Explain the working principle of three phase induction motor.

1
A three phase induction motor has a stator and a rotor. The stator carries a 3-phase winding called as stator winding
while the rotor carries a short circuited winding called as rotor winding. The stator winding is fed from 3-phase supply
and the rotor winding derives its voltage and power from the stator winding through electromagnetic induction.
Therefore, the working principle of a 3-phase induction motor is fundamentally based on electromagnetic induction.

 When the stator winding is connected to a balanced three phase supply, a rotating magnetic field (RMF) is
setup which rotates around the stator at synchronous speed (Ns). Where,
NS=120fPNS=120fP

 The RMF passes through air gap and cuts the rotor conductors, which are stationary at start. Due to relative
motion between RMF and the stationary rotor, an EMF is induced in the rotor conductors. Since the rotor circuit
is short-circuited, a current starts flowing in the rotor conductors.
 Now, the current carrying rotor conductors are in a magnetic field created by the stator. As a result of this,
mechanical force acts on the rotor conductors. The sum of mechanical forces on all the rotor conductors produces
a torque which tries to move the rotor in the same direction as the RMF.
 Hence, the induction motor starts to rotate. From, the above discussion, it can be seen that the three phase
induction motor is self-starting motor.
 The three induction motor accelerates till the speed reached to a speed just below the synchronous speed.
Difference between a squirrel cage and slip ring three phase induction motor ?
Squirrel cage
Has a simple, robust design with a rotor made of bars that are shorted at the ends by end rings. This
design is known for its durability, but it has reduced control of speed and resistance.
Slip ring
Has a more complex design with a wound rotor that includes slip rings and brushes. This design gives
the motor more flexibility and control, but it's also more complex.
Here are some other differences between the two types of motors:
 Starting torque: Slip ring motors have a higher starting torque than squirrel cage motors.
 Starting current: Squirrel cage motors have a higher starting current than slip ring motors.
 Speed control: Slip ring motors can be controlled with an external resistance circuit, but squirrel cage
motors cannot.
 Efficiency: Squirrel cage motors are more efficient than slip ring motors because they have lower rotor
copper loss.
 Maintenance: Slip ring motors require more frequent maintenance because they contain brushes.
 Uses: Slip ring motors are used in places that require high starting torque, while squirrel cage motors are
used in fans, blowers, and lathe machines.

What is synchronous speed? Define slip. Discuss how slip varies with load.

Synchronous speed is the rotational speed of a revolving field in an alternating-current (AC) machine. It's
a key term in the theory and practice of synchronous and induction motors, which are both AC motors
with rotating magnetic fields.
Slip define: To slide out of place or away from a support or one's grasp.
 Light load: The slip is very low and the speed is close to synchronous speed.
 Heavy load: The torque is inversely proportional to slip.
 Unstable region: The slip increases with load, but torque decreases. This region is also called the high-
slip region.
 Full-load slip: The slip when the motor is operating under its rated load. A higher full-load slip can
indicate higher torque capabilities, but it might also mean lower efficiency and speed stability
The relationship between slip and load is not linear and can vary depending on the motor's design. An
acceptable range of slip values is normal for a given motor size, design, and application.
Phasor Diagram of Three Phase Induction Motor 2

In a 3-phase induction motor, the stator winding is connected to 3-phase supply and the rotor winding is short-
circuited. The energy is transferred magnetically from the stator winding to the short-circuited, rotor winding.
Therefore, an induction motor may be considered to be a transformer with a rotating secondary (short-circuited).
The stator winding corresponds to transformer primary and the rotor finding corresponds to transformer secondary.
In view of the similarity of the flux and voltage conditions to those in a transformer, one can expect that the
equivalent circuit of an induction motor will be similar to that of a transformer. Fig. 3.8 shows the equivalent circuit
per phase for an induction motor. Let discuss the stator and rotor circuits separately.

Discuss how rotating magnetic field is developed in a three phase induction motor.

The stator of a three-phase induction motor contains overlapping windings, offset by an

electrical angle of 120°. When connected to a three-phase A.C. supply, the stator creates a
rotating magnetic field that rotates at synchronous speed.

When 3-phase supply is fed to the stator winding of the 3-phase induction motor, a rotating
magnetic field (RMF) is produced. This magnetic field is such that its poles do not remain in a fixed
position on the stator but go on shifting their positions around the stator. For this reason, it is
known as rotating magnetic field (RMF) or RMF.

Mathematically, it can be shown that the magnitude of this rotating magnetic field is constant
The speed of the rotating magnetic field is known as synchronous speed (NS). The value of
synchronous speed depends upon the number poles (P) on the stator and the supply frequency
(f). Therefore,

Synchronousspeed,NS=120fPRPM

3
Draw the equivalent circuit of a three phase induction motor and explain the various terms

The equivalent circuit of a 3-phase induction motor represents the motor's electrical characteristics and performance
through an analogous circuit of resistors, inductors, and voltage sources. This model helps in understanding and
predicting the motor's behavior under various operating conditions. The equivalent circuit is a simplified lumped
parameter representation of the motor in the form of resistances and reactances. It models the stator, and rotor
circuits and their interaction along with losses and power transfer using concepts similar to a transformer model.
4

Here, R1 is the winding resistance of the stator.

X1 is the inductance of the stator winding.
Rc is the core loss component.
XM is the magnetizing reactance of the winding.
R2/s is the power of the rotor, which includes output mechanical power and copper loss of the rotor.
The complete equivalent circuit of an induction motor includes all the parameters that affect the motor's
performance:
Stator resistance (R1) and leakage reactance (X1): Represent the resistance and reactance of the stator windings.
Rotor resistance (R2) and leakage reactance (X2): Represent the resistance and reactance of the rotor windings,
referred to as the stator side.
Magnetizing branch (Rm and Xm): Represents the core losses and magnetizing inductance.
Rotor slip (s): Indicates the difference between synchronous speed and actual rotor speed.

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.

Soln: (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 = √( R2 2 + sX2 2) = 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 3 phase, 15 hp, 460 V, 60 Hz, 1728 rpm induction motor delivers full [power output to a load connected to its
shaft. The friction and windage loss of the motor is 750 W. Determine the: (i) slip (ii) air gap power (iii) mechanical
power developed (iv) rotor copper losses (v) ratio of rotor copper loss to mechanical power developed.

To determine the rotor copper loss in a 3-phase induction motor, we can follow these
structured steps:

Calculate the full load shaft power. The motor has a rating of 15 horsepower (Hp). Since
1 Hp is equivalent to 746 Watts, we can compute the full load shaft power as follows:
Full load shaft power = 15 Hp × 746 W/Hp = 11190 W

Account for the windage and friction losses. The total mechanical power developed by
the motor can be calculated by adding the windage and friction losses (750 W) to the full
load shaft power:
Mechanical power developed = 11190 W + 750 W = 11940 W

Calculate the synchronous speed. The synchronous speed Ns for a 4-pole motor
operating at 60 Hz can be calculated using the formula:
120 × f 120 × 60
=
Ns = P 4 = 1800 rpm

Determine the slip s . The slip can be calculated as the difference between synchronous
speed and rotor speed divided by synchronous speed:
Ns − Nr 1800 − 1728
s= = = 0.04
1800
Ns

Calculate the air gap power Pag . The air gap power can be determined using the
mechanical power developed and the slip:
Pag = Mechanical power developed 11940 W
= = 12437.5 W
1−s 1 − 0.04

Finally, calculate the rotor copper loss. The rotor copper

loss can be calculated bymultiplying the slip by the air
gap power

Rotor copper loss = s × Pag = 0.04 × 12437.5 W

= 497.5 W

4
Explain the advantages and disadvantages of full voltage starting method for a three
phase induction motor.

Advantages:

1. High Efficiency: 3-phase induction motors are generally more efficient than
single-phase motors, especially in larger sizes. They convert electrical energy to
mechanical energy with minimal losses.
2. Smoother Operation: The 3-phase power supply provides a continuous and
smooth torque output, reducing vibration and noise compared to single-phase
motors.
3. Self-Starting: These motors can start under load without requiring any
additional starting mechanisms, which simplifies their design and operation.
4. Less Maintenance: Induction motors have fewer moving parts (no brushes or
commutators), leading to lower maintenance requirements and longer service
life.
5. Cost-Effective: They are typically less expensive to manufacture and install
than equivalent synchronous motors, making them a cost-effective choice for
many applications.
6. Robustness: 3-phase induction motors are rugged and can operate in harsh
environments, which is ideal for industrial settings.
7. Wide Range of Applications: They are suitable for a variety of applications,
from small appliances to large industrial machines.
Disadvantages:

1. Starting Torque: While they can start under load, the starting torque may not
be as high as that of some specialized motors, which can be a limitation for
specific applications.
2. Power Factor: 3-phase induction motors can have a low power factor,
especially under light load conditions, which can lead to higher energy costs
and reduced efficiency in power systems.
3. Complexity in Control: While basic operation is straightforward, variable
speed control and other advanced features may require additional equipment
like variable frequency drives (VFDs), adding to the complexity and cost.
4. Size and Weight: These motors tend to be larger and heavier than single-
phase motors for the same power output, which can be a disadvantage in
space-constrained applications.
5. Dependence on 3-Phase Supply: They require a 3-phase power supply, which
may not be available in all locations, especially in residential areas.
6. Limited Speed Regulation: Induction motors generally have fixed speed
characteristics, making them less suitable for applications requiring precise
speed control without additional equipment.
5
Explain the advantages and disadvantages of reduced voltage starting method for a three
phase induction motor. 6

