Question

A 13.8kV three-phase wye-connected synchronous machine has an effective armature resistance of 0.1Ω per phase and a synchronous reactance of 3.1Ω per phase. It is operating at 0.6 power factor lagging with a line current of 100Amps and the synchronous machine is absorbing real power. What is the internal generated voltage?

a) 7,718 volts and is acting as a synchronous motor
b) 7,718 volts and is acting as a synchronous generator
c) 13,555 volts and is acting as a synchronous motor
d) 13,555 volts and is acting as a synchronous generator

Answer 1

The internal generated voltage of the synchronous machine is 7,718 volts and it is acting as a synchronous generator.

Step-by-step explanation:

The internal generated voltage of a synchronous machine can be calculated using the equation:

V = IR + IZ

Where V is the line voltage, I is the line current, R is the effective armature resistance per phase, and Z is the synchronous reactance per phase.

In this case, the line voltage is 13.8kV, the line current is 100A, the armature resistance is 0.1Ω per phase, and the synchronous reactance is 3.1Ω per phase. Plugging these values into the equation:

V = (100A)(0.1Ω) + (100A)(3.1Ω) = 7,718 volts

Therefore, the internal generated voltage is 7,718 volts. Since the synchronous machine is absorbing real power, it is acting as a synchronous generator.