Department of Electrical Engineering and Computer Science
EEL4205 Electric Machinery
Homework Set No. 7
Names: ____________________; _____________________; ____________________;
Problem 1.
A 220 V, three phase, two pole, 50 Hz induction motor is running at a slip of 5 percent.
Find:
(1) the speed of the magnetic fields in rpm;
(2) the speed of the rotor in rpm;
(3) the slip speed of the rotor;
(4) the rotor frequency in Hz.
Answer:
MatLab code:
Problem 2.
A three phase, 60 Hz induction motor runs at 890 rpm at no load and at 840 rpm at full
load.
(1) How many poles does this motor have?
(2) What is the slip at rated load?
(3) What is the speed at one quarter of the rated load?
(4) What is the rotor’s electrical frequency at one quarter of the rated load?
Answer:
MatLab code:
Problem 3.
A 208 V, two pole, 60 Hz, Y connected wound rotor induction motor is rated at 15 hp. Its
equivalent circuit (see figure below) components are
R1  0.2 
R2  0.12 
X M  15 
X 1  0.41  X 2  0.41 
Pmech  250 W
Pmisc  0
Pcore  180 W
(1) For a slip of 0.05, find
a. the line current;
b. the stator copper losses;
c. the air gap power;
d. the power converted from electrical to mechanical form;
e. the induced torque;
f. the load torque;
g. the overall machine efficiency;
h. the motor speed in rpm and rad/s.
(2)
a. What is the slip at the pullout torque?
b. What is the pullout torque of this motor?
(3)
a. Calculate and plot the torque-speed characteristic of the motor;
b. Calculate and plot the output power versus speed curve of the motor .
(4)
a. How much additional resistance (referred to the stator circuit) would it be
necessary to add to the rotor circuit to make the maximum torque occur at
starting conditions (when the shaft is not moving)?
b. Plot the torque-speed characteristic of this motor with the additional resistance
inserted.
(5) If the motor is to be operated on a 50 Hz power system,
a. What must be done to its supply voltage? Why?
b. What will the equivalent circuit component values be at 50 Hz?
Answer:
MatLab code:
Problem 4.
A 440 V, 50 Hz, two pole, Y connected induction motor is rated at 75 kW. The
equivalent circuit (shown in last problem) parameters are
R1  0.075  R2  0.065  X M  7.2 
X 1  0.17  X 2  0.17 
Pmech  1 kW Pmisc  150 W Pcore  1.1 kW
(1) For a slip of 0.04, find
a. the line current;
b. the stator power factor;
c. the rotor power factor;
d. the stator copper losses;
e. the air-gap power;
f. the power converted from electrical to mechanical form;
g. the induced torque;
h. the load torque;
i. the overall machine efficiency;
j. the motor speed in rpm and rad/s.
(2)
a. What is the pullout torque?
b. What is the slip at the pullout torque?
c. What is the rotor speed at the pullout torque?
(3) Plot the following quantities as slip varies from 0% to 10%:
a. induced torque;
b. power converted from electrical to mechanical form;
c. output power; (Also answer at what slip does out power equal the rated power
of the machine?)
d. efficiency.
(4) If the motor is to be driven from a 440 V, 60 Hz power supply,
a. What will the pullout torque be?
b. What will the slip be at pullout?
Answer:
MatLab code: