Is this motor over-excited or under-excited

[engineeringsdt]

Homework Statement

A three phase eight pole 50 hz star connected synchronous generator operating at nominal voltage of 6.6kv line, has a synchronous reactance of 6.6 ohm and negligible losses. When the field current is set to give an open circuit voltage of 4.5kv per phase the output power from the generator is 2.5Mw.

Homework Equations

The Attempt at a Solution

I think its overexcited because when i analyze it with the current source replaced with a voltage source E and the synchronous reactance in series with the output, the voltage source E is greater than the input voltage 3810V terminal on stator so its supplying current from the current source but I am not sure if I am right :/??,

 

[KataKoniK]

Dear student,

Thank you for your post. Your analysis is correct, the generator is indeed overexcited. When the field current is set to give an open circuit voltage of 4.5kv per phase, this means that the voltage source E is greater than the input voltage of 3810V. This results in the generator supplying current to the system, hence producing an output power of 2.5MW.

To further confirm this, we can also calculate the power factor of the generator. The power factor is given by the ratio of the real power (in watts) to the apparent power (in volt-amperes). In this case, the apparent power can be calculated as 3 * 6.6kV * 3810V = 75.858MVA. The real power is given as 2.5MW. Therefore, the power factor is 2.5MW/75.858MVA = 0.033, which is a leading power factor. This further confirms that the generator is overexcited.

I hope this helps. Let me know if you have any further questions.