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.

• 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.

Coil and a coil group

- 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, σ

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 αs

(electrical) .

e1

e10

e9

e8 e7e6

e5

e4

e3

e2e12

e11

1

11

10

9

8

76

5

4

3

212

A

C

B

306

radianS

Ps

e1

e4e3

e2

e5

e6

e8

e7

e12

e11

e10e9

1200

1200

1200

EC

EA

EB

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 β = 2π/m electrical radians; where m is the no. of phases.

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.

• 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: αs = 2π/S = 2π/12 = 300

Thus for a phase spread of 600, two adjacent slots must belong to the same phase. Therefore,

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.

e1

e10

e9

e8 e7e6

e5

e4

e3

e2e12

e11

1

11

10

9

8

76

5

4

3

212

A

C

B

A’

B’

C’

e1

-e4-e3

e2

e5

e6

-e7

-e12

-e11

e10e9

EC

EA

EB

-e8

• 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-A -B-C

CB

1 2 3 4 5 6 7 8 9 10 1 2

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:

1.Single layer winding and

2.Double layer winding

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.

Coilside

• 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

1.Concentric windings ( Unequal coil span)

2.Chain windings (equal coil span)

3.Mush windings (equal coil span)

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.

q

Start (S)

Finish(F)

Jumper

A coil-group with 3-coils

Y3

Y1

Y2

1

2

310

12

11

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

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

P

SYS

mP

Sq

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.

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.

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.

Example 1• Given

S=24; p=4;m=3; a=1; type=Concentric

a) The number of coil groups,K

62

43

23K P

b)The number of slots per pole per phase, q

243

24

pm

Sq

c) Coil pitch

64

24

p

SYS

i.e. there is two coil groups per phase

i.e. there are two coils in a group

Full-Pitch ( average pitch)

coil pitch The shorter = YS-1=6-1=5

The larger coil pitch = YS+1=6+1=7

d) The electrical angle,

7204180180 Pe) The angle between adjacent slots,

3024

720

S

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 1+2=1+8=9

slots430

120120

Phase sequence

B

B’

A’

A

C

C’600

A A C’

C’

B B A’

A’

C C B’

B’

A A C’

C’

B B A’

A’

C C B’

B’

connection Diagrams

A

A’

Phase A

1 8

2 7

13 20

14 19

I

IV

+7

+5

+7

+5

B

B’

Phase B

5 12

6 11

17 24

18 23

II

V

C’

C

Phase C

9 16

10 15

21 4

22 3VI

III

1

2 8

7

6

5

4

3 9

10

19

18

11 17

1614

1513

12

23

22

21

20 24

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.

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

3024

720

S

slots430

120120

1

2 8

7

6

5

4

3 9

10

19

18

11 17

1614

1513

12

23

22

21

20 24

Coil Groups of Phase C

1

2 8

7

6

5

4

3 9

10

19

18

11 17

1614

1513

12

23

22

21

20 24

3

4

3

4

22

21

21

22

Current direction

1

2 8

7

6

5

4

3 9

10

19

18

11 17

1614

1513

12

23

22

21

20 24

21

22 3

4

22

21

3

4

NSNS

N

1-6

S

7-12

N

13-18

S

19-24

Phase A – Coil groups interconnection

• 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:-

1

2 8

7

6

5

4

3 9

10

19

18

11 17

1614

1513

12

23

22

21

20 24

21

22 3

4

22

21

3

4

NSNS

A B’A’C’ CB

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.

Coil pitch

MUSH WINDING

Basket winding

Points to be rememberedThe 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 36/4=9 while for a 4 pole 24 slot machine, the coil span should not be 24/4=6; 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.

Example 2Given data

S=12; p=2;m=3; a=1; type=Mush

32

23

23K P

Solutiona) The number of coil groups, K

i.e. there is one coil group per phase

b) The number of slots per pole per phase, q

223

12

pm

Sq

i.e. there are two coils in a group

c) Coil pitch

62

12

p

SYS 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.

d)The electrical angle,

3602180180 P

3012

360

S

e) The angle between adjacent slots,

f) The distance between the beginning of each phase,

slots430

120120

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 1+2=1+8=9

Phase sequence

B

B’

A’

A

C

C’600

1 2 3 4 5 6 7 8 9 10 11 12

A A C’ C’ B B A’ A’ C C B’ B’

Connection Diagrams

A

A’

Phase A

1 8 L

2 7 R

+5

+5

B

B’

Phase B

5 12 L

6 11 R

C’

CPhase C

9 4 L

10 3 R

Coil group of Phase A• Lay down coil-group belonging to phase A inside

the slots 1,2 and 7,8.

