Where vph and iph are the phase voltage and phase current

Solved Step by Step With Explanation- AC Motor Parameters and Analysis

Questions

2.1.1 Calculate the required field current and the load angle (6)

2.1.2 Draw the corresponding phasor diagram (4)

2.3.4 If the terminal voltage remains at 2300V, 60Hz, what is the minimal field current required to maintain operation as a motor with load of 70kW? (2)

Answer

P = √3 * V * I * cos(θ), where P is power, V is voltage, I is current, and θ is the phase angle.

Synchronous machine power:

cos(θ) = 1 / √(1 + (2 * π * f * Lm * IF)^2), where f is the frequency.

The maximum power during regenerative braking occurs at a load angle of 90 degrees.

Vph = 2300 V

f = 60 Hz

if = Iph = 0.024 A

Using the relation IF / if = 1.8:

θ ≈ cos^(-1)(0.9961) ≈ 5.2 degrees (approximately)

2.1.2 Draw the corresponding phasor diagram:

pf = 0.82 leading

Repeat the same steps as in 2.1.1, but with the new power factor:

IF = 1.8 * if = 1.8 * 0.026 A = 0.0468 A

The load angle is 90 degrees.

2.3.4 If the terminal voltage remains at 2300V, 60Hz, what is the minimal field current required to maintain operation as a motor with a load of 70kW?

To find the minimal field current, you can use the same steps as in 2.1.1, but with P = 70 kW and pf = 0.89 leading.

IF = 1.8 * if = 1.8 * 0.016 A = 0.0288 A

So, the minimal field current required is 0.0288 A.