Calculation of Eddy Current Losses in Permanent Magnets of ...

OverviewFachbereich Elektrotechnik und Informationstechnik- Introduction- Considered PM synchronous motors- Loss calculation methods- Loss estimation from thermal measurements- ConclusionsInstitut für ElektrischeEnergiewandlungDipl.-Ing. Csaba Deak 1

Loss calculation methodsFachbereich Elektrotechnik und Informationstechnik1000 rpm, no-load operationFlux density for Motor AB(x) at upper surfaceInstitut für ElektrischeEnergiewandlungFEMAG-DC(no eddy currents considered!)Dipl.-Ing. Csaba Deak 5

Loss calculation methodsFachbereich Elektrotechnik und Informationstechnik1000 rpm, no-load operationUppersurfaceMiddlesurfaceBottomsurfaceFlux density for Motor AInstitut für ElektrischeEnergiewandlungFEMAG-DC(no eddy currents considered!)Dipl.-Ing. Csaba Deak 6

Loss calculation methodsFachbereich Elektrotechnik und InformationstechnikFlux density at no-load operationMotor AFlux densityMotor BMotor C1000 rpm, upper surfaceMotor DInstitut für ElektrischeEnergiewandlungFEMAG-DC(no eddy currents considered!)Dipl.-Ing. Csaba Deak 7

Loss calculation methodsFachbereich Elektrotechnik und InformationstechnikInstitut für ElektrischeEnergiewandlungFlux density at load operationMotor ASinusoidal currentMotor BMotor C Motor D1000 rpm, upper surfaceFEMAG-DC(no eddy currents considered!)Dipl.-Ing. Csaba Deak 8

Loss calculation methodsMethod 1: 1 FEMAG-DC & Analytical FormulaFachbereich Elektrotechnik und InformationstechnikVector potentialCurrent densityAlternating current density∫b MLosses in magnetsb~Jz( x)⋅dx=b0Considered in each of the three surfaces (upper, middle, bottom)~Institut für ElektrischeEnergiewandlungDipl.-Ing. Csaba Deak 9

Loss calculation methodsMethod 2: 2 FEMAG DC - Version 05/2007Fachbereich Elektrotechnik und Informationstechnik- No reaction field of eddy currents considered- Maxwell equations- Fast calculation rotE= −∂B/ ∂t J = κE- For magnets with rather low conductivity (small eddy currents)Method 2 is similar to Method 1, butis considered over the magnet cross section and not onlyin the three surfaces∫A MJz( x,y)⋅ dx ⋅dy= 0Institut für ElektrischeEnergiewandlungDipl.-Ing. Csaba Deak 10

Loss calculation methodsInfluence of eddy current reaction fieldFachbereich Elektrotechnik und InformationstechnikPenetration depth:dE=κMg⋅π⋅1fB,Mg⋅ µRatio b Mg/ d E≤ 1 → no eddy current reaction fieldEx.: n = 3000 rpm; f s= 400 Hz; f B,Mg= 1200 Hz (q = ½)Motor A Motor Bb Mg,A= 3.6 mmb Mg,B= 27.3 mmκ Mg,A= 0.62 · 10 6 S/m κ Mg,B= 0.43 · 10 6 S/md E,A= 17.8 mmd E,B= 21.6 mmb Mg,A/ d E,A= 0.2 b Mg,B/ d E,B= 1.26MgMotor Ab Mg,AMotor Bb Mg,BInstitut für ElektrischeEnergiewandlungDipl.-Ing. Csaba Deak 11

Loss calculation methodsMethod 3: 3 2D Time-step calculationFachbereich Elektrotechnik und Informationstechnik- Reaction field of eddy currents considered- Full set of Maxwell equationsrotErotH= −∂B/ ∂t= κE- For general purpose up to medium frequencies valid- Very time consumingJ=JB= µ HInstitut für ElektrischeEnergiewandlungDipl.-Ing. Csaba Deak 12

