Induction Motor Power Problem

Question

I have this textbook problem I am not sure how to go about doing it:

A 3 phase, 460V, 60HZ, 20KW induction Machine draws 25A at a power factor of 0.9 lagging when connected to an equivalent power supply. The core loss is 900W, stator copper loss is 1100W, Rotor Copper loss is 550W, Friction and Winding Loss is 300W. Calculate:

A) The air gap power B) The mechanical power developed C) The output horse power D) The efficiency

I calculated the Pelec to be 17927W and the pshaft is given as 20KW. Why is my power drawn lower than my output shaft power? I thought you had to subtract all the losses from pin to get the pout. I dont understand whether it is a motor or a generator, or how you would go about subtracting in the case of a generator.

Answer 1

20 kW is the rated mechanical output power. The actual operating power depends on the load. Subtract the core loss and the stator copper loss to get the air gap power (the power transferred from the stator to the rotor across the air gap). Subtract the rotor copper loss, friction and windage (air drag) losses from the air gap power to get the mechanical power delivered to the load in watts (746 W = 1 Hp).

You are correct; n < ns indicates operation as a motor. If n > ns, you would add the losses to the electrical power instead of subtracting and the electrical side figures would be the output and the mechanical side would be the input.