Basics of Permanent Magnet - Machines

Transcription

1 Basics of Permanent Magnet - Machines 1.1 Principles of energy conversion, force & torque 1.2 Basic design elements 1.3 Selection of PM-Machine topologies 1.4 Evaluation and Comparison Permanent Magnet Synchronous Motor Design Sect. 1/1

2 1.1 Principles of energy conversion, force & torque F = Force F on current i : J B dv i V Ψ 2 i 2 i 1 L 12 dl12 dψ 2 T = i1 i2 = i2 dα dα Force F on magnet : F = V H div J M dv J M S N i1 dψ 1 T = i1 dα Ψ 1 Force F on iron : i dl1 1 dψ 1 T = i1 = i1 2 dα 2 dα Ψ 1 L 1 Permanent Magnet Synchronous Motor Design Sect. 1/2

3 Force calculation on a surface: Total force F on a surface area df : ( Maxwell s Stress) F = O p df p p n t = = ( B n B t 2 µ 1 B µ n B t ) B p n n df α B t B α p t p Permanent Magnet Synchronous Motor Design Sect. 1/3

4 Thrust force : f S fs = Bn A In el. Machines: Bn A f s B B µ n t p t = = B n H t = f S Ht f s Tangential field strength H t from winding with current: current loading: A = H t Air gap induction B n from field windings or magnets Permanent Magnet Synchronous Motor Design Sect. 1/4

5 Lorentz force F on Permanent magnets : h m One pole : Technical Limits: J M τp δ J M Equivalent current loading for PM: A = 2 h M H c /τ p Field current Flux density B: < 1.4 T ( Magnets, saturation, cos ϕ ) Coercitive field strength: H c < 1000 ka/m, h M / τ p > 0.1 f s < 280 kn/m 2, Single tooth winding: f s ~ 1/τ p ~ p Force, torque: linear, controllable, field weakening, high efficiency Positive Aspects: Application: Synchronous -Machines: B : travelling field: f s < 80 kn/m2 Distributed Winding : B Aτ p = µ o fs µ o H 2( h + δ) m c A Permanent Magnet Synchronous Motor Design Sect. 1/6

6 Reluctance force F on iron : F x One pole : Technical Limits: Positive Aspects: Application: Field current Flux density B < 1.5 T ( Saturation ) Current loading A < 60 ka/m ( Losses, cooling, AR ) f s < 170 kn/m 2 ( δ/τ p <= 0.1), f s ~ 1/τ p ~ p Simple rotor design, distributed and single tooth windings Switched-Reluctance-Machine: f s < 25 kn/m 2 Stepping motor, current unipolar, Reluctance machine, distributed winding: f s < 30 kn/m2 Vernier-Machine: f s < 35 kn/m 2 Permanent Magnet Synchronous Motor Design Sect. 1/6

7 Developement trends : Power electronics support the use of non conventional conversion principles: Force on magnets, reluctance force or combination of both forces Use of non conventional windings: Single coil and ring windings Optimization of magnetic circuits and windings Minimization of secondary effects: Forces, cogging & load pulsation torques, eddy currents, losses, demagnetization, reactances Permanent Magnet Synchronous Motor Design Sect. 1/7

8 1.2 Basic design elements Magnetic circuits: Flux: longitudinal, transversal, axial Air gap : homogeneous or reluctant Windings : distributed-wound (q > 1), concentric (q < 1), ring Permanent magnets: surface-, embedded radial, tangential Rotor structure: homogeneous or reluctant Air gap field: Rotating field from distributed or single coil winding Mechanical design: cylinder, disk, internal or external rotor Stator/Rotor arrangement: one - or multi sections Cooling: air, water, internal, external Permanent Magnet Synchronous Motor Design Sect. 1/8

9 Magnetic circuits: Longitudinal flux machines: Example: Turbogenerator ( one half section ) Transversal flux machines: Example: Stepping motor Ringwinding Statorwinding Stator Magn. Flux Rotor Rotor Magnets Permanent Magnet Synchronous Motor Design Sect. 1/9

10 Air gap : thrust force, energy transfer f = B H = B S n t n A Homogeneous: Synchron -Machine Sector of a SM with 56 poles and 336 slots Magnet -Machine Sector of a MM with 40 poles and 48 slots Permanent Magnet Synchronous Motor Design Sect. 1/10

11 Air gap : thrust force, energy transfer both stator and rotor with teeth: => reluctance R Vernier -Machine Stator: m-phase distributed winding Q s <> Q r with : Q s = 24, Q r = 20, p = 2 (half of a Vernier -Machine ) Switched-Reluctance - Machine with : Q s = 12, Q r = 8, m = 3 Permanent Magnet Synchronous Motor Design Sect. 1/11

12 Air gap : thrust force, energy transfer Non symmetric air gap Magnet -Single-Phase-Machine Sector from a machine with 6 poles and 6 slots 1 1 Permanent Magnet Synchronous Motor Design Sect. 1/12

13 Windings : voltage, magnetic field generation S Distributed winding b S c c a b Concentric winding (single tooth winding) S a b N N c b a N B a N S B c Longitudinal flux machines: windings: one layer several layers Windings are located in: slots air gap Winding direction: axial radial (disk machines.) Permanent Magnet Synchronous Motor Design Sect. 1/13

14 Magnetic field: Stator: 3-phase ac-currents Stator field: AC-Field Distrubuted windings Single coil windings Air gap field: rotating field produced by all coils Rotor field: DC-field Air gap field: AC-field from singel coils Rotor field: DC and AC field Permanent Magnet Synchronous Motor Design Sect. 1/14