Advantages
Reduces starting current: This can help reduce current surges and voltage fluctuations in the
supply system.
Protects from overloads: This prevents the motor from drawing too much current, which can
cause overheating and damage.
Limits current inrush: This can help prevent excessive power line disturbances.
Disadvantages
Reduces starting torque: This can extend the acceleration time.
Not suitable for some applications: This method can't be used for some applications because
of the load's starting torque requirements.
A reduced voltage starter is a device that starts motors with reduced power supplied at start-
up. It can also stop, reverse, accelerate, and protect motors.

Establish the torque equation for three phase induction motor.

The torque equation for a three-phase induction motor is T=kϕI2cosθ2

Here are some other things to know about the torque of a three-phase induction motor:

Torque and supply voltage: Torque is directly proportional to the square of the supply
voltage.

Torque and slip: Torque is also directly proportional to slip, so the torque-slip
characteristics are linear in the lower slip region.

Starting torque: The starting torque is the torque produced when the motor starts, and is also
known as the standstill torque. To calculate the starting torque, set 𝑠=1 in the torque equation.

Maximum torque: The maximum torque is directly proportional to the square of the rotor
induced emf at standstill, and inversely proportional to the rotor reactance.

Torque is the rotational equivalent of linear force, and is also known as the moment of force.
The symbol for torque is the lowercase Greek letter tau, or 𝑀 when referred to as moment of
force.
Draw and explain the torque slip characteristics for a three phase induction motor
The torque of a 3-phase induction motor under running conditions is given by,

From the eqn. (1), it can be seen that if R2 and X2 are kept
constant, the torque depends upon the slip 's'. The torque-slip characteristics curve can
be divided into three regions, viz.

 Low-slip region 7
 Medium-slip region
 High-slip region

Low-Slip Region: At synchronous speed, the slip s = 0, thus, the torque is 0. When the
speed is very near to the synchronous speed, the slip is very low and the term (𝑠𝑋2)2 is
negligible in comparison with R2. Therefore,

If R2 is constant, then τr∝s…(2)

Eqn. (2) shows that the torque is proportional to the slip. Hence, when the slip is small, the
torque-slip curve is straight line.

Medium-Slip Region: When the slip increases, the term (𝑠𝑋2)2 becomes large so that
𝑅22 may be neglected in comparison with (𝑠𝑋2)2. Therefore,

If X2 is constant, then

Thus, the torque is inversely proportional to slip towards standstill conditions. Hence, for
intermediate values of the slip, the torque-slip characteristics is represented by
a rectangular hyperbola. The curve passes through the point of maximum torque when R2 =
𝑠𝑋2

High-Slip Region: The torque decreases beyond the point of maximum torque. As a
result of this, the motor slows down and eventually stops. The induction motor
operates for the values of slip between s = 0 and s = sm, where sm is the value of
slip corresponding to maximum torque. For a typical 3-phase induction motor, the
breakdown torque is 2 to 3 times of the full-load torque. Therefore, the motor can
handle overloading for a short period of time without stalling.

Why it is possible to attain maximum starting torque only for slip ring induction motor.

A slip ring induction motor can attain maximum starting torque because external
resistance can be added to increase the rotor winding's resistance:
Explanation: The starting torque of an induction motor is a function of the rotor
resistance and slip. When the rotor resistance equals the rotor reactance, the
starting torque is at its maximum. 8

How it works: In a slip ring induction motor, external resistance can be added to the
rotor circuit through the brush. This increases the rotor resistance, which lowers the
current in the rotor circuit. The improved power factor of the rotor circuit during
startup also increases the starting torque.
Advantages: Slip ring induction motors are often used in heavy industries because
they can handle higher starting loads with lower starting currents.
Find the ratio of maximum torque to full load torque for a three phase induction motor

For a 3-phase induction motor, the full-load torque is given by,

Where, s is slip corresponds to full-load.

The starting torque is given by,

And the maximum torque is given by,

Therefore, (1) Ratio of maximum torque to full-load torque −

Dividing the numerator and denominator on RHS by we have,

where, Slip corresponding to maximum torque

 i) Discuss the no-load test and blocked rotor test for a three phase induction motor.
ii) A 4 pole 50 Hz, 1440 rpm, three phase induction motor develops a maximum
torque of 60 N-m at 1350 rpm. Determine its full load torque. 9

i) The no-load test and blocked rotor test are used to determine the parameters of a
three-phase induction motor:

 No-load test: Determines the magnetizing branch parameters, such as Rc and Xm

 Blocked rotor test: Determines the series parameters, such as R1, R2, X1, and X2
Here are some details about each test:

 No-load test
The motor is powered at different voltages between 60% and 125% of the rated
voltage. Electrical parameters, thermal resistance, and winding temperature are
acquired for each supply voltage.
 Blocked rotor test
The rotor is prevented from rotating by tightening the belt or by hand. A low voltage
is applied to the stator terminals so that the rotor's speed is zero and full load
current passes through the stator winding. The stator voltage is then slowly
increased until the motor current reaches its rated value.
Full load torque: the torque necessary to produce the rated horsepower oa at full
load speed. In lb at 1 ft radius, it is equal to the horsepower x 5,250 divided by the
full load speed.