1

2 8

7

6

5

4

3 9

10

11

12

8

8

1

1

Coil group of Phase B

1

2 8

7

6

5

4

3 9

10

11

12

125

12

8

8

5

1

1

Coil group of Phase C

1

2 8

7

6

5

4

3 9

10

11

12

12

3

5

12

10

8

8

10

5

3

1

1

Current direction

1

2 8

7

6

5

4

3 9

10

11

12

12

3

5

12

10

8

8

10

5

3

1

1

SN

N

1-6

S

7-12

Phase A: Coil group interconnection

1

2 8

7

6

5

4

3 9

10

11

12

12

3

5

12

10

8

8

10

5

3

1

1

SN

Phase A & B: Coil group interconnections

1

2 8

7

6

5

4

3 9

10

11

12

12

3

5

12

10

8

8

10

5

3

1

1

SN

Phase A,B & C Coil group interconnections and

Terminals

1

2 8

7

6

5

4

3 9

10

11

12

12

3

5

12

10

8

8

10

5

3

1

1

SN

A A’B B’C’ C

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.

1

2

7

6

5

4

3

Example 3• Using the data and the solution of Example 2,

construct the single-layer chain winding diagram.• Connection diagrams

A

A’

Phase A

2 7 R

1 8 L

+5

+5

B

B’

Phase B

6 11 R

5 12 L

C’

C

Phase C

10 3 R

9 4 L

Connection of phases A,B and C and End terminals

1

2 8

7

6

5

4

3 9

10

11

12

5

12

10

8

8

10

12

3

51

1

A B’A’C’ CB

3

DOUBLE LAYER Three phase WINDINGDouble 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.

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.

P

SYS

• 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)

2

1

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

A1

1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 20 1 2 3 4

-A1

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.

mP

Sq

Pm

K mPK

Example 4 Given:- S = 12; p = 2; m = 3; a = 1; type = Double layer, shortened

by one slot

6233K P

Solution

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

223

12

pm

Sq

i.e. there are two coils in a group

and is Integral-slot winding

c) Coil pitch

62

12

p

SYS Full-Pitch

Let us shorten the pitch by one slot and make YS = 5.

3602180180 P

d) The electrical angle,

e) The angle between adjacent slots,

3012

360

S

f) The distance between the beginning of each phase,

slots430

120120

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 1+2=1+8=9

Connection DiagramsA

A’

Phase A

1 6'

2 7'

7 12'

8 1'

I

IV

+5

+5

+5

+5

B

B’

Phase B

5 10'

6 11'

11 4'

12 5'

III

VI

+5

+5

+5

+5

C’

C

Phase C

9 2'

10 3'

3 8'

4 9'

II

V+5

+5

+5

+5

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.

1 1' 2'2 3'3 4 4' 5'5 6'6 7 7' 8'8 9'9 10 10' 11 11' 12 12'

Phase A Coil groups

1 1' 4'43'32'2 5 5' 109'6 98'7' 876' 1211'1110' 12'

1'

8

8

1'

Phase A & B Coil groups

1 1' 4'43'32'2 5 5' 109'6 98'7' 876' 1211'1110' 12'

4'

5'

1'

4'

5'

1'

8 12

11

8

12

11

Phase A, B & C Coil groups

1 1' 4'43'32'2 5 5' 109'6 98'7' 876' 1211'1110' 12'

4'2'

3'

5'

1'

2'

3'

4'

5'

1'

8 12

11

10

9

8

12

10

9

11

Current direction

1 1' 4'43'32'2 5 5' 109'6 98'7' 876' 1211'1110' 12'

4'2'

3'

5'

1'

2'

3'

4'

5'

1'

8 12

11

10

9

8

12

10

9

11

N S

N

1-6S

7-12

Each Phase coil groups interconnections & End Terminal leads

1 1' 4'43'32'2 5 5' 109'6 98'7' 876' 1211'1110' 12'

4'

A B’A’C’ CB

2'

3'

5'

1'

2'

3'

4'

5'

1'

8

12

11

10

9

8

12

10

9

11

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-A1

1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 20 1 2 3 4

Integral-slot, full pitch double layer winding. (PHASE A)

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.

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, andThe magnitude of certain harmonics in the emf and also mmf is suppressed.

Example 5• Given:- S =12, p = 2, 600 phase spread, chorded by 5/6.

angle b/n adjacent slots α = 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 -AB -BC-C

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.

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:-

236

36

Xq

2

32

1138

36

Xq

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:

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:-

2

52

122

5

2

32

q

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

d

cq

In the example above, c=5 and d=2

To obtain a balanced or symmetrical winding, it is necessary that be equal to a whole number.

mt

S

Where, S - being the number of slots, t - the largest common factor for S and P, andm - the number of phases.

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.

Example - 6Given:- S = 27, p = 6, m = 3, q = 1½ = 3/2Solution 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.

No. Of

PolesPHASE A PHASE C 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

N

S

S

N

S

Table arranging coil groups for 600 elec. Phase spread.

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

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.

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.

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.