(Solved): 3. Circuit analysis of a three-phase induction machine, torque calcaultion: A 125-kW, 460-V three-ph ...

3. Circuit analysis of a three-phase induction machine, torque calcaultion: A 125-kW, 460-V three-
phase, four-pole, 50-Hz induction machine has the following parameters in (ohms-per-phase): R1 = 0.033,
R2 = 0.045, X1 = 0.28, X2 = 0.31, Xm = 7.1. (not in p.u.!)

Figure 3: Problem 3: An induction motor (IM) is connected to a voltage source through a line.

• Calculate the real and reactive power consumption of the machine when the motor is connected to a 460-V
source through a line and the line’s impedance is Xline = 0.30 p.u..
• At steady state, the motor’s speed is 1750 round per minute. Calculate the motor’s real and reactive
power consumption. Calculate the torque of the motor.
• Please develop a computer program to plot the terminal voltage magnitude of the motor V1, the motor’s
electromagnetic torque, the real power, and reactive power consumption vs. the motor speed.
• Comment why starting a motor is problematic and what could be the issue.
Note: this problem is beyond the usual scope of studying machine performance. Here the machine is connected
to a grid through a line. This problem is aimed to demonstrate the impact of IM on the voltage of a feeder.