Write short note on: DOL starter, autotransformer starter and star-delta starter
A direct on line (DOL) starter is a simple method for starting a motor by applying full
line voltage to the motor terminals. It's made up of a contactor, circuit breaker, and
overload relay:

 Contactor: An electromagnetic switch that connects the motor windings to the

supply voltage when the start button is pressed.
 Circuit breaker: A safety device.
 Overload relay: Protects the motor from overheating by opening the contactor circuit
if there's an overload.
An autotransformer starter (ATS) is a motor starter that uses a reduced voltage to
start large induction motors. It's used when the current is limited and the motor
needs a minimum starting torque.
A star-delta starter is a device that reduces the starting current and torque of a motor
when it starts up. It's often used to start three-phase induction motors, but it can only
be used when the motor is started without a load and the starting current is relatively
low.
 Autotransformer starter Application ,Advantage,Disadvantages: 10
 How it works
The motor is first connected to a reduced voltage output, and then the leads are
switched to the full voltage once the current has reached the running value.
 Applications
ATSs are used for activating slip ring and squirrel cage induction elect motors,
boosting circuit incoming voltages, and operating interconnect systems at the
required threshold voltages.
 Advantages
ATSs provide a solution to transient problems and can be adjusted for different
starting current and torque requirements.
 Disadvantages
ATSs have some disadvantages, including:
 No galvanic isolation between the input and output ports
 Higher short-circuit fault level
 Difficulty in providing effective over-voltage protection
 Complex voltage regulation under load conditions
 Safety concerns due to the direct connection of live parts

1. The operating speed on a three phase induction motor is 970 rpm. Possible no. of poles is:
(a) 2 (b) 4 (c) 6 (d) 8

2. The supply frequency of a three phase induction motor is 50 Hz and the rotor frequency is 10 Hz.
The value of slip is: (a) 0.1 (b) 0.2 (c) 0.3 (d) 0.4

3. End rings are used to: (a) Short circuit the stator conductors for squirrel cage induction motor (b)
Short circuit the rotor conductors for squirrel cage induction motor (c) Short circuit the stator
conductors for slip ring induction motor (d) Short circuit the rotor conductors for slip ring induction
motor
4. External resistances are used to: (a) Short circuit the stator conductors for squirrel cage induction
motor (b) Short circuit the rotor conductors for squirrel cage induction motor (c) Short circuit the
stator conductors for slip ring induction motor (d) Short circuit the rotor conductors for slip ring
induction motor

5. Power factor of a three phase induction motor: (a) Increases with load (b) Decreases with load (c)
Is independent of the load (d) Increases or decreases depending on the type of load

6. The maximum value of slip is: (a) 0.5 (b) 1.0 (c) 1.5 (d) 2.0
7. The maximum possible value of synchronous speed in India is: (a) 1500 rpm (b) 3000 rpm (c) 1800
rpm (d) 2000 rpm 11

1. The rotor resistance of a three phase slip ring induction motor is doubled. The maximum torque
will become:(a) double(b) one-fourth(c) four times(d) none of the above

2. The rotor reactance at standstill of a three phase induction motor is made double. The slip at which
maximum torque occurs becomes:(a) double(b) remains the same(c) half(d) one-fourth

3. For determining the stator resistance which of the following test is performed:
(a) No load test(b) Blocked rotor test(c) Both (a) and (b)(d) Load test

4. The autotransformer starter becomes equivalent to a star delta starter with a tapping of:
(a) 0.5(b) 0.58(c) 0.4(d) 0.3

5. If the tapping of an autotransformer is set at 0.5, then the ratio of starting torque with
autotransformer starting to DOL starting will be: (a) 0.25(b) 0.5(c) 1(d) 1.25

6. The rotor resistance of a three phase induction motor is 5 ohms. For obtaining maximum starting
torque, the rotor reactance at standstill should be:
(a) 5 ohms(b) 2.5 ohms(c) 10 ohms(d) 1.5 ohms

7. If the supply voltage is made double, then the torque of a three phase induction motor becomes:
(a) 4 times(b) Double(c) Half(d) One-fourth