11/27/2019
Electrical Machines ( )
Torque of Induction Motor
Year / Semester : 3 / 2
Lecture Notes (5)
Oct. 2019
Dr. Izzeldin Idris Abdalla 1
Example # 1
A 415 V, 10hp, four pole, 60 Hz, Y-connected induction motor
has a full-load slip of 5 percent.
1) What is the synchronous speed of this motor?
2) What is the rotor speed of this motor at rated load?
3) What is the rotor frequency of this motor at rated load?
4) What is the shaft torque of this motor at rated load?
Solution 1)
2)
3)
4)
Dr. Izzeldin Idris Abdalla 2
1
11/27/2019
Example # 2
The stator of a 3-Φ induction motor has 3 slots per pole
per phase. If supply frequency is 50 Hz, calculate:
1) number of stator poles produced and total number of
slots on the stator.
2) speed of the rotating stator flux (or magnetic field).
Solution
1) P = 2n = 2 × 3 = 6 poles
Total Number of slots = 3 slots/pole/phase × 6 poles × 3
phases = 54
2) Ns = 120 f/P = 120 × 50/6 = 1000 rpm.
Dr. Izzeldin Idris Abdalla 3
Example # 3
A 4-pole, 3-phase induction motor operates from a supply
whose frequency is 50 Hz. Calculate :
(i) The speed at which the magnetic field of the stator is rotating.
(ii) The speed of the rotor when the slip is 0.04.
(iii) The frequency of the rotor currents when the slip is 0.03.
(iv) The frequency of the rotor currents at standstill.
Solution
(i) Stator field revolves at synchronous speed, given by
Ns= 120 f/P = 120 × 50/4 = 1500 rpm.
(ii) Rotor (or motor) speed, N r= Ns (1 − s) = 1500(1 − 0.04) = 1440 rpm.
(iii) Frequency of rotor current, fr = sf = 0.03 × 50 = 1.5 Hz.
(iv) Since at standstill, s = 1, fr sf = 1 × f = f = 50 Hz
Dr. Izzeldin Idris Abdalla 4
2
11/27/2019
Relation Between Torque and Rotor Power Factor
The torque is proportional to the product of flux per stator
pole and the rotor current. one more factor that has to be
taken into account the power factor of the rotor.
Dr. Izzeldin Idris Abdalla 5
Starting Torque
The torque developed by the motor at the instant of starting is
called starting torque. In some cases, it is greater than the
normal running torque, whereas in some other cases it is
somewhat less.
Dr. Izzeldin Idris Abdalla 6
3
11/27/2019
Starting Torque, Cont.
Dr. Izzeldin Idris Abdalla 7
Starting Torque
Condition for Maximum Starting Torque
It can be proved that starting torque is maximum when rotor resistance
equals rotor reactance.
Effect of Change in Supply Voltage on Starting Torque
Clearly, the torque is very sensitive to any changes in the supply voltage.
Dr. Izzeldin Idris Abdalla 8
4
11/27/2019
Example # 4
A 3-Φ induction motor having a star-connected rotor has an induced emf
of 80 volts between slip-rings at standstill on open-circuit. The rotor has a
resistance and reactance per phase of 1 Ω and 4 Ω respectively. Calculate
current/phase and power factor when (a) slip-rings are short-circuited
(b) slip-rings are connected to a star-connected rheostat of 3 Ω per phase.
Dr. Izzeldin Idris Abdalla 9
Torque Under Running Conditions
Dr. Izzeldin Idris Abdalla 10
5
11/27/2019
Torque Under Running Conditions
where k1 is another constant. Its value can be proved to be
equal to 3/2 πNs. Hence, in that case, expression for torque
becomes
Dr. Izzeldin Idris Abdalla 11
Condition for Maximum Torque Under Running Conditions
The torque of a rotor under
running conditions is
The condition for maximum torque may be obtained by differentiating
the above expression with respect to slip s and then putting it equal to
zero. However, it is simpler to put Y = 1 /T and then differentiate it.
Hence, torque under running condition is maximum at that value of the
slip s which makes rotor reactance per phase equal to rotor resistance per
phase. This slip is sometimes written as sb and the maximum torque as Tb.
