Dynamical Models for Eddy

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1、866IEEETRANSACTIONSONMAGNETICS,VOL.44,NO.6,JUNE2008DynamicalModelsforEddyCurrentinFerromagneticCoresIntroducedinanFE-TunedMagneticEquivalentCircuitofanElectromagneticRelayFabienSixdenier,Marie-AngeRaulet,RomainMarion,RenéGoyet,GuyClerc,andFaridAllabUni

2、versitéLyon1,VilleurbanneF-69622,FranceSchneiderElectric31,Eybens38320,FranceElectromagneticrelaymodelingiselaboratedusingamagneticequivalentcircuit(MEC).ThelumpedparametersoftheMECarefittedwithrespectto3-Dfinite-elementsimulationbyusingclassicaloptimizational

3、gorithms.Anaccuratedynamicmateriallawhastobetakenintoaccountinthemodeling,consideringthemassivecoreofthecircuit.Twoaccuratedynamicalmodelsforrepresentingeddycurrentsarestudied.Thesimulationoftherelayiscarriedoutforseveralexcitationfrequencies.Acomparisonbetw

4、eenmeasurementsandsimulatedquantitiesisprovided.IndexTerms—ACcircuitbreakers(CBs),eddycurrents,magnetichysteresis,optimizationmethods.I.INTRODUCTIONHEdifferentialcircuitbreaker(CB)isessentialtoensureTlifesafety.Suchadeviceiscomposedofthreeparts:thedifferenti

5、alcurrentsensor[1],theelectroniccircuit,andtheelectromagneticrelay.Toreducetheproblem,wefocusontherelaythatissupposedtobeclosed.Theelaborationofanewprototyperequiresaccuratemodels[2].A3-Dfieldcalculation,includingaccuratedynamicalmateriallaws[3]andacouplingwi

6、ththeelectricalcircuits,wouldideallysuittheproblem,butwouldleadtoprohibitivecomputationtimes.Hence,wehaveFig.1.Geometryoftherelay.chosenadifferentapproach,byconsideringmagneticequiva-lentcircuits(MECs)[4]withaccuratedynamicalbehaviorofthemagneticmaterial.The

7、developmentofthismodelrequirestwosuccessivesteps:1)elaborationofthefluxtubesnetwork;2)introductionofdynamicaleffectsduetoeddycurrentinthedifferentmagneticfluxtubes.Anoptimizationofthelumpedparametersofthefluxtubenetworkbasedonautomaticalgorithmsispresented.Twoa

8、c-curatedynamicallawsofthemagneticmaterialareconsidered[5],[6]andtested.Oncetheassociationofdifferentfluxtubesiscarriedout,simulationsoftherelayareperformedatseveralfre-quencies.Anexperimentalval