### Controlling Number of Poles

The method is called pole changing method of controlling the speed. In this method, it is possible to have one, two or four speeds in steps, by the changing the number of stator poles. A continuous smooth speed control is not possible by this method.
The stator poles can be changed by following methods :
1. Consequent poles method
2. Multiple stator winding method
3. Pole amplitude modulation method.
1.1 Consequent Poles Method
In this method, connections of the stator winding are changes with the help of simple switching. Due to this, the number of stator poles get changed in the ratio 2 : 1. Hence either of the two synchronous speed can be selected.
Consider the pole formation due to single phase of a three phase winding, as shown in the Fig.1. There are three tapping points to the stator winding. The supply is given to two of them and third is kept open.
It can be seen that current in all the parts of stator coil is flowing in one direction only. Due to this, 8 poles get formed as shown in the Fig. 1. So synchronous speed possible with this arrangement with 50 Hz frequency is  Ns = 750 r.p.m. Fig.1 Pole winding
If now the two terminals to which supply was given either are joined together and supply is given between this common point and the open third terminal, the poles are formed as shown in the Fig. 2. 4 pole winding
It can be seen that the direction of current through remaining two. Thus upward direction is forming say S pole and downward say N. it can be observed that in this case only 4 poles are formed. So the synchronous speed possible is 1500 r.p.m. for 50 Hz frequency.
Thus series/parallel arrangements of coils can produce the poles in the ratio 2 : 1. But the speed change is in step and smooth speed control is not possible. Similarly the method can be used only for the squirrel cage type motors as squirrel rotor adjusts itself to same number of poles as stator which is not the case in slip ring induction motor.
1.1 Multiple Stator Winding Method
In this method instead of one winding, two separate stator winding are placed in the stator core. he windings are placed in the stator slots only but are electrically isolated from each other. Each winding is divided into coils to which, pole changing with consequent poles, facility is provided.
Thus giving supply to one of the two windings and using switching arrangement, two speeds can be achieved. Same is true for other stator winding. So in all four different speeds can be obtained.
The various limitations of this method are,
1. Can be applied to only squirrel cage motor.
2. Smooth speed control is not possible. Only step changes in speed are possible.
3. Two different stator windings are required to be wound which increases the cost of the motor.
4. Complicated from the design point of view.
Typical speed-torque characteristics of pole changing induction motor are shown in the Fig. 3. Fig. 3

1.2 Pole Amplitude Modulation Method
The basic disadvantage of other methods which is nonavailability of smooth speed control, is eliminated by this method. The ratio of two speeds in this method, need not be necessarily 2 : 1.
The basic principle of this method is the modulation of two sinusoidally varying m.m.f. waves, with different number of poles.
Consider sinusoidally distributed m.m.f. wave one phase of the stator as,
where    P = Number of poles
and        θ = Mechanical angle
This wave is modulated by another sinusoidal m.m.f. wave having PM number of poles, expressed as,
The resultant m.m.f. wave after modulation is,
Thus the resultant wave is equivalent to two m.m.f. waves having two separate number of poles as,
P1 = P - PM           and        P2 = P + PM
This is called suppressed carrier modulation.
If we succeed in suppressing one of the two poles then there exists rotating magnetic field with number of poles as P1 or P2. And while suppressing, the method can be used such that the resultant number of poles retained is as required from the speed point of view.
Now if the three stator windings are placed such that angle between their phase axes is (2π/3)r radians where r is an integer which is not divisible by 3 then the phase axes angle for modulated poles is given by,
Now to suppress one of the two poles, the angle between its phases axes must be multiple of 2π.
So if r and n are selected so as to satisfy one of the above relations, then either  P1 or P2 get suppressed and field corresponding to other pole exists. So speeds corresponding to P poles without modulation and corresponding to either P1 or P2 with modulation, can be achieved. The negative sign in equation (1), gives suppression of P2 and existence of P2 = P + PM while positive sign in equation (1), gives suppression  P2 of and existence of P1 = P - PM  poles.
For example, stator has 8 poles while values of n and r are selected as 1 and 4 respectively. r is not divisible by 3.
Let poles of modulation function PM  are 2.
From equation (1) we can see that,
Thus P1 gets suppressed and we get poles P2 = P + PM = 10.
So two speeds corresponding to P and P2 can be obtained.
Similarly if the poles of modulation function PM are 4 and n and r are selected as 1 and 2 then,
In this case gets suppressed and we get poles P1 = P - PM = 4.
This method is advantages as it reduced the size to a great extent and hence cost of the machine.
The limitation that it can be used only for squirrel cage motors still continues.
Practically the rectangular wave is used for modulation. This is achieved by dividing stator coil into groups and then by dropping alternate group, other groups are connected in series opposition.

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