A fast semi-analytical model for the slotted structure of induction motors

Abstract- Afast,semi-analyticalmodelforinductionmotors(IMs)with36/28stator/rotorslotcombinationispresented.Incomparisontotraditionalanalyti-calmodelsforIMs,suchaslumpedparameter,magneticequivalentcircuitandanisotropiclayermodels,thepresentedmodelcalculatesacontinuousdistri-butionofthemagneticfluxdensityintheairgapandboththestatorandrotorslotsoftheIM.Duetoitssemi-analyticalnature,thecomputationtimeofthemodelisshortincomparisontoFiniteElementAnalysis(FEA)simulations.Also,itisshownthatthemodelresultsareingoodagreementwithlinearFEAsimulationresults.Thismakesthemodelverysuitablefordesigntools. Keyword- Harmonicmodeling,inductionmotor,semi-analytical,slotting 1 I NTRODUCTION Acrucialelementinthedesignofinductionmotors(IMs)istheavailabilityofasuitableelectromagneticmodeltopredicttheperformanceofthemotor. Typ-ical demandsforsucha modelare shortcomputa-tiontimes,highaccuracyandflexibilitywithrespecttoparametervariations. Historically,thelumpedpa-rametermodelisveryextensivelyusedforIManal-ysisanddesign[1,2]. Thismethodgenerallyhasashortcomputationtime, buttheaccuracyislimitedduetoitsdependenceonthemodelparametercalcu-lation. Manyeffectsareestimatedbycorrectionfac-tors,whichmeansthatthephysicaleffects,suchasleakageflux,arenotmodeledindetail. Ontheotherhand, a moreaccurateanddetailedanalysis ofIMperformanceisoftenobtainedusingFiniteElementAnalysis(FEA)[3].Thismethodcantakenon-linearsoft-magneticmaterialsandcomplexgeometriesintoaccount,butatthepriceofamuchlongercomputationtime. Also,parametervariationrequiresre-meshing,whichfurtherincreasescomputationtime.AlternativemethodsthathavebeeninvestigatedforIM analysis include Magnetic Equivalent Circuit(MEC)modeling[4,5]andAnisotropicLayerTheory(ALT)modeling[6,7].Boththesemethodscanhaverelativelyshortcomputationtimesandareabletotakeglobalsaturationeffectsintoaccount. However,forMEC modeling, themagneticfluxpathsshouldbeknowna-prioritoavoidverycomplexanddetailedmodelimplementations.Thisisnotpracticalforade-signtool.Furthermore,theALTmethodtakestheef-fectofthestatorandrotorslotsintoaccountglobally,butthelocalmagneticfluxdistributionisneglected.In this work, a semi-analytical model is presentedthat calculatesthestatic magneticfield distributionintheairgapandboththestatorandrotorslotsofanIM.Themodelisbasedontheharmonicmethoddescribedin[8]andimplementedforabenchmarkmotortopologyinpolarcoordinates. Theresultingmodelconsistsof33regionsand476systemequa-tions. Thetotalcomputationtimeforthismodelisintheorderoftenthsofasecond,includingthegen-erationoftheequationmatrix. ItisshownthattheresultsofthedevelopedmagneticfieldmodelareingoodagreementwithlinearFEAresults.Regardingthefuture,thedevelopedmodelpresentsthefirststeptowardsanadvancedsemi-analyticalde-signtoolforIMs. Althoughitisassumedthatthepermeabilityofthesoft-magneticmaterialisinfinite,theeffectsofsaturationcanbeaccountedforusingahybridcouplingtoasaturationmodel,e.g. basedonALTorMEC[9]. Furthermore,fixedcurrentdensi-tiesareappliedtothestatorandrotorslotsinordertovalidatethemagneticmodel.However,themagneticmodelcanbecoupledtostatorandrotorcircuitmod-elstoobtainasteady-stateoreventransientmodel.Fig.1.Halfofthebenchmarkmotorgeometry

[1]  T. Lubin,et al.  Analytic Calculation of Eddy Currents in the Slots of Electrical Machines: Application to Cage Rotor Induction Motors , 2011, IEEE Transactions on Magnetics.

[2]  E. A. Lomonova,et al.  General Formulation of Fringing Fields in 3-D Cylindrical Structures Using Fourier Analysis , 2012, IEEE Transactions on Magnetics.

[3]  Johannes J. H. Paulides,et al.  General Formulation of the Electromagnetic Field Distribution in Machines and Devices Using Fourier Analysis , 2010, IEEE Transactions on Magnetics.

[4]  Timothy J. E. Miller,et al.  An analytical iterative model (AIM) for induction motor design , 1996, IAS '96. Conference Record of the 1996 IEEE Industry Applications Conference Thirty-First IAS Annual Meeting.

[5]  Jarmo Perho,et al.  Reluctance Network for Analysing Induction Machines , 2002 .

[6]  W. R. Jones,et al.  Convergence of Numerical Solutions of Iris-Type Discontinuity Problems , 1970 .

[7]  E. A. Lomonova,et al.  Electric circuit coupling of a slotted semi-analytical model for induction motors based on harmonic modeling , 2014, 2014 IEEE Energy Conversion Congress and Exposition (ECCE).

[8]  A. Boglietti,et al.  Algorithms for the computation of the induction motor equivalent circuit parameters - Part II , 2008, 2008 34th Annual Conference of IEEE Industrial Electronics.

[9]  Valéria Hrabovcová,et al.  Design of Rotating Electrical Machines , 2009 .

[10]  Johannes J. H. Paulides,et al.  Analytical Hybrid Model for Flux Switching Permanent Magnet Machines , 2010, IEEE Transactions on Magnetics.

[11]  E. Mishkin,et al.  THEORY OF THE SQUIRREL-CAGE INDUCTION MACHINE DERIVED DIRECTLY FROM MAXWELL'S FIELD EQUATIONS , 1954 .

[12]  Ion Boldea,et al.  The Induction Machines Design Handbook , 2009 .

[13]  A. C. Smith,et al.  Field analysis for rotating induction machines and its relationship to the equivalent-circuit method , 1980 .

[14]  J. Jansen,et al.  Three-Dimensional Analytical Modeling Technique of Electromagnetic Fields of Air-Cored Coils Surrounded by Different Ferromagnetic Boundaries , 2013, IEEE Transactions on Magnetics.

[15]  E. A. Lomonova,et al.  Calculation of induced rotor current in induction motors using a slotted semi-analytical harmonic model , 2014, 2014 International Conference on Electrical Machines (ICEM).

[16]  Yacine Amara,et al.  Overview of analytical models of permanent magnet electrical machines for analysis and design purposes , 2013, Math. Comput. Simul..

[17]  A. B. J. Reece,et al.  Finite Element Methods in Electrical Power Engineering , 2000 .

[18]  A. Boglietti,et al.  Algorithms for the computation of the induction motor equivalent circuit parameters - Part I , 2008, 2008 34th Annual Conference of IEEE Industrial Electronics.

[19]  Vlado Ostović,et al.  Dynamics of Saturated Electric Machines , 1989 .