Problem 107-3    Source:   Example 5.2 - page 218 - SEN, P.C. -    Book: Principles of Electric Machines and Electronics - 3rd Edition - Ed. Wiley - 2014.

A three-phase induction motor, 4 poles, 15 HP, 60 Hz, rotates at a speed of 1,728 rpm and delivers full power to a load connected to its axis. It has friction losses and 750 W fan. It is requested:

a) the mechanical power developed by the engine, P_mec ;

b) the power in the air gap, P_gap ;

c) the rotor copper losses, P_jr .

Solution of the Problem 107-3   

Item a

The mechanical power developed by the motor is the sum of the shaft power plus the losses. Transforming HP to watts, we have:

Adding the losses we have the mechanical power that the motor rotor develops, according to eq. 107-31.

Item b

To answer this item we must find the slip value of the engine. Using the eq. 107-02, repeated below, let's calculate the synchronous speed of a 4 pole motor.

Substituting for numerical values ​​and performing the calculation, we get:

Then the slip, using eq. 107-04, is:

Then the power in the air gap, which is the power that the motor absorbs from the supply network, is given by:

Item c

The copper losses of the rotor are given by: