2. Poly phase IM windings

1
2. Poly phase IM windings

• Introduction
• The winding of a machine is the arrangement of
• conductors' designed to produce emfs by
  relative
• motion in a magnetic field.
• Electrical machines employ groups of
  conductors
• distributed in slots over the periphery of
  the
• armature.
• The groups of conductors are connected in
  various
• types of series-parallel combination to form
• armature winding.

2

• The conductors are connected in series so as to
  increase the voltage rating.
• They are connected in parallel to increase the
  current rating.
• Terminologies associated with ac windings
• - Conductor a length of wire which takes active
  part in the energy converting process.
• - Turn One turn of wire consists of two
  conductors.
• - Coil A coil may consist of a single turn or
  may consist of many turns, placed in almost
  similar magnetic position, connected in series.
• - Coil-Side A coil consists of two coil sides,
  which are placed in two different slots, and are
  almost a pole pitch apart.

3
Coil and a coil group
4
(No Transcript)
5

• - Pole pitch The peripheral distance
  between identical points on the two adjacent
  poles. It is always equal to 1800 electrical.
• - Coil span or coil pitch The distance
  between two coil sides of a coil. It is usually
  measured in terms of teeth, slots or electrical
  degrees.
• - Chorded coil If the coil span is equal to
  the pole pitch, then the coil is termed as a full
  pitch coil. In case the coil pitch is less than
  pole pitch, then it is called chorded, shorten,
  or fractional pitch coil.
• - Phase belt the group of adjacent slots
  belonging to one phase under one pole-pair. (
  Phase band, phase group)
• - Phase spread the angle subtended by one
  phase-belt is called phase spread, s

6

• Consider the case of a 12-slot armature having
  two poles and wound for three phases as shown in
  the fig. If the flux density wave shape is
  considered to be sinusoidal, the emfs of the
  conductors in the adjacent slots can be
  represented as phasors displaced from each other
  by an angle as (electrical) .

7
SEQUENCE of PHASES AND PHASE BELT

• In poly phase windings it is essential that,
• The generated emfs of all the phases are of
  equal magnitude
• The wave forms of the phase emfs are identical
• The frequency of the phase emfs are equal and
• The phase emfs have mutual time-phase
  displacement of ß 2p/m electrical radians
  where m is the no. of phases.

8

• If the winding is divided into three groups (one
  for each phase) spread over two pole pitches, the
  electrical displacement in space between the
  groups is 2?/3 electrical radian or 1200
  electrical.
• Each phase is located in four consecutive slots
  and so the phase spread is 4 x 300 1200
  electrical.
• If the conductors in the slots are connected as
  per the phasor diagram (in additive arrangement),
  the summation of conductor emfs would give three
  emfs displaced 1200 in time, following a phase
  sequence of ABC in time. The space sequence is
  also 1200.

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• The conductors in adjacent slots 1,2,3 and 4
  belong to phase A, Forming phase belt, phase
  band, phase group of phase A.
• Similarly, conductors 5,6,7, and 8 and conductors
  9,10,11,and 12 form phase belts of phase B and
  phase C respectively.
• Sequence of phase belt

• Let us Consider the case of a 12-slot armature
  having two
• poles and wound for three phases.
• The 12 conductors can be used to obtain
  three-phase single layer winding having a
  phase spread of 600.
• The coil span Ys S/p 12/2 6
• Slot angular pitch as 2p/S 2p/12
  300
• Thus for a phase spread of 600, two adjacent
  slots must belong to the same phase. Therefore,

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• Conductors of phase A coil groups are placed in
  slots, 1,2 and 7,8.
• Conductors of phase B are placed in slots 5,6 and
  11,12.
• Conductors of phase C are placed in slots 3,4 and
  9,10.
• Conductors in slot 7,8 are return conductors for
  conductors in slots 1,2.
• Conductors in slots 11,12 are return conductors
  for conductors in slots 5,6.
• Conductors in slots 3,4 are return conductors for
  conductor in slots 9,10.
• If the conductors were connected as represented
  by the phasor diagram , we would still get three
  equal emfs displaced by 1200 in time, following a
  phase sequence A C B A C B in space for a
  phase sequence of A B C supply voltage.

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• In this winding diagram, phase belt consisting of
  conductors in slot 1 and 2 are designated by A
  whereas, the phase belt made up of return
  conductors 7,8 is denoted by A.
• For a three phase winding, phase B must start
  1200 away from start of phase A and phase C must
  start 1200 away from phase B.

-A
-B
-C
A
C
12
TYPES OF AC MACHINES WINDINGS

• There are two basic physical types for ac machine
  windings. They behave differently with
  arrangements of coils in sequence around the
  armature.
• The two types are
• Single layer winding and
• Double layer winding

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1. SINGLE LAYER WINDING

• The fig. below shows an arrangement for a single
  layer winding. In this type of winding
  arrangement, one coil side of a coil occupies the
  whole slot.

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• Single layer windings are not used for machines
  having commutator. Single layer winding allow the
  use of semi-closed and closed types of slots.
• TYPES OF SINGEL LAYER WINDINGES
• The three most common types of single layer
  windings are
• Concentric windings ( Unequal coil span)
• Chain windings (equal coil span)
• Mush windings (equal coil span)

15
CONCENTRIC WINDING

• Three-phase concentric winding consists of coil
  groups laid in the slots so that all the coils of
  each group are concentric.
• That is, the coil with the smallest slot pitch is
  surrounded by the coil with the next larger slot
  pitch and so on to make up a coil group.

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• Each coil consists of several turns and the
  cross-over from one coil to the next is indicated
  by a short slanted line (jumper).
• In order to construct the diagram for a winding,
  the following date must be known
• S - The number of slots in the stator
• P The number of poles
• m The number of phases
• YS The pitch of the winding
• a The number of parallel circuits in
  the
• windings

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• The pitch of the winding is determined by the
  formula
• The pitch is the distance between two sides of a
  coil expressed as the difference between the
  numbers of the slots in which the sides lie.
• Another important value of the winding of ac
  machines is the number of slot per phase per pole
  denoted by the letter q. It can be determined by
  the formula

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• Sometimes q is called a pole-phase group, and is
  defined as a group of coils of a phase under one
  pole.
• The number of slots per pole per phase in
  concentric winding can be seen directly from the
  diagram. It is equal to the number of coils in a
  coil group.

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CONNECTTNG COIL GROUPS INTO PHASES

• As soon as all the coils have been laid in the
  slots, the coil groups are connected in to
  phases.
• Each group is provided with two leads for the
  start and finish of the group.
• The total number of leads is therefore twice the
  number of coil groups.
• A stator winding must have six leads brought out
  to the terminal panel these leads being the
  beginnings and ends of the three phases.
• All the reaming leads must be interconnected in
  the respective phases with in the winding.
• It is now necessary to decide in order to
  determine the beginnings and ends of each phase.

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IN GENERAL TWO MAINS RULES ARE FOLLOWED

• The distance between the beginning of the phase
  and the distance between the beginning of another
  phase must be equal to 120 electrical degrees.
• Any slot can be chosen as the beginning of the
  first phase.
• The coil groups in each phase should be
  interconnected by joining there unlike leads,
  i.e. start to finish, or finish to start.

