AC Machines
Module 6: Polyphase Induction Motor
• Rotor e.m.f. and Rotor Current
• Torque
• Effect of Change in Supply Voltage on
Starting Torque and Slip
• Full-Load Torque and Maximum Torque
• Starting Torque and Maximum Torque
Rotor e.m.f and Rotor Current
Rotor e.m.f
When the rotor is stationary, an induction motor is
equivalent to a 3-phase transformer with secondary short-
circuited. Thus,
Where:
EBR = Rotor emf at standstill (s = 1)
ES = applied voltage at stator
NR = number of rotor turns
NS = number of stator turns
*note ER = sEBR
where:
ER = induced emf of rotor per phase
Rotor e.m.f and Rotor Current
Rotor current
At standstill:
At slip ‘s’:
Where:
IR = rotor current per phase
Rr = rotor winding resistance per phase
XBR = rotor winding reactance at stand still per phase
*note (XR = sXBR)
Rotor e.m.f and Rotor Current
Power factor of rotor current
Torque
T = kEBRIRcosθR, where k is any constant
Substituting the value of IR and cosθR, we have
At starting (s = 1):
Maximum Torque:
Torque will be maximum when s = Rr / XBR, thus
Torque
or lb-ft
or N-m
Where:
T = Torque
Po = output power or power developed
RIP = Rotor Input Power
Nr = Rotor speed
NS = synchronous speed
Effect of Change in Supply voltage
on Starting Torque and Slip
Full-Load Torque and Maximum Torque
Where;
a = ratio of rotor resistance to rotor standstill reactance
Starting Torque and Maximum Torque
Examples:
Example 1:
A three-phase 60-cycle six-pole 220-volt wound-rotor induction
motor has a stator that is connected in delta and a rotor connected
in wye. The rotor has half as many turns as the stator. For a rotor
speed of 1,110 rpm, calculate:
i) the blocked rotor voltage per phase Answer: 110V
ii) the rotor generated voltage per phase Answer: 8.25V
iii) the rotor volage between terminals Answer: 14.29V
iv) the rotor frequency Answer: 4.5Hz
v) the rotor current, if the rotor resistance per phase is 0.1Ω and
rotor reactance at stand still is 0.5Ω/phase
Answer: 77.25 A
Examples:
Example 2:
A 3-phase induction motor operates with a slip of 2% and takes
11.0A and 3500 watts when driving its normal load. When operated
without load, the motor takes 4.3A and 290W. When the rotor of this
machine is blocked, 440 W are required to circulate a current of
14A. Calculate the output torque of this motor in (a)lb-ft and in (b)N-
m.
Answer: (a) 17.84 & (b) 24.20
Example 3:
A 5 Hp, 500-V, 3-phase motor is developing its full load output of
960 rpm. The starting torque is equal to the full load torque. What
will be the starting torque if the supply voltage falls to 400 volts?
Answer: (a) 23.74 N-m
Examples:
Example 4:
A 3-phase, 4-pole, 230V, 60 Hz wound-rotor induction motor has
both its stator and rotor connected in Y. The rotor has half as many
turns per phase as the stator. If the rotor is turning at 1725 rpm, Rr =
0.075 Ω and XBR = 0.375 Ω, determine the torque developed by the
motor
Answer: (a) 27.543 lb-ft
Example 5:
A 3,300V, 24-pole, 50 Hz, 3-phase star-connected induction motor
has a slip-ring rotor resistance of 0.016 Ω and standstill reactance of
0.265 Ω per phase. Calculate the ratio of full-load torque to
maximum torque if full-load torque is obtained at 247 rpm.
Answer: 0.382
