# What is the importance of slip in an induction motor?

The  induction motor can’t run if there is no slip.What is slip in induction motor? let us first understand about the slip in induction motor.

### What is Slip?

When the induction motor is fed with three phase supply, a rotating magnetic field is produced. The speed of the rotating magnetic field is known as a synchronous speed(Ns) of the motor.The magnetic field produced in the motor gets linked to the rotor conductors which are short-circuited by the end rings.

The linked flux to the rotor conductors induces voltage in the rotor, and as the rotor conductors are short circuited, the current starts flowing through the rotor conductors.Due to an interaction between the magnetic field and the rotor current, the torque is produced and the rotor starts rotating. Let the rotating speed of the rotor is N.

In an induction motor the rotor speed always lags the synchronous speed of the rotating magnetic field. The induction motor is called asynchronous motor because the actual speed of the motor ia always less than the synchronous speed of the motor.

The difference between the speed of the rotating magnetic field or synchronous speed and the actual speed of the rotor or motor is known as the slip of the motor. The slip can be mathematically expressed as;

s = Ns – N

The slip is in RPM.

The slip is usually  expressed as percentage of the synchronous speed.

Percentage slip,

For example :

A 4 poles,50Hz induction motor having 1480 RPM at full load.

Synchronous Speed of the motor

Ns = 120f/P
Ns = 120 x 50/4
Ns = 1500 RPM
s = Ns -N
= 1500-1480
s = 20 RPM

% slip = [(Ns-N) /Ns] x 100

= [(1500-1480) /1500] x 100

= [20 /1500] x 100

% slip =1.33 %

Why Slip is must for operation of an Induction Motor?

The torque is produced when the current flows in the rotor conductor. If the slip is zero, no EMF will be induced in the rotor conductor and hence there will be no flow of the current in the rotor circuit. The torque is produced due to an interaction of the main flux and the rotor current. If the rotor current is zero, motor will produce no torque.  In absence of the slip, the operation of motor is not possible. Th torque produced in an induction motor is proportional to the slip.The torque equation of the induction motor is as given below.

From above torque equation of an induction motor, it is clear that if the slip is zero the torque will be zero. When the load on the motor increase the slip gets increased and speed of the motor decreases slightly, thus the motor delivers  higher torque for driving the load.

The slip plays very vital role in the operation of an induction motor. At no load , the slip of the induction motor is less and the slip gets increased with increased loading on the motor. The slip of the motor gets self adjusted according to the torque demands from the load side.

The other parameters of an induction motor is governed according to the value of the slip of the motor.

Rotor Induced EMF

The EMF induced in the rotor is directly proportional to the slip. At standstill condition the slip is unity and the maximum voltage is induced in the rotor circuit.
E2(r)   (Ns-N)
E2(r)   s
E2(r)  = s E2

where,
E2  is the rotor induced voltage / Phase when motor is at standstill after applying the stator voltage.

E2 is the rotor induced EMF/ Phase in running condition

At standstill condition

s= (Ns – N)/Ns = (Ns -0)/Ns = 1
so,  E2(r)  = s E2
E2(r)  = 1 x E2 = E2
E2(r)  = E2

The EMF induced in the rotor at standstill is equal to the maximum rotor voltage (OCV) or equal to the open circuit voltage of the rotor.

Frequency of Rotor Induced EMF
At standstill condition, the frequency of the rotor induced EMF is equal to the stator frequency. The frequency of the rotor induced EMF decreases as the motor starts accelerating and the frequency is minimum when the motor attains its rated speed. The mathematical relationship between the frequency of the rotor induced EMF and the stator frequency is as given below.

fr =sfs

At standstill condition

s= (Ns – N)/Ns = (Ns -0)/Ns = 1
fr =fs

Rotor Resistance

The rotor resistance is independent of the slip and hence the rotor resistance remains constant irrespective of the speed of the motor.
R2 = Constant
Rotor Reactance

The rotor reactance decrease with increase of the motor speed. The rotor reactance is least when the motor runs on its rated speed. At standstill condition the slip is unity and the frequency of the rotor induced EMF is equal to the supply frequency.