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Example 1

• Given
• S24 p4m3 a1 typeConcentric
• a) The number of coil groups,K

i.e. there is two coil groups per phase
b)The number of slots per pole per phase, q
i.e. there are two coils in a group
c) Coil pitch
Full-Pitch ( average pitch)
coil pitch The shorter YS-16-15
The larger coil pitch YS1617
22

• d) The electrical angle, ?

e) The angle between adjacent slots, ?
f) The distance between the beginning of each
phase, ?
If the beginning of Phase A is slot 1, then the
beginning of phase B is slot 1?5 and the
beginning of phase C is slot 12?189
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Phase sequence
A A C C B B A A C C B B A A C C B B A A C C B B
24

• connection Diagrams

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Coil Groups of Phase A

• The first and second slots will be occupied by
  left-hand
• sides of the first coil group of phase A.
• Leave four, or 2q slots free for other two phases
  occupy
• slots 7 8 with the right hand side of the
  first coil
• group.
• Next to it will lie a second coil group of the
  same size
• which occupies slots 9,10,15,16.

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Coil Groups of Phase B

• In order to find, where the second phase (B)
  should begin, it is necessary to know the angle
  between slots in electrical degrees.
• ?180.P 180.4 7200 Electrical degree

• The angle between adjacent slots, ?
• The distance between phase beginnings will have

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Coil Groups of Phase C
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Current direction
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Phase A Coil groups interconnection
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• Connection of other two phases is exactly similar
  to that of phase A.
• The three phases interconnection within the
  phase coil groups and completed end terminals of
  the motor winding is as follows-

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MUSH WINDING

• This winding is very commonly used for small
  induction motors having circular conductors.
• This is a single layer winding where all the
  coils have same span (unlike the concentric
  winding where coils have different spans).
• Each coil is wound on a former, making one coil
  side shorter than the other.
• The winding is put on the core by dropping the
  conductors, one by one into previously insulated
  slots.
• The short coil sides are placed first and then
  the long coil sides. The long and short coil
  sides occupy alternate slots.
• It will be also observed that the ends of coil
  situated in adjacent slots cross each other i.e.
  proceed to left and right alternatively.
• That is why sometimes it is known as a basket
  winding.

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MUSH WINDING
Coil pitch
33
Basket winding
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Points to be remembered

• The following should be kept in mind while
  designing a
• mush winding, that is
• The coils have a constant span.
• There is only one coil side per slot and
  therefore the number of coil sides are equal to
  number of slots.
• There is only one coil group per phase per pole
  pair and therefore, the maximum number of
  parallel paths per phase is equal to pole pair.
• The coil span should be odd. Thus for a 4 pole 36
  slot machine, coil span should be 36/49 while
  for a 4 pole 24 slot machine, the coil span
  should not be 24/46 it should be either 5 or 7
  slots. This because a coil consists of a long and
  a short coil side. The long and short coil sides
  are placed in alternate slots and hence one coil
  will be in an even numbered slot and the other in
  an odd numbered slot giving a coil span which is
  an odd integer.

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Example 2

• Given data
• S12 p2m3 a1 typeMush

Solution

1. The number of coil groups, K

i.e. there is one coil group per phase

1. The number of slots per pole per phase, q

i.e. there are two coils in a group

1. Coil pitch

Full-Pitch
This is an even number and hence the winding is
not possible with an even coil span . There fore
, it is shortened by one slot and a coil span of
5 slots is used.
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• d)The electrical angle, ?

e) The angle between adjacent slots, ?
f) The distance between the beginning of each
phase, ?
g) If the beginning of Phase A is slot 1, then
the beginning of phase B is slot 1?5 and the
beginning of phase C is slot 12?189
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Phase sequence
1 2 3 4 5 6 7 8 9 10 11 12
A A C C B B A A C C B B
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Connection Diagrams
39
Coil group of Phase A

• Lay down coil-group belonging to phase A inside
  the slots 1,2 and 7,8.

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Coil group of Phase B
41
Coil group of Phase C
42
Current direction
43
Phase A Coil group interconnection
44
Phase A B Coil group interconnections
45
Phase A,B C Coil group interconnections and
Terminals
46
CHAIN WINDING

• In all aspects, this winding is similar to that
  of mush winding except that both coil sides of a
  coil have equal length and diamond shape.

