Armature winding and Introduction to Harmonics

1. Electrical Machines-II
6th Semester, EE and EEE
By
Dr. Binod Kumar Sahu
Associate Professor, Electrical Engg.
Siksha ‘O’ Anusandhan, Deemed to be University,
Bhubaneswar, Odisha, India
Lecture-3

2. 2
Learning Outcomes: - (Previous Lecture_02)
Students will be able to:
 Classify different types of alternators from construction point of view.
 Know the advantages of stationary armature (rotating field) type construction
over rotating armature (stationary field) type construction.
 Know which type of alternator is suitable for a particular application.
 Determine the generated emf in an alternator.

3. 3
Learning Outcomes: - (Today’s Lecture_03)
Students will be able to:
 Know the various terms related to armature winding.
 Analyse the concept of harmonics and its sources in alternator.
 Determine the RMS value of complex waveforms.
 Know the disadvantages of harmonic components.

4. 4
Armature winding: -
 We know that any rotating electrical machine has a rotor and a stator.
 In an alternator stator is the armature and rotor is the field system.
 So stator carries a three phase AC winding whereas, the rotor carries a field
winding fed form a DC source.
 The stator is slotted on its inner periphery to carry the 3-phase armature or
stator winding.
 Three phase stator winding is an open winding where as that of a DC machine
is of closed type.

5. 5
DC Machine Armature Winding (Closed type): -
Armature Slot
Armature Teeth
Armature winding in slot
Paper insulation between
armature conductor and armature core
Commutator Segment Insulation between Commutator Segment

6. 6
AC Machine Armature Winding (Open type): -
Three armature terminals
after delta connection
Four armature terminals
(three for phases and one neutral)
after star connection
R1
R2
B1
Y1Y2
B2
R1
R2
Y1
Y2
B2
B1

7. 7
Important terms related to Armature Winding: -
I. Electrical angle and mechanical angle: -
 For the simple loop generator shown in
the figure, one revolution of the rotor
gives rise to one cycle of induced emf.
 One revolution of the rotor is 3600
mechanical and one cycle of induced
emf corresponds to 3600 electrical.
 So, for a two pole machine electrical
angle is same as the mechanical angle.
N
S




X
.

8. 8
Electrical angle and mechanical angle (Contd…): -
 For the simple loop generator having 4 poles
shown in the figure, one revolution of the rotor
gives rise to two cycles of induced emf.
 One revolution of the rotor is 3600 mechanical
and two cycles of induced emf corresponds to
2x3600 = 7200 electrical.
 So, for a four pole machine electrical angle twice
the mechanical angle.
 So, in general
𝒆𝒍𝒆𝒄𝒕𝒓𝒊𝒄𝒂𝒍 𝒂𝒏𝒈𝒍𝒆
=
𝑷
𝟐
× 𝒎𝒆𝒄𝒉𝒂𝒏𝒊𝒄𝒂𝒍 𝒂𝒏𝒈𝒍𝒆
i.e. 𝜽 𝒆 =
𝑷
𝟐
× 𝜽 𝒎, where, P is the number of poles.
X
N
SS
N



 


..
X

9. 9
II. Pole Pitch: -
 It is the peripheral distance between identical locations of two consecutive
poles. Normally it is measured between the centres of two consecutive poles.
 It can be measure in terms of distance in ‘m’ or ‘cm’, number of slots,
number of conductors/coil sides or electrical degrees.
 A coil has two coil sides and 𝟐 × 𝑵 number of conductors, where ‘N’ is the
number of turns in the coil.
Overhang or inactive length
Overhang or inactive length
Overhang or inactive length

10. 10
Pole Pitch X
N
SS
N



 


