## Speed Control of Three Phase Induction Motor

Table of Contents

Speed Control of Three Phase Induction Motor

Since a three phase Induction motor is essentially a constant speed motor, Controlling its speed can be Challenging. The induction motor’s speed is controlled at the expense of Efficiency loss and a low electrical power factor. The fundamental formulas for speed and torque of a Three-phase Induction motor should be understood before Discussing speed control techniques, as these Formulas are the foundation of such techniques.

## Speed Control of Three Phase Induction Motor

### Synchronous Speed

Where, f = frequency and P is the number of poles

The speed of Induction motor is given by,

N=Ns(1-S)

Where,

N is the speed of the rotor of an Induction motor,

N_{s} is the Synchronous speed,

S is the slip.

The torque produced by three phase induction motor is given by,

##### When the rotor is at standstill slip, s is one.

So the equation of torque is,

Where,

E_{2} is the rotor emf

N_{s} is the synchronous speed

R_{2} is the rotor resistance

X_{2} is the rotor inductive reactance

##### Both the rotor and the stator of an induction motor can change the speed. The three phase induction motor’s speed control from the stator side is further divided into:

- Controlling supply voltage.
- V / f control or frequency control.
- Changing the number of stator poles.
- Adding rheostat in the stator circuit.

From the rotor side, three phase induction motor speed controls are further divided into the following categories:

- Adding external resistance on rotor side.
- Cascade control method.
- Injecting slip frequency emf into rotor side.

### Speed Control from Stator Side

**V / f Control or Frequency Control **Whenever three phase supply is given to three phase induction motor rotating magnetic field is produced which rotates at synchronous speed given by

##### In three phase induction motor emf is induced by induction similar to that of transformer which is given by

Where, K is the winding constant, T is the number of turns per phase and f is frequency. Now, synchronous speed will change if frequency is changed, but frequency decreases will result in an increase in flux, which causes the rotor and stator cores to become saturated and increase the motor’s no load current. Therefore, maintaining flux at a constant value is crucial, and doing so requires changing the voltage. In other words, if we lower the frequency, the flux increases, but if we lower the voltage, the flux decreases as well, causing no change in flux and remaining constant. Therefore, we are maintaining a constant V/f ratio here. V/ f method is the result of this. For controlling the speed of three phase induction motor by V/f method we have to supply variable voltage and frequency which is easily obtained by using converter and inverter set.

**Controlling Supply Voltage** The torque produced by running three phase induction motor is given by

In low slip region (sX)^{2} is very very small as compared to R_{2}. So, it can be neglected. So torque becomes

Since rotor resistance, R_{2} is constant so the equation of torque further reduces to

We know that rotor induced emf E_{2} ∝ V. So, T ∝ sV^{2}.

The aforementioned equation makes it clear that torque will also decrease if supply voltage is reduced. The only way to maintain the same torque while supplying the same load is to increase slip, which will cause the motor to operate at a slower speed. This method of speed control is rarely employed because it results in an overheated induction motor because a small change in speed necessitates a large voltage reduction.

**Changing the number of stator poles:** The stator poles can be changed by two methods

##### Multiple stator winding method.

**Pole amplitude modulation method (PAM)**

**Method for Winding Multiple Stators** We offer two different windings in the stator for this method of three phase induction motor speed control. These two stator windings, which have two different numbers of poles each, are electrically isolated from one another. Speed control is possible by using a switching arrangement, which limits supply to one winding at a time. This method has the drawback of being unable to control speed smoothly. Due to the necessity of using two different stator windings, this method is more expensive and less effective. Only squirrel cage motors can use this speed control technique.

##### Pole Amplitude Modulation Method (PAM) In this method of speed control of three phase induction motor the original sinusoidal mmf wave is modulated by another sinusoidal mmf wave having the different number of poles.

Let f _{1}(θ) be the original mmf wave of induction motor whose speed is to be controlled.

f_{2}(θ) be the modulation mmf wave.

P_{1} be the number of poles of induction motor whose speed is to be controlled.

P_{2} be the number of poles of modulation wave.

After modulation resultant mmf wave

So we get, resultant mmf wave

Therefore the resultant mmf wave will have two different number of poles

Therefore by changing the number of poles we can easily change the speed of three phase induction motor.

