ALTERNATING CURRRENT Machine Windings I.pdf

This is the introduction to mechanical energy conversion from electrical.

1. 1
EEE3091F: ENERGY CONVERSION
AC Machine Windings
(Appendix A – PC Sen)

2. 2
Topics:
Turn, coil, winding
Field distribution in elementary machine
Magnetic circuit of elementary machine
Windings –general
Concentrated winding configuration
Distributed winding configuration
3-Phase winding configuration

3. 3
Turn, Coil, Winding:Concepts:
“S”- Start
“F” –Finish
No. of conductors
No. of turns
Coil sides, End conn.

4. 4
Turn, Coil, Winding:
Concepts:
Mmf of coil
Plane, axis of coil

5. 5
Turn, Coil, Winding:Concepts:
No. of turns winding
Mmf of winding
Plane, axis of winding

6. 6
Turn, Coil, Winding:Concepts:
Interconnection of
coils to form 3
windings

7. 7
Topics:
Turn, coil, winding
Field distribution in elementary machine
Magnetic circuit of elementary machine
Windings –general
Concentrated winding configuration
Distributed winding configuration
3-Phase winding configuration

8. 8
Field distribution in elementary machine

9. 9
Concepts:
Spatial distribution of
field in airgap
Mechanical versus
electrical angle
Field distribution in elementary machine

10. Mechanical angular displacement = ½ Electrical angle
In general:
10
2
ed
md
θ
θ=
poles ofnumber where;
2
== p
p
ed
md
θ
θ
Concepts:
Relationship: Mech vs
Elec angle
Field distribution in elementary machine

11. 11
Topics:
Turn, coil, winding
Field distribution in elementary machine
Magnetic circuit of elementary machine
Windings –general
Concentrated winding configuration
Distributed winding configuration
3-Phase winding configuration

12. 12
Magnetic circuit of elementary machine
Concepts:
Rotor:
2 coils in series = field
winding
2 poles
Mmf of Field winding

13. 13
Magnetic circuit of elementary machine

14. 14
Magnetic circuit of elementary machine

15. 15
If core is infinitely permeable, then Rc = 0 =>
HBµ=
g
o
og
l
Ni
HB
2
µ
µ
==
g
ll
l
Ni
HNidlH
⋅=
=⇒=
∫
2 :Where
.






+⋅
==Φ
2
2
cR
Rg
Ni
R
F
;
2
gR
Ni
=Φ
;
gA
B
Φ
=
go
g
gA
l
Rµ
=
Recall:
Magnetic circuit of elementary machine

16. 16
Topics:
Turn, coil, winding
Field distribution in elementary machine
Magnetic circuit of elementary machine
Windings –general
Concentrated winding configuration
Distributed winding configuration
3-Phase winding configuration

17. 17
Windings:
Concepts:
Stator, rotor, slots,
airgap

18. 18
Windings:
Concepts:
Stator, slots,
coils, winding

19. 19
Windings:
Concepts:
Stator, slots, coils,
winding

20. 20
Windings:
Concepts:
Stator, slots, coils,
winding

21. 21
Windings:

22. 22
Windings:

23. 23
Topics:
Turn, coil, winding
Field distribution in elementary machine
Magnetic circuit of elementary machine
Windings –general
Concentrated winding configuration
Distributed winding configuration
3-Phase winding configuration

24. 24
Concepts:
Coil sides in 2 stator
slots
Nonspecific rotor
What’s the spatial
distribution of Mmf in
airgap?
Use Ampere’s Circuit
Law:
Concentrated Winding Configuration:
∫∑=⋅
→→
i dH

25. 25
gll
l
Ni
HNidlH
⋅=
=⇒=
∫
2 :Where
.
Concepts:
Square-wave spatial
distribution of Mmf
What’s effect of
current on Mmf?
What if current is
time-varying?
Concentrated Winding Configuration:

26. 26
MMF
l
Ni
B
g
o
g ∝=
2
µ
Concentrated Winding Configuration:
Concepts:
Field distribution
What’s effect of
current on field?
Field distribution rich
in harmonics

27. 27
Features of Concentrated Winding:
Full-pitch coils: Coil sides in diametrically opposite slots
How can we increase B
g?
Increase current
Increase winding turns
More coils in series
More coil sides/slot
Problems:
Coil sides in 2 slots
2 Big slots needed for coil sides
Large portion of stator unused
g
o
g
l
Ni
B
2
µ
=

28. 28
More Problems:
Air gap flux density waveform rich in harmonics
(Square wave)
Leads to harmonic torques, which produce speed
pulsations in machine
Also, leads to harmonic core losses (Eddy, Hysteresis,
Stray)
SINE WAVE MMFand Flux Density desirable!
Features of Concentrated Winding:

29. 29
Topics:
Turn, coil, winding
Field distribution in elementary machine
Magnetic circuit of elementary machine
Windings –general
Concentrated winding configuration
Distributed winding configuration
3-Phase winding configuration

30. 30
Distributed Winding Configuration:
Concepts:
Coil sides in several
slots
Nonspecific rotor
What’s the spatial
distribution of Mmf in
airgap?
Use Ampere’s Circuit
Law:
∫∑=⋅
→→
i dH

31. 31
Distributed Winding Configuration:
Concepts:
Stepped distribution
of Mmf and B
What’s effect of
current on Mmf and
B?
What if current is DC
?
MMF
l
Ni
B
g
o
g
∝=
2
µ

32. 32
Features of Distributed Winding
Coil sides in several slots around periphery of stator
Stepped MMF/ Flux Density distribution
Resembles desired Sinewave
Less harmonics than Square- wave
in concentrated winding
Large portion of stator utilised
Full-pitch coils
Coil sides in diametrically opposite slots

33. Stator with 1 coil shown
Note:
Rotor poles of Synchronous Machines
Slots,
Teeth,
End connection
33

34. Stator with 1 coil shown
24 Slots, 4 poles
Pole-pitch (span) in [°mech]:
= 360° mech / 4poles
= 90°mech
Pole-pitch (span) in [°elec]:
= 90°mech x 4/2 pole pairs
= 180° elec
Pole-pitch (span) in [slots]:
= 24slots / 4poles
= 6slots
34

35. Stator with 1 coil shown
24 Slots, 4 poles
Pole-pitch (span): 24/4 = 6 slots = 90°mech = 180° elec
Coil-pitch (span): 5 slots = 75°mech = 150° elec < Pole-pitch
=> 5/6 of a pole-pitch => Short-pitched coils
Slot-pitch: 1 slot
= 360° /24
= 15°mech
= 30°elec
35