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Example 3

• Using the data and the solution of Example 2,
  construct the single-layer chain winding diagram.
• Connection diagrams

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Connection of phases A,B and C and End terminals
49
DOUBLE LAYER Three phase WINDING

• Double layer windings differ from single layer
  winding mainly on the
• following main points
• Each slot is occupied by the side of two coils
  and each coil is arranged to form two layer round
  stator.
• One layer of the winding lies in the bottom half
  of the slots and the other in the top half of
  slots.
• Unlike the concentric winding double layer
  winding consists of identical coils all of the
  same shape and pitch.
• In a double layer winding, the coil pitch is the
  distance between the top and the bottom sides of
  the coil expressed by the number of slots spanned
  or by the coil sides or by the number of slots
  occupied by each coil side.
• A coil pitch may be full or fractional. Majority
  stator windings use a fractional pitch because
• The amount of copper used in the overhang (end
  winding) reduced and hence a saving on copper,
  and
• The magnitude of certain harmonics in the emf and
  also mmf is suppresed.

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• The full pitch is determined by
• Usually the full pitch is shortened by one-sixth
  i.e. for example if the full pitch is 12 a
  fractional will be 10.
• Since the coils are wound with a continuous
  length of wire there are no connections between
  turns.
• In ac machine winding, if the number of slots per
  pole per phase q S/mp is an integer, then the
  winding is called integral slot winding.
• In case the number of slots per pole per phase is
  not an integer, the winding is called fractional
  slot winding.

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• Examples
• Given a) S 24, p 4, m 3, then
• q S/mp 24/(3x4) 2, is an
  integer.
• ( Integral-slot winding)
• b) S 30, p 4, m 3, then
• q S/mp 30/(3x4) 5/2 2
  is not an integer.
• (fractional-slot
  winding)

52

• Fig. pertaining to double layer, full pitch
  integral- slot winding

A1
-A1
53

• The main value characterizing double layer
  winding is the number of slots per pole per
  phase.
• By looking double layer winding externally, it is
  not possible to determine q.
• The total number of coils in double layer winding
  is equal to the number of slots since each side
  of a coil occupies one half of a slot which is
  equivalent to occupying one full slot per coil.
• In order to avoid making solder joints between
  coils, several coils, depending upon slots per
  pole per phase, are generally wound from a single
  length of wire in to full coil group.
• The number of coil groups per phase is a equal to
  the number of poles of the whole winding. That is
• This is, twice that in a single-layer winding
  which is K (mp)/2.

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• Example 4
• Given- S 12 p 2 m 3 a 1 type
  Double layer, shortened by one slot

Solution

1. The number of coil groups, K

i.e. there is two coil groups per phase

1. The number of slots per pole per phase, q

i.e. there are two coils in a group and is
Integral-slot winding

1. Coil pitch

Full-Pitch
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Let us shorten the pitch by one slot and make YS
5.
d) The electrical angle, ?
e) The angle between adjacent slots, ?
f) The distance between the beginning of each
phase, ?
If the beginning of Phase A is beginning of slot
1, then the phase B is slot 1?5 and the
beginning of phase B is slot 12?189
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Connection Diagrams
57
PROCEDURE FOR CONSTRUCTING DOUBLE LAYER WINDINGS

• Draw 24 vertical lines to represent the two coil
  sides lying in each of the 12 slots. For each
  slot the full line at the left hand side will
  represent a top a coil side and broken line at
  the right hand side a bottom coil side.

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Phase A Coil groups
59
Phase A B Coil groups
60
Phase A, B C Coil groups
61
Current direction
62
Each Phase coil groups interconnections End
Terminal leads
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Rule for double layer windings

• The coil groups should be connected to each other
  by joining the leads of like polarity i.e. the
  finish of one group to the finish of the next
  group and the start of one group to the start of
  the next group.
• For full pitch integral-slot winding, each slot
  contains coil sides belonging to the same phase.

