Three Phase Winding in A.C. Machines

Three Phase Winding in A.C. Machines  

AU : May-07, 10, Dec.-07.

• In a three phase alternators, three different sets of windings are arranged in the armature (stator) slots in such a way that there exists a phase difference of 120° between the induced e.m.f.s in them. Each set of windings is for each phase of three phase induced e.m.f. Thus the three phase induced e.m.f has three different e.m.f.s given by,

e_R = E_m sin(ωt) ... R phase

e_Y = Em sin(ωt-120°) ... Y phase

e_B = Em sin(ωt-240°) ... B phase

 Induced e.m.f. in each set of winding is called phase e.m.f. denoted as E_ph. All the coils used for one phase are connected in such a way that their e.m.f.s help each other. And overall arrangement of three phase windings is such that the waveform of three phase induced e.m.f. is sinusoidal in nature.

1. Winding Terminologies

1) Conductor : The part of the wire, which is under the influence of the magnetic field and responsible for the induced e.m.f. is called active length of the conductor. The conductors are placed in the armature slots.

2) Turn : A conductor in one slot, when connected to a conductor in another slot forms a turn. So two conductors constitute a turn. This is shown in Fig. 2.10.1 (a)

3) Coil : As there are number of turns, for simplicity the number of turns are grouped together to form a coil. Such a coil is called multiturn coil. A coil may consist of single turn called single turn coil. The Fig. 2.10.1 (b) shows a multiturn coil.    

4) Coil side : Coil consists of many turns. Part of the coil in each slot is called coil side of a coil as shown in the Fig. 2.10.1 (b)

5) Pole pitch : It is centre to centre distance between the two adjacent poles. We have seen that for one rotation of the conductors, 2 poles are responsible for 360° electrical of e.m.f., 4 poles are responsible for 720° electrical of e.m.f. and so on. So 1 pole is responsible for 180° electrical of induced e.m.f. So 180° electrical is also called one pole pitch. Practically how many slots are under one pole which are responsible for 180° electrical, are measured to specify the pole pitch

• e.g. Consider 2 pole, 18 slots armature of an alternator. Then under 1 pole there are 18/2 i.e. 9 slots.

So pole pitch is 9 slots or 180° electrical. This means 9 slots are responsible to produce a phase difference of 180° between the e.m.f.s induced in different conductors.

• This number of slots/pole is denoted as 'n'.

ஃ Pole pitch = 180^o electrical

= Slots per pole (no. of slots/P) = n

6) Slot angle (β): The phase difference contributed by one slot in degrees electrical is called slot angle β.

 As slots per pole contributes 180° electrical which is denoted as 'n', we can write,

ஃ 1 slot angle = 180°/n

ஃ β = 180°/n

In the above example,

n = 18/2 = 9, while β = 180^o = 20°

Note : This means that if we consider an induced e.m.f. in the conductors which are placed in the slots which are adjacent to each other, there will exist a phase difference of β° in between them. While if e.m.f. induced in the conductors which are placed in slots which are 'n' slots distance away, there will exist a phase difference of 180° in between them.

2. Types of Three Phase Windings

• In general, the types of three phase windings used in a.c. machines are,

1. Single layer and double layer

2. Full pitch and short pitch

3. Concentrated and distributed.

a. Single Layer and Double Layer Winding

• If a slot consists of only one coil side, winding is said to be single layer. This is shown in the Fig. 2.10.3 (a). While there are two coil sides per slot, one at the bottom and one at the top the winding is called double layer as shown in the Fig. 2.10.3 (b).

• A lot of space gets wasted in single layer hence in practice generally double layer winding is preferred.

b. Full Pitch and Short Pitch Winding

• As seen earlier, one pole pitch is 180° electrical. The value of 'n', slots per pole indicates how many slots are contributing 180° electrical phase difference. So if coil side in one slot is connected to a coil side in another slot which is one pole pitch distance away from first slot, the winding is said to be full pitch winding and coil is called full pitch coil.

• For example in 2 pole, 18 slots alternator, the pole pitch is n = 18/2 = 9 slots. So if coil side in slot No. 1 is connected to coil side in slot No. 10 such that two slots No. 1 and No. 10 are one pole pitch or n slots or 180° electrical apart, the coil is called full pitch coil.

• Here we can define one more term related to a coil called coil span.

Coil Span

•It is the distance on the periphery of the armature between two coil sides of a coil. It is usually expressed in terms of number of slots or degrees electrical. So if coil span is 'n' slots or 180° electrical the coil is called full pitch coil. This is shown in the Fig. 2.10.4.

• As against this if coils are used in such a way that coil span is slightly less than a pole pitch i.e. less than 180° electrical, the coils are called, short pitched coils or fractional pitched coils. Generally coils are shorted by one or two slots.

• So in 18 slots, 2 pole alternator instead of connecting a coil side in slot No. 1 to slot No.10, it is connected to a coil side in slot No.9 or slot No. 8, coil is said to be short pitched coil and winding is called short pitch winding. This is shown in Fig. 2.10.5.

Advantages of Short Pitch Coils

In actual practice, short pitch coils are used as it has following advantages:

a) The length required for the end connections of coils is less i.e. inactive length of winding is less. So less copper is required. Hence economical.

b) Short pitching eliminates high frequency harmonics which distort the sinusoidal nature of e.m.f. Hence waveform of an induced e.m.f. is more sinusoidal due to short pitching.

c) As high frequency harmonics get eliminated, eddy current and hysteresis losses which depend on frequency also get minimised. This increases the efficiency.

c. Concentrated and Distributed Winding

• In three phase alternators, we have seen that there are three different sets of windings, each for a phase. So depending upon the total number of slots and number of poles, we have certain slots per phase available under each pole. This is denoted as 'm'.

m = Slots per pole per phase = n/number of phases

n/3 (generally no. of phases is 3)

For example in 18 slots, 2 pole alternator we have

= 18/2 = 9 and m = 9/3 = 3

• So we have 3 slots per pole per phase available. Now let 'x' number of conductors per phase are to be placed under one pole. And we have 3 slots per pole per phase available. But if all 'x' conductors per phase are placed in one slot keeping remaining 2 slots per pole per phase empty then the winding is called concentrated winding. So in concentrated winding all conductors or coils belonging to a phase are placed in one slot under every pole.

 • But in practice, an attempt is always made to use all the 'm' slots per pole per phase available for distribution of the winding. So if 'x' conductors per phase are distributed amongst the 3 slots per phase available under every pole, the winding is called distributed winding. So in distributed type of winding all the coils belonging to a phase are well distributed over the 'm' slots per phase, under every pole. Distributed winding makes the waveform of the induced e.m.f. more sinusoidal in nature. Also in concentrated winding due to large number of conductors per slot, heat dissipation is poor.

Key Point: So in practice, double layer, short pitched and distributed type of armature winding is preferred for the alternators.

Review Questions

1. Explain why distributed field winding is employed in cylindrical rotor synchronous machine.

 AU: May-07, 10, Marks 6

2. What are full chorded and short chorded coils ?

AU: Dec.-07, Marks 4