelicalline.AnappropriatecylindricalcoordinatesystemfordescribingthespatialarrangementofaconductorisshowninFig.2togetherwiththerelevantparameterssuchasaastheradiusofthehelicallinewithrespecttothecentrelineofthecableandthepitchdistancepasthetwistlengthofthecable,i.e.thelengthofthecableperrotationoftheconductors.Forsimplicityreasonsonlyoneconductorisshown.Thefurthern-1conductorscanberepresentedassimilarlinesandtheyarerotatedbyanangle=3600/nwithrespecttothatoneshowninFig.2.Fig.1:Multi-corepowercableoftypeNYYCommonModeVoltagesinPowerCablesThemagneticfluxdensityBcausedbythecurrentsintheindividualconductorscanbecalculatedbymeansoftheBiot-Savartlaw,aslongasthesituationatthepowerfrequencyrangeisconsidered:B=μ0I4π∫Cdr'×(r−r')r3(1)Irepresentsthephasoroftheexcitingalternatingcurrent,rwithitscylindricalcoordinatesr,,zdenotestheobservationpointandr’withitscylindricalco...