..
X
N
S




X
.
2-Pole, Single Phase Machine 4-Pole, Single Phase Machine

11. 11
Let both the machines are identical and have the following specifications:
Diameter = 150 cm, number of slots = 48, number of coils = 24 with
each coil having 8 turns.
So, for the 1st machine with 2-poles, 𝑷𝒐𝒍𝒆 𝑷𝒊𝒕𝒄𝒉 =
𝝅𝑫
𝑷
=
𝝅×𝟏𝟓𝟎
𝟐
= 𝟐𝟑𝟓. 𝟔𝟐 𝒄𝒎
=
𝑵𝒖𝒎𝒃𝒆𝒓 𝒐𝒇 𝒔𝒍𝒐𝒕𝒔
𝑵𝒖𝒎𝒃𝒆𝒓 𝒐𝒇 𝒑𝒐𝒍𝒆𝒔
=
𝟒𝟖
𝟐
= 𝟐𝟒 𝒔𝒍𝒐𝒕𝒔
Each single turn has two conductors.
So, the total number of armature conductors
𝑍 𝑇 = 𝑛𝑢𝑛𝑚𝑒𝑟 𝑜𝑓 𝑐𝑜𝑖𝑙𝑠 × 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓𝑡𝑢𝑟𝑛𝑠/𝑐𝑜𝑖𝑙 × 2 = 24 × 8 × 2 = 𝟑𝟖𝟒.
So, pole pitch in terms of number of conductors =
𝑇𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑐𝑜𝑛𝑑𝑢𝑐𝑡𝑜𝑟𝑠
𝑃
=
384
2
= 𝟏𝟗𝟐.
In terms of angle, pole pitch = 𝟏𝟖𝟎 𝟎
mechanical = 𝟏𝟖𝟎 𝟎
electrical. (As it is a 2-
pole machine).

12. 12
For the same machine specifications:
Diameter = 150 cm, number of slots = 48, number of coils = 24 with
each coil having 8 turns.
For the 2nd machine with 4-poles, 𝑷𝒐𝒍𝒆 𝑷𝒊𝒕𝒄𝒉 =
𝜋𝐷
𝑃
=
𝜋×150
4
= 117.81 𝑐𝑚
=
𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑠𝑙𝑜𝑡𝑠
𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑝𝑜𝑙𝑒𝑠
=
48
4
= 𝟏𝟐 𝒔𝒍𝒐𝒕𝒔
Each single turn has two conductors.
So, the total number of armature conductors
𝑍 𝑇 = 𝑛𝑢𝑛𝑚𝑒𝑟 𝑜𝑓 𝑐𝑜𝑖𝑙𝑠 × 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓
𝑡𝑢𝑟𝑛𝑠
𝑐𝑜𝑖𝑙
× 2 = 24 × 8 × 2 = 𝟑𝟖𝟒.
So, pole pitch in terms of number of conductors =
𝑇𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑐𝑜𝑛𝑑𝑢𝑐𝑡𝑜𝑟𝑠
𝑃
=
384
4
= 𝟗𝟔 conductors.
In terms of angle, pole pitch 𝟗𝟎 𝟎 mechnical =
𝑷
𝟐
× 𝟗𝟎 𝟎 = 𝟏𝟖𝟎 𝟎electrical.
** So, for any machine, pole pitch is always 𝟏𝟖𝟎 𝟎
electrical.

13. 13
Armature Winding of a simple loop generator
Single Phase Three Phase
Has a single turn coil. (Two conductors) Has three single turn coils, each phase
having one coil. (Six conductors, two for
each phase i.e. two for R-phase, two for
Y-phase and two for B-phase).
Two conductors are separated by a pole
pitch i.e. 1800 electrical.
Two conductors of same phase (let R-
phase) are separated by a pole pitch i.e.
1800 electrical.
NA
The three coils of the three phases are
separated by 1200 electrical (i.e.
separation between the R-phase coil, Y-
phase coil and B-phase coil must be 1200
electrical) (As their induced emfs has a
phase difference of 1200 electrical)

14. 14
1200
N
S




X
.
Pole Pitch
1800 electrical
Single phase simple loop generator Three phase simple loop generator