15 Verteilte Spulenwicklung Lochzahl: q >= 1 Polpaarzahl : p Strangzahl : m Nutzahl: Q = 2 q p m Lagenzahl: u = 1, 2... Bei q gebrochen u > 1 Beispiel: m = 3, Q = 21, 2p = 6 Ueberprüfung mit Methode Nutenspannungsstern Wahl der Nutzahl Q : Einzelspulenwicklung Anzahl parallele Zweige: c Polpaarzahl/Zweig : " = Wähle t = 1, 2... so dass " 2 p ± m t geradzahlig p p / c Nutzahl Q = Anzahl Spulen S : Q = ( 2 p " ± t ) c Ist t geradzahlig so ist S = Q / 2 d.h. nur jeder zweite Zahn bewickelt Einschränkend : 2 p Q m ± 1 = ; m 2 p Q m ± 1/ 2 = m Beispiel: m = 3, Q = 48, 2p = 52, 44, 40 oder 38 Permanent Magnet Synchronous Motor Design Sect. 1/15

16 Wirbelstromverluste im Magnet % 219 % % D.Ishak, Z.Q.Zhu, D. Howe, Eddy-Current Losses in the Rotor Magnets. IEEE Trans Magnetics 41, September 2005 Permanent Magnet Synchronous Motor Design Sect. 1/16

17 Air gap winding Rhombus winding Applikation: open, m phases closed, m-entries Advantage: small reactance no slot harmonics Disadvantage: Small windingsfactor kw = 2/π large air gap Permanent Magnet Synchronous Motor Design Sect. 1/17

18 Permanent magnets: Surface magnets, radial or parallel magnetized Flux concentration embedded magnets Halbach-Magnet: r r r M = er M cos pα ± e M sin pα α α Permanent Magnet Synchronous Motor Design Sect. 1/18

19 Lamination Reluctance topologies: Air or conductor Iron L q > L d Permanent Magnet Synchronous Motor Design Sect. 1/19

20 Hybrid topologies: Reluctance & Permanent magnets L d < L q L d > L q Permanent Magnet Synchronous Motor Design Sect. 1/20

21 δ δ ϖ )sin ( 2 sin 2 d q d M s X X U m X U m T + Ψ = q q d M s d X U I X U I δ ϖ δ sin cos = Ψ = d L q L < d L q L > Permanent Magnet Synchronous Motor Design Sect. 1/21

22 L d < L q L d > L q Permanent Magnet Synchronous Motor Design Sect. 1/22

23 L d < L q L d > L q Permanent Magnet Synchronous Motor Design Sect. 1/23

24 L d < L q L d > L q Permanent Magnet Synchronous Motor Design Sect. 1/24

25 Basic Magnet topologies: Current = 14 A Permanent Magnet Synchronous Motor Design Sect. 1/25

26 Power [kw] Current [A] cos ϕ Angle β [degr] M-losses [%] Ld [H/m] Lq [H/m] PSIM [vs/m] I-fieldweak [A] Permanent Magnet Synchronous Motor Design Sect. 1/26

27 Flux-Concentration Single-coil-windings 96 slots, 80 poles Permanent Magnet Synchronous Motor Design Sect. 1/27

28 Hybrid topologies: Double-salient -PM-Motor : Flux-Reversal -PM-Motor : Permanent Magnet Synchronous Motor Design Sect. 1/28

29 Mechanical design : Longitudinal flux machine cylinder disk windings Magnets Magnets outer stator + inner rotor auter rotor + inner stator 2 x outer stator + inner rotor Sector machine : e.g. Rotor: Magnets, Stator : Sector of windings Permanent Magnet Synchronous Motor Design Sect. 1/29

30 Survey on El. Machines Topologies : Permanent Magnet Synchronous Motor Design Sect. 1/30

31 1.3 Evaluation and Comparison Criteria Thrust force f S, Torque/Volume T/V, Utilization factor C Cogging torque, Load pulsation torque Synchronous reactances: X d, X q, power factor cos ϕ Losses, efficiency, eddy current losses in magnets Limitations: Over load, demagnetization, cooling, speed capability for field weackening Redundancy, reliabilty Requirements on power electronics and sensors Permanent Magnet Synchronous Motor Design Sect. 1/31

32 Comparison PM Synchronous machines: distributed windings single coil windings Synchronous reactance X d + Power factor cos ϕ + Stator-I2R-losses + Rotor losses + Torque - pulsation + High Speed capability + Demagnetization limit: + Field weakening + Redundancy + Requirements sensors, PE : equal + : larger : smaller Permanent Magnet Synchronous Motor Design Sect. 1/32

33 Comparison PM Synchronous machines: surface magnets embedded magnets Synchronous reactance X d + + Power factor cos ϕ + Stator-I2R-losses + Rotor losses + Torque - pulsation + Demagnetization limit: + + Field weakening + + Redundancy + + Requirements sensors, PE : equal + : larger : smaller Flux concentration Permanent Magnet Synchronous Motor Design Sect. 1/33

34 Eddy current losses in the rotor Stator: 3-ph-ac currents Stator: ac - field Rotor: dc - field distributed windings Stator: ac - field Rotor: dc + ac - field single coil winding Eddy current losses in magnet surface Sloting modulation air gap field : frequency high, Magnets and yoke solid Eddy current losses in magnet and yoke Due to the leakage field of the coils: frequency = ac - frequency Magnet and yoke laminated Permanent Magnet Synchronous Motor Design Sect. 1/34

35 Eddy currents in magnets FE-L [W/mm3].577E E E E E E E E E E E E FEMAG - DC Version: Oct 2007 Permanent Magnet Synchronous Motor Design Sect. 1/35

36 Comparison Induction / PM Machines: -Efficiency -Rotor losses -Costs -Reliability Permanent Magnet Synchronous Motor Design Sect. 1/36