I am given the rated apparent power, frequency, rated speed, and rated voltage of a 3-phase wye-connected synchronous generator. Also, I know that the generator delivers the rated apparent power at leading power factor. Given the armature resistance Ra, Xd, and Xq, and the power angle, how can I solve for the power factor? Note that I am not given the real power.


2 Answers 2


enter image description here Here is a generic approach for finding parameters from given ones in such situations. Starting from the equivalent circuit where $R_a$ is the armature resistance and $jX_{ar}$ is the armature reactance, $V_{T}$ is the rated terminal voltage and $E_f$ is the excitation voltage. Corresponding parameters are:

  • rated apparent power : Use this to calculate $I_a$
  • frequency : see Xd and Xq
  • rated speed : -
  • rated voltage : $V_T$
  • Ra : $R_a$
  • Xd, and Xq : Use these to calculate armature reactance (depending on the type of generator [salient pole or cylindrical])
  • and the power angle : $\delta$
  • power factor : $\cos \theta$
  • $\begingroup$ Thanks. However, this is only possible for cylindrical. How about salient pole? Salient pole have no equivalent circuit and is solved using phasor diagrams. I know how to solve for the power factor when armature resistance is neglected (I.e. using the power angle) but not when it's not. Is it even possible to solve for the power factor given the circumstances? Also, the power factor is the cosine of theta. $\endgroup$
    – Joel S.
    Nov 28, 2015 at 10:37

enter image description here

For salient pole generators, it is merely an extension of Anonymous's answer. The armature current needs only to be broken down into its perpendicular components and applied correspondingly to the respective inductances.


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