Is This Method Correct for Calculating Power Factor in Synchronous Generators?

[Idea04]

I'm trying to calculate the power factor of a three phase synchronous generator

torque angle = arctan^-1 (impedance)
(sin torque angle/ current x voltage)
90 - torque angle - sin = XYZ
power factor is cosine XYZ

Is this the correct calculation to use?

 

[tiny-tim]

Hi Idea04!

torque angle = arctan^-1 (impedance)

i think i know what you mean, but that's not how to write it

it's arctan or tan^-1, not arctan^-1

and they are for real numbers, not complex numbers, you need arg for that

impedance is a complex number, and Z = X + iY = |Z|e^iφ

φ = arctan(Y/X) = tan^-1 Y/X = arg(impedance)

(sin torque angle/ current x voltage)
90 - torque angle - sin = XYZ
power factor is cosine XYZ

sorry, i don't understand this … eg what is the angle XYZ ?

add the three complex voltages (as complex numbers), then find the arg ​