15. 15
Harmonics in generated emf of an alternator: -
 EMF generated in the alternator is not sinusoidal, as distribution of flux in the air gap is not
perfectly sinusoidal rather it is distorted due to the following reasons:
i. Armature reaction.
ii. Slot harmonics
iii. Non-linear loads etc. (i.e. Transformers under no load and light loads, Saturated
Reactors, Thyrister controlled motor drives, Arc Furnaces, Arc Welders,
Conduction Furnaces, CFL/fluorescent tube lights, UPS, etc.) .
 In this lecture we will consider the 2nd reason i.e. distorted flux distribution due to slot
harmonics. After few lecturers we will consider the other two effects.
 We have already seen that the armature of the alternator is slotted at its inner periphery
to carry the armature winding.
 So, in the teeth region of the armature, air gap is less and hence it offers low reluctant
path.
 Whereas, in the slot region, air gap is more and hence this region offers a comparatively
high reluctant path for the flux.
 So, in the teeth region magnetic flux strength is more as compared to slot region.

16. 16

17. 17
Slot Teeth

18. 18
Fourier Series: -
Baron Jean Baptiste Joseph Fourier (1768−1830) introduced the idea that any
periodic function can be represented by a series of sine and cosine functions which
are harmonically related.

19. 19
 So the distorted flux distribution waveform
as shown in figure can be mathematically
expressed as:
𝐵 = 𝐵 𝑚1 𝑠𝑖𝑛𝜔𝑡 + 𝐵 𝑚2 𝑠𝑖𝑛2𝜔𝑡 +
𝑩 𝑚3 𝑠𝑖𝑛3𝜔𝑡 + 𝐵 𝑚4 𝑠𝑖𝑛4𝜔𝑡+….

20. 20
𝐵 = 𝐵 𝑚1 𝑠𝑖𝑛𝜔𝑡 + 𝐵 𝑚2 𝑠𝑖𝑛2𝜔𝑡 + 𝑩 𝑚3 𝑠𝑖𝑛3𝜔𝑡 + 𝐵 𝑚4 𝑠𝑖𝑛4𝜔𝑡+….
So, each component of the magnetic flux distribution gives its own emf waveform.
The 1st component is the fundamental component, 2nd component is the 2nd harmonic
component, 3rd component is the 3rd harmonic component, and so on.

21. 21
Flux distribution waveform containing harmonics (up to 7th Harmonics)

22. 22
EMF Calculation with Harmonics: -
If the flux has only the fundamental component i.e. 𝐵 = 𝐵 𝑚1 𝑠𝑖𝑛𝜔𝑡, maximum value
the flux/pole 𝜑 𝑚 =
𝐵 𝑚
𝐴𝑟𝑒𝑎 𝑢𝑛𝑑𝑒𝑟 𝑜𝑛𝑒 𝑝𝑜𝑙𝑒 𝑝𝑖𝑡𝑐ℎ
=
𝐵 𝑚
𝜋𝐷𝐿
𝑃
where, ‘D’ is the inner diameter
of the stator and ‘L’ is the length of the machine.
Average value of the flux/pole, 𝜑 =
2𝜑 𝑚
𝜋
.
So the RMS value of induced emf/phase, 𝐸 𝑝ℎ = 4.44𝑓𝜑𝑇𝑝ℎ.