- Adding Rheostat in Stator Circuit In this method of speed control of three phase induction motor rheostat is added in the stator circuit due to this voltage gets dropped. In case of three phase induction motor torque produced is given by T ∝ sV
_{2}^{2}. If we decrease supply voltage torque will also decrease. But for supplying the same load, the torque must remains the same and it is only possible if we increase the slip and if the slip increase motor will run reduced speed.

### Speed Control from Rotor Side

Adding External Resistance on Rotor Side In this method of speed control of three phase induction motor external resistance are added on rotor side. The equation of torque for three phase induction motor is

The three-phase induction motor operates in a low slip region. In low slip region term (sX)^{2} becomes very very small as compared to R_{2}. So, it can be neglected. and also E_{2} is constant. So the equation of torque after simplification becomes,

Now, as rotor resistance is increased, R2 torque decreases, but torque must remain constant to supply the same load. Therefore, we increase slip, which will further cause the rotor speed to decrease. In order to reduce the speed of the three-phase induction motor, we can increase the resistance in the rotor circuit. The main benefit of this method is that starting torque increases with the addition of external resistance, but it also has some drawbacks when it comes to controlling the speed of three-phase induction motors.

##### The speed above the normal value is not possible.

Large speed change requires a large value of resistance, and if such large value of resistance is added in the circuit, it will cause large copper loss and hence reduction in efficiency.

Presence of resistance causes more losses.

This method cannot be used for squirrel cage induction motor.

##### Cascade Control Method The two three-phase induction motors used in this method of speed control are linked together on a single shaft and are referred to as cascaded motors. The main motor is one motor, and the auxiliary motor is a different motor. The main motor’s stator receives a three-phase supply, and the auxiliary motor receives its power at a slip frequency from the slip ring of the main motor.

Let N_{S1} be the synchronous speed of the main motor.

N_{S2} be the synchronous speed of the auxiliary motor.

P_{1} be the number of poles of the main motor.

P_{2} be the number of poles of the auxiliary motor.

F is the supply frequency.

F_{1} is the frequency of rotor induced emf of the main motor.

N is the speed of set, and it remains same for both the main and auxiliary motor as both the motors are mounted on the common shaft.

S_{1} is the slip of main motor.

The auxiliary motor is supplied with same frequency as the main motor i.e

Now put the value of

So Now at no load , the speed of auxiliary rotor is almost same as its synchronous speed i.e N = N_{S2}

Now rearrange the above equation and find out the value of N, we get,

This pair of cascaded motors will now operate at a new speed with the addition of poles (P1 + P2). According to the above method, the main and auxiliary motors’ torque will act in the same direction, resulting in a total of (P1 + P2) poles. Cumulative cascading is the name given to this kind of cascading. There is one more kind of cascading in which the main motor’s torque is produced in the opposite direction from the auxiliary motor’s torque. Differential cascading is a form of cascading in which the number of poles determines the speed (P1 – P2).

In this method of speed control of three phase induction motor, four different speeds can be obtained

When only main induction motor work, having speed corresponds to

.

When only auxiliary induction motor work, having speed corresponds to

.

##### So When cumulative cascading is done, then the complete set runs at a speed of

.

When differential cascading is done, then the complete set runs at a speed of

.

Injecting Slip Frequency EMF into Rotor Side When the speed control of three phase induction motor is done by adding resistance in rotor circuit, some part of power called, the slip power is lost as I^{2}R losses. Therefore the efficiency of three phase induction motor is reduced by this method of speed control. This slip power loss can be recovered and supplied back to improve the overall efficiency of the three-phase induction motor, and this scheme of recovering the power is called slip power recovery scheme and this is done by connecting an external source of emf of slip frequency to the rotor circuit.

The injected emf can either work in opposition to the rotor-induced emf or in its favour. If it opposes the rotor-induced emf, the total rotor resistance rises and, as a result, the speed is reduced; if it assists the main rotor emf, the total falls and, as a result, the speed rises. Therefore, the speed can be easily controlled by adding induced emf to the rotor circuit. The main benefit of this type of three phase induction motor speed control is that it allows for a wide range of speed control, whether it is above normal speed or below normal speed.