Loss calculation methodsFachbereich Elektrotechnik und InformationstechnikP Mg [W]350300250200150100500Motor ANo-load 1000 rpmMethod1: FEMAG + AnalyticalMethod2: FEMAGMethod3: Time steppingA B C D G HComparisonP Mg [W]350300250200150100500No-load 3000 rpmMethod1: FEMAG + AnalyticalMethod2: FEMAGMethod3: Time steppingA B C D G HMotor B Motor C Motor D Motor G Motor HInstitut für ElektrischeEnergiewandlungq = ½q = ¼Dipl.-Ing. Csaba Deak 13

Loss calculation methodsFachbereich Elektrotechnik und InformationstechnikP Mg [W]2000180016001400120010008006004002000Load 1000 rpmMethod1: FEMAG + AnalyticalMethod2: FEMAGMethod3: Time steppingA B C D G HComparisonSinusoidal currentP Mg [W]22002000180016001400120010008006004002000Load 3000 rpmMethod1: FEMAG + AnalyticalMethod2: FEMAGMethod3: Time steppingA B C D G HMotor A Motor B Motor C Motor D Motor G Motor HInstitut für ElektrischeEnergiewandlungq = ½q = ¼Dipl.-Ing. Csaba Deak 14

Loss estimation from thermal measurementsLosses at adiabatic heatingFachbereich Elektrotechnik und InformationstechnikTemperature [°C]1009080706050403020100Losses:∆tMagnet temperature∆ϑ0 30 60 90 120 150 180 210 240Time [min]P = m·c·dϑ/dtMotor A: 1000 rpmload operationUseful only as the ratio of the dϑ/dt valuesby the different motor configuration!!Motor ATemperature sensorMotor GInstitut für ElektrischeEnergiewandlungDipl.-Ing. Csaba Deak 15

Fachbereich Elektrotechnik und InformationstechnikP Mg / P Mg0,A9080706050403020100Loss estimation from thermal measurementsNo- load 1000 rpmCalculatedMeasuredA B C E F GComparison(all values related to Motor A, 1000 rpm, no-load operation P Mg0,A)Losses in rotor iron. bridge and magnetsP Mg / P Mg0,A9080706050403020100No- load 3000 rpmCalculatedMeasuredLosses in rotor iron. bridge and magnetsA B C E F GMotor A Motor B Motor C Motor E Motor F Motor Gq = ½Institut für ElektrischeEnergiewandlungq = ¼Dipl.-Ing. Csaba Deak 16

Loss estimation from thermal measurementsFachbereich Elektrotechnik und InformationstechnikP Mg / P Mg0,A9080706050403020100Comparison(all values related to Motor A, 1000 rpm, no-load operation P Mg0,A )Load 1000 rpmCalculatedMeasuredLosses in rotor iron. bridge and magnetsA B C E F GP Mg / P Mg0,A200180160140120100806040200Load 3000 rpmCalculatedMeasuredLosses in rotor iron. bridge and magnetsA B C E F GMotor A Motor B Motor C Motor E Motor F Motor Gq = ½Institut für ElektrischeEnergiewandlungq = ¼Dipl.-Ing. Csaba Deak 17

ConclusionsFachbereich Elektrotechnik und Informationstechnik- 3 loss calculation methods: FEMAG-DC & analytical formulaFEMAG-DC- 8 motors : 2 Stators (q = ½ ; q = ¼ )Time stepping4 Rotors (segmented/non-segmented; surface/buried)- eddy-current losses in magnets are possible to be calculatedwith DC method (no eddy current reaction field) due to the ratherlow conductivity of rare-earth magnets- loss estimation from adiabatic thermal heating is possiblemainly for surface-mounted permanent magnets- for buried magnets: influence of bridge losses to beinvestigated furtherInstitut für ElektrischeEnergiewandlungDipl.-Ing. Csaba Deak 18

Calculation of Eddy Current Lossesin Permanent MagnetsFachbereich Elektrotechnik und InformationstechnikThank you for your attention!Institut für ElektrischeEnergiewandlungcdeak@ew.tu-darmstadt.deDipl.-Ing. Csaba Deak 19