Question

A three-phase, four-pole, 50-hp, 480-V, 60-Hz, Y-connected induction motor has the following parameters per phase:

r1 = 0.10 ? , x1 = 0.35 ? , r2' = 0.12 ?, x2' = 0.40 ? .



It is known that the stator core losses amount to 1200 W and the rotational losses equal 950 W. Moreover, at no-load the motor draws a line current of 18 A at a power factor of 0.089 lagging.



When the motor operates at a slip of 3.5%, find :
The input line current and power factor

Answer 1

To find the input line current and power factor of the motor operating at a slip of 3.5%, we need to use the equivalent circuit and formulas for a three-phase induction motor. Substituting the values will give us the input line current and power factor.

Step-by-step explanation:

To find the input line current and power factor of the motor operating at a slip of 3.5%, we need to use the equivalent circuit and formulas for a three-phase induction motor. The formula for input line current is:

Iinput = (Pinput / (Vline * √3 * cos(φ))) + Irotor

Where:

• Pinput = 50 hp * 746 W/hp = 37,300 W
• Vline = 480 V
• φ = arccos(0.089) = 1.479 radians
• Irotor = (s / smax) * IFL

With the given slip and full load current (IFL), we can calculate the input line current. The power factor can be obtained using the formula:

Power factor = cos(φ) = (Pinput / (Vline * √3 * Iinput))

Substituting the values will give us the input line current and power factor.