Dr. Izzeldin Idris Abdalla 12
6
11/27/2019
Condition for Maximum Torque Under Running Conditions
Dr. Izzeldin Idris Abdalla 13
Effect of Change in Supply Voltage and Frequency on
Torque and Speed
Effect of Change in Supply Voltage on Torque and Speed:
Obviously, torque at any speed is proportional
to the square of the applied voltage.
Effect of Changes in supply Frequency on Torque and Speed:
A 50-Hz motor operates well on a 60-Hz line provided its terminal voltage is raised
to 60/50 = 6/5 (i.e. 120%) of the name-plate rating. In that case, the new breakdown
torque becomes equal to the original breakdown torque and the starting torque is
only slightly reduced. However, power factor, efficiency and temperature rise remain
satisfactory.
Similarly, a 60-Hz motor can operate satisfactorily on 50-Hz supply provided its
terminal voltage is reduced to 5/6 (i.e. 80%) of its name-plate rating.
Dr. Izzeldin Idris Abdalla 14
7
11/27/2019
Full-load Torque and Maximum Torque
Let sf be the slip corresponding to full-load torque, then.
Dividing both the numerator and the denominator by X22, we get.
where a = R2/X2 = resistance/standstill reactance
Dr. Izzeldin Idris Abdalla 15
Starting Torque and Maximum Torque
Dr. Izzeldin Idris Abdalla 16
8
11/27/2019
Example # 5
A 50 kW, 440 V, 50 Hz, 10hp, Six-pole, induction motor has a
slip of 6 percent when operating at full-load conditions. At
full-load conditions, the friction and windage losses are 300 w,
and the core losses are 600 W. Find the following values for
full-load conditions:
1) The shaft speed Nr.
2) The output power in watts.
3) The load torque Tload in newton-meters.
4) The induced torque Tin in newton-meters.
5) The rotor frequency in hertz.
Solution:
1) The Ns of this machine is
Therefore the shaft speed is
Dr. Izzeldin Idris Abdalla 17
Example # 5
Dr. Izzeldin Idris Abdalla 18
9
11/27/2019
Torque/Speed Curve
The torque developed by a conventional 3-phase motor depends
on its speed but the relation between the two cannot be
represented by a simple equation. It is easier to show the
relationship in the form of a curve. In this diagram, T represents
the nominal full-load torque of the motor. As seen, the starting
torque (at N = 0)
is 1.5 T and the
maximum torque
(also called
breakdown
torque) is 2.5 T. Nominal torque T
Typical torque-
speed
characteristics of
induction motor
Dr. Izzeldin Idris Abdalla 19
Complete Torque/Speed Curve of a Three-Phase Machine
The directions of torque and rotor rotation are in the same direction in the
motor. The motor can be used as an asynchronous generator when driven at a
speed greater than the synchronous speed. In this case, it receives mechanical
energy in the rotor and supplies electrical energy from the stator.
The torque and speed are oppositely-directed.
Dr. Izzeldin Idris Abdalla 20
10
11/27/2019
Induction Motor Operating as a Generator
When run faster than its synchronous speed, an induction motor runs as a
generator called an Induction generator. It converts the mechanical energy
it receives into electrical energy and this energy is released by the stator
figures below show an ordinary squirrel-cage motor which is driven by a
petrol engine and is connected to a 3-phase line. As soon as motor speed
exceeds its synchronous speed, it starts delivering active power P to the 3-
phase line. However, for creating its own magnetic field, it absorbs reactive
power Q from the line to which it is connected. As seen, Q flows in the
opposite direction to P.
Dr. Izzeldin Idris Abdalla 21
Induction Motor Operating as a Generator
The active power is directly proportional to the slip above the synchronous
speed. The reactive power required by the machine can also be supplied by
a group of capacitors connected across its terminals. This arrangement
can be used to supply a 3-phase load without using an external source. The
frequency generated is slightly less than that corresponding to the speed of
rotation.
The terminal voltage increases with capacitance. If capacitance is insufficient, the generator
voltage will not build up. Hence, capacitor bank must be large enough to supply the reactive
power normally drawn by the motor.
Dr. Izzeldin Idris Abdalla 22
11
11/27/2019
Dr. Izzeldin Idris Abdalla 23
12