-A1
Integral-slot, full pitch double layer winding.
(PHASE A)
A1
64
Advantages of double layer winding over single
layer windings

• Easier to manufacture and lower cost of the
  coils,
• Fractional-slot winding (slot per pole per phase
  is not an integer) can be used,
• Corded winding is possible,
• Lower leakage reactance, and therefore, better
  performance of the machine,
• Better emf wave form in case of generators.

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Integral-slot chorded winding

• Coil pitch in poly phase machines is usually less
  than pole-pitch and such a winding arrangement is
  called short pitch or chorded or fractional
  winding.
• Usually the coil pitch varies from 2/3 pole pitch
  to full pole pitch.
• A coil span less than 2/3 pole pitch is not used
  in practice. Because a chording more than 1/3
  pole pitch would noticeably reduce the phase emf.
• As explained earlier, advantages of short
  pitched,( chorded, fractional) windings are-

• The amount of copper used in the overhang (end
• winding) reduced and hence a saving on copper,
  and
• The magnitude of certain harmonics in the emf and
• also mmf is suppressed.

66
Example 5

• Given- S 12, p 2, 600 phase spread, chorded
  by 5/6.
• angle b/n adjacent slots a 360/12
  300
• Full pole-pitch, Ys S/p 12/2 6
  slots, i.e. 6x30 1800 elec. chorded coil-pitch,
  Ys 5/6 pole pitch, i.e. (5/6)x6 5 slots
• slots perphase per pole, q s/mp 12/(3x2)
  2
• 1 2 3 4 5 6
  7 8 9 10 11 12

A
-A
B
-B
C
-C
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• Note that-
• In integral full pitch winding, a slot contains
  coil sides of the same phase.
• In integral chorded pitch winding, some slots
  contain coil sides pertaining to different
  phases.
• Interconnection between the phase belts of
  chorded three phase winding is done in a similar
  manner to that explained earlier for full pitch
  winding.

Fractional slot winding

• As explained previously, We frequently come
  across
• windings in which the number of slots per
  phase per
• pole is not a whole number.
• The slots per pole per phase are expressed as a
  whole
• number plus a fraction.

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• For example
• A motor stator with 36 slots is wound for six
  poles.
• Such a motor will have a speed near 1,000 rpm
  and the number of slots per pole per phase is -
• If the same stator must be rewound for the lower
  speed of 750 rpm, i.e., for 8 poles, the number
  of slots per pole per phase will then be-

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• In induction motors such cases usually arise when
  stators with the same number of slots are wound
  for more than one number of poles.
• For fractional slot windings, however, from the
  view point of symmetry, the number of slots must
  be divisible by the number of phases. i.e 3.
• Limitations of fractional slot windings are
• - It can be used only with
  double-layer windings
• - The number of parallel circuits
  is limited
• The fractional-slot winding differs from the
  integral-slot winding in that it must be composed
  of coil groups with different numbers of coils
  and each phase must occupy the same number of
  slots, otherwise the winding would be unbalanced.
  
• Usually, the fractional-slot winding is a
  combination of two types of coil groups

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• One in which the number of coils in the group is
  equal to the integer part of the number of slots
  per pole per phase.
• The other in which the number of coils is one
  greater than in the first type.
• If for example, the number of slots per pole per
  phase is 2 ½, the winding will be built up of
  alternating coil groups containing two and three
  coils each, every two-coil group being followed
  by a three-coil group.
• 2-3-2-3-2-3.
• Because of the alternation, the number of slots
  per pole per phase is-

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• Sometimes the fractional number of slots per pole
  per phase is expressed as an improper fraction,
  i.e.

