Question

A three-phase star-connected alternator working at 1600 KVA,50 Hz,2200 V, has an armature dc resistance of 0.12 Ω. Assume the ac resistance is 1.3 times the dc resistance. A field current of 70 A produces a short circuit current of 360 A and for the same field current the open circuit voltage is 800 V. Determine

a} Synchronous reactance of the machine

Answer 1

To find the synchronous reactance of the alternator, one must subtract the ac resistance from the ratio of the open circuit voltage to the short circuit current, resulting in approximately 2.067 ohms.

Step-by-step explanation:

The student has asked how to determine the synchronous reactance of a three-phase star-connected alternator. Given that the alternator produces a short circuit current of 360 A for a field current of 70 A, and an open circuit voltage of 800 V with the same field current, we can calculate the synchronous reactance (Xs) using the formula:

Xs = (Eo / Isc) - (a.c. resistance)

Where Eo is the open circuit voltage and Isc is the short circuit current.

The ac resistance is given to be 1.3 times the dc resistance, hence:

ac resistance = 1.3 × 0.12 Ω = 0.156 Ω.

Using the given values:

Xs = (800 V / 360 A) - 0.156 Ω ≈ 2.067 Ω.

So, the synchronous reactance of the machine is approximately 2.067 Ω.