23. 23
If the flux has fundamental and 3rd harmonic component,
i.e. 𝐵 = 𝐵 𝑚1 𝑠𝑖𝑛𝜔𝑡 + 𝐵 𝑚3 𝑠𝑖𝑛3𝜔𝑡,
Maximum value the fundamental component of flux/pole,
𝜑 𝑚1 = 𝐵 𝑚1 × 𝐴𝑟𝑒𝑎 𝑢𝑛𝑑𝑒𝑟 𝑜𝑛𝑒 𝑝𝑜𝑙𝑒 𝑝𝑖𝑡𝑐ℎ = 𝐵 𝑚1 ×
𝜋𝐷𝐿
𝑃
where, ‘D’ is the inner
diameter of the stator and ‘L’ is the length of the machine.
Average value of the flux/pole, 𝜑1 =
2𝜑 𝑚1
𝜋
.
So the RMS value of induced emf/phase, 𝐸 𝑝ℎ1 = 4.44𝑓𝜑1 𝑇𝑝ℎ.
Maximum value of 3rd harmonic component of the flux,
𝜑 𝑚3 = 𝐵 𝑚3 × 𝐴𝑟𝑒𝑎 𝑢𝑛𝑑𝑒𝑟 𝑜𝑛𝑒 𝑝𝑜𝑙𝑒 𝑝𝑖𝑡𝑐ℎ = 𝐵 𝑚3 ×
𝜋𝐷𝐿
3𝑃
***As the 3rd harmonic component, has a frequency of three times the
fundamental. So, it can be assumed that the effective number of poles for the 3rd
harmonic component is three times the actual number of poles of the machine.

24. 24
Average value of the 3rd harmonic flux/pole, 𝜑3 =
2𝜑 𝑚3
𝜋
.
So the RMS value of induced emf/phase, 𝐸 𝑝ℎ3 = 4.44(3 × 𝑓) 𝜑3 𝑇𝑝ℎ.
So, the effective value of the RMS value of induced emf, 𝐸 = 𝐸 𝑝ℎ1
2
+ 𝐸 𝑝ℎ3
2
.
If the flux distribution contains fundamental, 3rd and 5th harmonic components, then
effective RMS value of induced emf will be 𝐸 = 𝐸 𝑝ℎ1
2
+ 𝐸 𝑝ℎ3
2
+ 𝐸 𝑝ℎ5
2

25. 25
Actual number of poles for the
fundamental component.
Effective number of poles for the
2nd harmonic component.
N
S




X
.
X
N
SS
N



 


X

26. 26
The following points may be noted from the diagram shown in previous slide: -
 One revolution of the rotor gives rise to one cycle of induced emf of the
fundamental component.
 The same one revolution of rotor results in two cycles of induced emf of the 2nd
harmonic component.
 So, one revolution of rotor can produce ‘n’ cycles of induced emf of the nth
harmonic.
 Since a pair of pole produces one cycle of induced emf, the effective number of
poles for the ‘nth’ harmonic will be ‘n-time’ the actual number of poles in the
machine.

27. 27
A
B C
D
+
-
-
+
Topconductor
Bottomconductor
e e
2e
volt +-
A
B C
D
+
- -
+
Topconductor
Bottomconductor
e e
0
volt +-
 Directions of fundamental component of induced emfs in the conductors are such
that the total fundamental component of voltage across the coil is ‘N-times’ the
induced emf in one conductor, where ‘N’ is the number of turns in the coil.
 Directions of 2nd harmonic component of induced emfs in the conductors are
such that the total 2nd harmonic component of voltage induced in the coil is
zero.
 So the effect of even harmonic components in the induced emf can be ignored.
N
S




X
.
X
N
SS
N



 


X
Fundamental 2nd Harmonic Fundamental 2nd Harmonic

28. 28
Adverse effects of harmonics in the induced emf: -
The following are the effects of harmonics in the induced emf: -
 It distorts the waveform of voltage and current.
 Harmonic voltage and current cause increased heating in rotating machines due to additional iron
and copper losses at harmonic frequencies. This lowers the machine efficiency and affects the
torque developed.
 Since harmonic voltages produce harmonic currents with frequencies considerably higher than the
power system fundamental frequency, these currents encounter much higher impedances as they
propagate through the power system than does the fundamental frequency current.
 This is due to “skin effect” which is the tendency for higher frequency currents to flow near the
surface of the conductor.
 As the effective cross section of the conductor is reduced, the effective resistance of the conductor is
increased.
 The higher resistance encountered by the harmonic currents will produce a significant heating of the
conductor, since heat produced or power lost in a conductor is I2R, where I is the current flowing
through the conductor.
 This increased heating effect is often noticed in two particular parts of the power system: neutral
conductors and transformer windings.

29. 29
Thank you