Analytical modeling of eddy current losses in permanent magnet brushless AC machin

Page 1






H

j B t

E

B 0 E

0

B

H

j

E


2

A

A t




Rr Rm Rs Ks Im 1, 441 10 4 10

ym l

pr

7

6


H x ( x, 0)

K s ( x)


2

2

Az ( x, y ) x2

Az ( x, y ) y2

j2 f

0

Az ( x, y ) 0

yg

q

2

2

f

2

AA*dy 0

4

q 4

(

4

K s2 1 (1 e 4 3 cos( / 2) 4 )

2

1 f

24

4

4

cos( /2) ym /

)

arctan ( ) 2


100

2

Power Loss Density (W/m )

Specific Wavelength

25

20

15

10

backward rotating harmonics forward rotating harmonics

5

0

14

29

44

59

74

Harmonic Order

89

104

119

80

60

40

20

0

0

5

10

15

20

25

30

Specific Wavelength

35

40

45

50


1

Power Loss (p.u.)

0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0

0

20

40

60

80

100

120

Magnet Width (mm)

140

160

180

200


1

<<1

Power Loss

0.6 0.4 0.2 0 0

1.6 3.2 4.8 6.4

8

Speed

9.6 11.2 12.8 14.4 16 17.6 19.2 20.8 22.4 24 25 Speed (rad/s) >>1 Power Losses

Power Loss (p.u.)

0.8

Speed




P

Pcn

Pan

n 1

Pcn

q 2 o2 a J n2 (nps 8 n 2 ps2 Rm Rs

2 nps

2 s

2 m

pr ) 2

R R 1 (2nps 2)

Rr Rm

2

2 nps

2

Rr Rs

2 nps

Rs2 Rr2 Fn

Rr Rs

2 nps

Rs2 Rm2

Rr2

/ 1

Rr Rs

2 nps

2


q2 a

Pan Rm Rs

nps

2 o

J n2 (nps n 4 ps4 2 m

Rs R 1 (nps 2)

sin 2 ( nps ( Rm2

Rr2 ) 1

Rr Rm

2

nps 2

Rr Rs

2

nps

Rs Rr2Gn

a ) 2 2 nps

Rr Rs Rm Rr

Gn

pr ) 2

nps 2

( nps R ln m Rr

2

Rm Rr

1 2)

, nps , nps

1 1

Fn

2 nps

( 2nps ln

Rm Rr

1 2)

, nps

2

, nps

2


1

Losses (p.u.)

0.8 0.6 0.4 0.2 0 0

3.2

6.4

9.6

12.8

Speed (rad/s)

16

19.2

22.4

25


1

Losses(p.u.)

0.8 0.6 0.4 0.2 0 1

2

3

4 5 6 7 Number of segements

8

9

10


Power Loss (p.u.)

1 0.8 0.6 0.4 0.2 0 22.4

19.2

16

12.8

Speed (rad/s)

9.6

6.4

3.2

0

2 1 3 4 6 5 7 8 10 9 Number of Segments


1

Power Loss (p.u.)

0.8

0.6

0.4

0.2

0 0

10

20

30 Harmonic Order

40

50

60



ACKNOWLEDGMENT THE

WORK PRESENTED IN THIS PAPER HAS BEEN DEVELOPED WITHIN THE

THALES-DEFKALION PROJECT. THIS RESEARCH HAS BEEN COFINANCED BY THE EUROPEAN UNION (EUROPEAN SOCIAL FUND – ESF) AND GREEK NATIONAL FUNDS THROUGH THE OPERATIONAL PROGRAM "EDUCATION AND LIFELONG LEARNING" OF THE NATIONAL STRATEGIC REFERENCE FRAMEWORK (NSRF) - RESEARCH FUNDING PROGRAM: THALES: REINFORCEMENT OF THE INTERDISCIPLINARY AND/OR INTER-INSTITUTIONAL RESEARCH AND INNOVATION.

FRAMEWORK OF THE



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