Question

a. A 75kW, three (3) phase, star-connected, 4-poles, 50Hz and 440V synchronous motor (cylindrical rotor type) operates at full load capacity with 0.8 p.f. leading. The motor rotor efficiency is 95% and the synchronous impedance is 2.592. Calculate the motor; i. Mechanical or synchronous speed ii. Developed mechanical power iii. Armature current iv. Back E.M.F ​

Answer 1

Step-by-step explanation:

Given information:

Power input (P) = 75 kW

Power factor (p.f.) = 0.8 (leading)

Voltage (V) = 440V

Synchronous impedance (Zs) = 2.592

Rotor efficiency = 95%

i. Mechanical or synchronous speed:

The synchronous speed (Ns) of a motor can be calculated using the formula:

Ns = (120 * Frequency) / Number of poles

In this case, the frequency is 50Hz and the number of poles is 4.

Ns = (120 * 50) / 4

Ns = 1500 RPM

Therefore, the mechanical or synchronous speed of the motor is 1500 RPM.

ii. Developed mechanical power:

The developed mechanical power (Pd) of the motor can be calculated using the formula:

Pd = P * Rotor efficiency

Pd = 75 kW * 0.95

Pd = 71.25 kW

Therefore, the developed mechanical power of the motor is 71.25 kW.

iii. Armature current:

To calculate the armature current (Ia), we can use the formula:

Ia = P / (√3 * V * p.f.)

Ia = 75 kW / (√3 * 440V * 0.8)

Ia = 75,000 / (1.732 * 440 * 0.8)

Ia ≈ 84.8 A

Therefore, the armature current of the motor is approximately 84.8 A.

iv. Back EMF:

The back electromotive force (E) of the motor can be calculated using the formula:

E = V - (Ia * Zs)

E = 440V - (84.8 A * 2.592)

E ≈ 440V - 219.0976V

E ≈ 220.9024V

Therefore, the back electromotive force (E) of the motor is approximately 220.9024V.

Please note that these calculations are based on the given data and assumptions.