Generator Loss of Field Impedance locus diagram

[rockman7892]

Can someone explain to me the significance of a generator impedance locus diagram when looking at loss of field protection. I cannot seem to find a good reference as to what exactly the impedance locus represents. I understand that is a plot of generator/system X and R parameters and shows how those parameters are effected when the generator field is lost but I'm having trouble understanding and visualizing exactly how the starting points are derived as well as understanding how the locus path travels.

I understand the concept of the LOF distance protection concept and the impedance circles, I just cant seem to understand the impedance locus.

For instance given a generator MVA and PF value in PU as well as generator and system reactance's how do you go about plotting the initial starting X and R points. Why does a generator with a higher PU load and PF have a different starting X and R points vs a lightly loaded generator given the same system reactance's?

Thanks for the help!

 

[davidbeach]

Starting point is the unit operating MW/MVAr point converted to the impedance plane. Ending point is the same MW value but with all of the machine's excitation needs supplied by the system MVArs into the machine; a different point to be translated to the impedance plane.

 

[rockman7892]

davidbeach

I see that for the transformation the equation Z=KV^2/MVA is used to convert MVA rating into impedance. This Z value is then plotted on the X-R plane with Z being a phasor at an angle Beta. I'm assuming this angle Beta is derived from the generators operating power factor, with the angle on the X-R plot being between Z and unity power factor (R axis). I'm guessing that the X and R values are then derived from taking the Cosine and Sine values of the angle Beta?