In the example above, c5 and d2
To obtain a balanced or symmetrical winding, it
is necessary that be equal to a whole
number.
Where, S - being the number of slots, t
- the largest common factor for S and P, and m
- the number of phases.
72
Arranging fractional slot windings with the aid
of tables

• The coil groups in a fractional-slot winding are
  easily arranged with the aid of a table.
• Taking a sheet of millimeter lined paper, the
  table is drawn with as many horizontal lines as
  there are poles, and each line is divided into 3C
  boxes, where C is the numerator of the improper
  fraction representing the slots per pole per
  phase and 3 is no. of poles.
• The table is next divided by vertical lines
  forming three equal columns for the thre phases
  with C boxes per phase.
• Following this, in ordinal succession, the boxes
  are filled in with the numbers of the slots at
  intervals of d boxes, where d is the denominator
  of the fraction expressing the number of slots
  per pole per phase.

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• Example - 6
• Given- S 27, p 6, m 3, q 1½ 3/2
• Solution
• The largest common factor t for S 27 and p
  6 is-
• 27 3x3x3
• 6 2x3
• then, t 3 and S/(txm) 27/(3x3) 3
  is a whole number.
• 1. draw a table where no. rows no. of poles
  and each column of three phases with C no. of
  sub columns.
• where, C is the numerator of the improper
  fraction.
• 2. Fill the boxes starting from the extreme left
  top box with cross or consecutive numbers
  (representing adjacent sots). Proceed to the
  right marking crosses/numbers separated from each
  other by denominator of the improper fraction of
  no. of slots per phase per pole.

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No. Of Poles PHASE A PHASE A PHASE A PHASE C PHASE C PHASE C PHASE B PHASE B PHASE B
N 1 2 3 4 5
6 7 8 9
10 11 12 13 14
15 16 17 18
19 20 21 22 23
24 25 26 27
S
N
S
N
S
Table arranging coil groups for 600 elec. Phase
spread.
75
Winding table Interpretation

• Reading the table horizontally line by line,
  write down the letter of the respective phase
  each time a cross/number appears in its column.
• This reveals the following sequence of the coils
  of each phase under consecutive poles.
• AACBB, ACCB, AACBB, ACCB, AACBB, ACCB.
• Each letter indicates the coils of each phase,
  and like letters succeeding one another indicate
  how many coils of the same phase the group will
  contain.
• Thus, in our example, the sequence shows that it
  is necessary to prepare nine groups of two coils
  each and nine single coils.
• They will occupy (9x2)9 27 slots with the
  following arrangement.
• 2,1,2 1,2,1 2,1,2 1,2,1 2,1,2 1,2,1.
• N S N S
  N S

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Slots per pole per phase Coil group sequence for phase sequence ACB
1 ½ (1-2), (1-2), (1-2), etc.
1 ¼ (1-1-1-2), (1-1-1-2), etc.
1 ¾ (1-2-2-2), (1-2-2-2), etc.
1 1/5 (1-1-1-1-2), (1-1-1-1-2), etc.
1 2/5 (2-1-2-1-1), (2-1-2-1-1), etc.
1 3/5 (1-2-1-2-2), (1-2-1-2-2), etc.
2 ½ (2-3), (2-3), etc.
3 ¼ (3-3-3-4), (3-3-3-4), etc.
4 1/5 (4 -4 -4 -4 -5), (4 -4 -4 -4 -5),etc.
77
Summary on Fractional-slot Winding

• When the integer before the fraction is greater
  than unity, the numbers in the sequence table
  must be that integer and a number increased by
  one.
• Thus, for example, when q 1 ½ , the sequences
  will contain repeating single and two-coil groups
  (1-2), while in the case where q 2 ½ the
  repeating sequences will contain two-coil and
  three coil groups (2-3).
• The number of integers in a period is equal to
  the denominator d of the improper fraction
  expressing the slots per pole per phase the sum
  of the integers is equal to c, the numerator of
  the improper fraction.
• Thus, when the period consists of five integers
• (1-2-1-2-2), the sum of the integers is 8,
  i.e., it is equal to the numerator of the
  fraction.

78

• Assignment
• Construct a winding table for the following
  given data of an IM and, draw the wining
  diagram.
• Given- S 84, P 20, m 3
• Type of the winding - double-layer winding.