- Three-Phase Induction Motor: A three-phase induction motor is an electromechanical device that operates primarily at a constant speed unless specific control methods are applied.
- V/f Control: By maintaining a constant voltage-to-frequency (V/f) ratio, this method effectively controls the speed of an induction motor while preventing core saturation.
- Rotor and Stator Controls: Speed adjustments can be made either from the rotor side, by adding resistance or using slip power recovery, or from the stator side, by changing pole numbers or adjusting the voltage.
- Torque Dynamics: The motor’s torque is influenced by voltage, resistance, and slip, which are critical factors in all speed control techniques.
- Efficiency Considerations: Although speed control is versatile, methods like adding rotor resistance or changing stator poles can decrease overall motor efficiency and increase operational costs.
A three phase induction motor on a fixed-frequency supply runs at nearly constant speed. Only slip changes with load. Speed of that induction motor can still be set from the stator or the rotor, because rotor speed is synchronous speed times (1 minus slip). Some older methods waste slip power and can lower electrical power factor. The speed and torque equations below are the ones those methods use.
Synchronous Speed
Where, f = frequency and P is the number of poles
The speed of induction motor is given by,
Where,
N is the speed of the rotor of an induction motor,
Ns 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,
E2 is the rotor emf
Ns is the synchronous speed
R2 is the rotor resistance
X2 is the rotor inductive reactance
Speed of an induction motor can be changed from the stator side or the rotor side. Stator-side methods are:
- V / f control or frequency control.
- Changing the number of stator poles.
- Controlling supply voltage.
- Adding rheostat in the stator circuit.
Rotor-side methods are:
- 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
A three-phase supply produces a rotating magnetic field whose speed is
The air-gap emf follows the same relation as a transformer:
Where K is the winding constant, T is the number of turns per phase and f is frequency. If frequency falls and voltage stays put, flux rises and the cores approach saturation, so no-load current rises. Flux φ stays nearly constant only if voltage changes with frequency: V/f held constant below base speed. Above base speed the voltage is already at the rating. Frequency still rises and flux is weakened. Variable voltage and frequency come from a converter plus 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 R2. So, it can be neglected. So torque becomes
Since rotor resistance, R2 is constant so the equation of torque further reduces to
We know that rotor induced emf E2 ∝ V. So, T ∝ sV2.
So a lower supply voltage lowers torque at a given slip. For the same shaft torque the slip must rise, and the motor runs slower. On a constant-torque load that means a large voltage cut for a small speed change, so the current rises and the induction motor can overheat. Fan and pump loads, where torque falls with speed, are the remaining uses.
Changing the number of stator poles:
The stator poles can be changed by two methods
Multiple stator winding method.
Pole amplitude modulation method (PAM)
Multiple Stator Winding Method
The stator carries two separate windings, electrically isolated and wound for two different pole numbers. A switch feeds only one winding at a time, so the machine has two discrete speeds. Smooth control is not possible. Two windings cost more and waste slot space. The method applies to a squirrel cage motor.
Pole Amplitude Modulation Method (PAM)
The original sinusoidal mmf wave is modulated by another sinusoidal mmf wave that has a different pole number. Switching the modulation changes the effective pole count of one winding.
Let f 1(θ) be the original mmf wave of induction motor whose speed is to be controlled.
f2(θ) be the modulation mmf wave.
P1 be the number of poles of induction motor whose speed is to be controlled.
P2 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
A stator rheostat drops terminal voltage. Torque still follows T ∝ sV22. A lower voltage lowers torque at a given slip, so the slip must rise to keep shaft torque, and the motor runs slower. The extra stator copper loss makes this a poor everyday method.
Speed Control from Rotor Side
Adding External Resistance on Rotor Side
External resistance is added in the rotor circuit of a wound-rotor machine. Torque is still
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 R2. So, it can be neglected. and also E2 is constant. So the equation of torque after simplification becomes,
If rotor resistance R2 rises, torque at a given slip falls. The slip must rise to keep shaft torque, so rotor speed falls. Extra rotor resistance therefore lowers running speed. Starting torque also rises, which is the useful side of the same curve. Limits are:- Speed above synchronous speed is not possible.
- A large speed drop needs a large resistance, and that resistance dissipates slip power, so efficiency falls.
- The added resistance itself is a continuous loss at reduced speed.
- This method cannot be used for squirrel cage induction motor.
Cascade Control Method
Two three-phase induction motors share a shaft (a cascaded or concatenated set). One is the main motor and the other is the auxiliary motor. The supply feeds the main stator. The auxiliary stator is fed at slip frequency from the main motor slip rings.
Let NS1 be the synchronous speed of the main motor.
NS2 be the synchronous speed of the auxiliary motor.
P1 be the number of poles of the main motor.
P2 be the number of poles of the auxiliary motor.
F is the supply frequency.
F1 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.
S1 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
Now at no load , the speed of auxiliary rotor is almost same as its synchronous speed i.e N = NS2
Now rearrange the above equation and find out the value of N, we get,
The set then runs at a speed that belongs to (P1 + P2) poles. When both torques act in the same direction the equivalent pole count is (P1 + P2). That connection is cumulative cascading. When the auxiliary torque opposes the main torque the equivalent pole count is (P1 – P2). That connection is differential cascading.
Four discrete speeds are available:- When only main induction motor work, having speed corresponds to
. - When only auxiliary induction motor work, having speed corresponds to
. - 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
.
- When only main induction motor work, having speed corresponds to
Injecting Slip Frequency EMF into Rotor Side
Rotor resistance control dumps slip power as I2R loss, so efficiency falls. That slip power can be taken out of the rotor and returned to the supply or to a second machine. The arrangement is slip-power recovery: an external emf at slip frequency is connected into the rotor circuit. If the injected emf opposes the rotor induced emf, effective rotor circuit voltage falls and speed falls. If it aids the rotor emf, the machine can run above the uncontrolled speed. Kramer and Scherbius sets are the historical forms. A converter-fed stator is now the usual way to get a wide range both below and above a given 50 Hz or 60 Hz base.