Let the reactance of the rotor is X2 .
X2 = ω L2

Where,

ω  = 2πfr
L2  = Rotor inductance
Therefore,

X2 = 2πfr L2
X2 = 2πfs L2    [ As fr =fs, at standstill condition]

The rotor induced frequency in running condition depends on the slip of the motor.

In running condition,
fr =sfs
The rotor reactance in running condition will be;

X2r = 2πs fr  L2
X2r = (2πfr  L2)
X2r =X2

Rotor Impedance
The rotor impedance/phase at standstill is as given below.

The rotor impedance/ phase in running condition is as given below.

Where,

Rotor Power Factor
The impedance, resistance and the reactance triangle of the rotor circuit is as given below.

The rotor power factor at standstill is as given below.

At running condition, the power factor of the rotor circuit is given by;

Illustrative Examples:

If the induced emf in the stator of 4 poles has frequency 50 Hz and that in the rotor is 1.5 Hz, at what speed motor is running and what is the slip of induction motor?

fr = 50 Hz
P =  4

Ns = 120f/P
Ns = 120 x 50/4 = 1500 RPM

fr = slip x stator frequency
1.5 =s x 50
s = 1.5/50 = 0.03

The speed of the motor
N = Ns(1 – s )
N = 1500(1 – 0.03 )
N = 1500 x 0.97
N = 1455 RPM

A three phase, 50 Hz, 4 pole slip ring induction motor has a star connected rotor. The full load speed of the motor is 1460 rpm. The rotor resistance and stand still reactance per phase are 0.1 ohm and 1.5 ohm respectively. The open circuit voltage on open circuit between the slip rings is 90 volts. Determine (i) percentage slip (ii) induced emf in rotor per phase (iii) the rotor reactance per phase at full load (iv) the rotor current and full load power factor.

(i) Ns = 120f/p = 120 x 50 /4 = 1500 rpm;
slip = (Ns – N) / Ns = (1500 – 1460)/ 1500 = 0.0266 Percentage       slip = 2.66 %

(ii) Induced emf per phase in rotor at stand still = 90/√3 =51.96            volts Rotor induced emf at full load Er = sE2 = 0.0266 x 51.96        = 1.382 volts

(iii) rotor reactance at stand still = 1.5 Ω / phase
Rotor reactance per phase at full load = sX2 = 0.0399 Ω / phase

(iv) rotor impedance per phase at full load = Z2 = √( R22 + sX22 )
= 0.1077 Ω
Rotor current per phase = 1.382/0.1077 = 12.83 amps
Full load power factor = R2/Z2 = 0.1/ 0.1077 = 0.929

A three phase slip ring induction motor has a star connected rotor. It has an induced emf of 60 volts on open circuit between the slip rings at stand still when the rated voltage is supplied to the stator. The resistance and stand still reactance of rotor per phase are 0.5 Ω and 5 Ω respectively. Determine the rotor current per phase (i) when the rotor is at stand still and connected to a star connected rheostat of resistance 5 Ω and reactance of 0.5 Ω per phase. (ii) when running at 4 % slip with rheostat short circuited.

Current through rotor at stand still = current at starting As external resistance is connected in series with rotor per phase R2 = 5.5 Ω; X2 = 5.5 Ω
(i) I2 = E2/ √(R22 2 + X22 2 )
I2 = (60/√ 3) / √ (5.52 + 5.52 ) = 4.454 amps

(ii) When running at 4% slip I2 = sE2/ √(R22 + (sX22 ) 2 )
= (0.04 x 60/√ 3) / √ (0.52 + (0.04 x 5)2 ) = 2.573 amps

A three phase, 12 pole, salient pole alternator is coupled to a diesel engine running at 500 rpm. It supplies an induction motor which has a full load speed of 1440 rpm. Find the percentage slip and number of poles of the induction motor.

Frequency of supply to the induction motor f = pn/120 = 12 x 500 / 120 = 50 Hz
Speed of Induction motor = 1440 rpm, Number of poles of induction motor = p = 120 f / n = 120 x 50/1440 = 4.16 The number of poles are to be even, selecting the nearest even number as the number of poles p = 4
Synchronous speed of the induction motor Ns = 120f/p = 120 x 50 /4 = 1500 rpm
slip = (Ns – N) / Ns = (1500 – 1440)/ 1500 = 0.04
Percentage slip = 4 %

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