Question 6.3: The resistance and reactance of a squirrel-cage induction mo...
The resistance and reactance of a squirrel-cage induction motor rotor at standstill are 0.125 ohm per phase and 0.75 ohm per phase, respectively. Assuming a transformer ratio of unity, from the eight-pole stator having a phase voltage of 120 V at 60 Hz to the rotor secondary, calculate the following:
A. rotor starting current per phase, and
B. the value of slip producing maximum torque.
A. At starting, s = 1:
I_{r} =\frac{120}{0.125+j0.75}
=157.823\angle -80.538A
B.
s_{\max _{T} } =\frac{R_{r} }{X_{T} } =\frac{0.125}{0.75} =0.1667
The following script implements Example 6.3 in MATLAB^{TM}:
% Example 6-3
% A squirrel cage induction motor
Rr=0.125; % ohm
XT=0.75; % ohm
V=120; % Volt
f=60; % Hz
% A. Rotor starting current per phase
% At starting s=1
Ir= V/(Rr+i*XT)
abs(Ir)
angle(Ir)*180/pi
% B. The value of slip producing
maximum torque
s_maxT=Rr/XT
The results obtained from MATLAB^{TM} are as follows:
EDU»
Ir = 2.5946e+001 - 1.5568e+002I
ans = 157.8230
ans = -80.5377
s_maxT = 0.1667