IEEE Std 1110-2019 pdf download – IEEE Guide for Synchronous Generator Modeling Practices and Parameter Verification with Applications in Power System Stability Analyses.
6.2 Representation of synchronous generator saturation in the steady state The effect of saturation on the synchronous generator steady-state performance has been recognized for at least 60 years when the initial concern was the accurate calculation of the field excitation for the exciter design and sizing. During the second half of this 60-year period, the effect of saturation on determining the internal angles of synchronous generators has received much attention as well. In general, the effect of saturation depends not only on the saturation curve in the axis of the resultant machine ampere-turns but also on the phase angle between the resultant ampere-turns and the resultant flux due to both the saliency and the different saturation levels in the different axes (El-Serafi and Demeter [B79], El-Serafi and Wu [B22], El-Serafi et al. [B71]). Since such information is not commonly available, empirical methods, which seem in most of the cases to represent the effect of saturation reasonably accurately and to give relatively closer agreement with the measured values, have been used in the synchronous generator phasor diagrams. Some of these empirical methods were documented in 1945 with the first AIEE test code for synchronous machines. These procedures now appear essentially in the same form in IEEE Std 115. Other publications and IEEE papers also treated the subject and discussed the difference in approach between salient-pole generators and round-rotor turbogenerators (El-Serafi and Abdallah [B21], Flores et al. [B28], Turner [B83]). These empirical methods depend mainly on calculating a saturation increment I FS (or in another form a saturation factor K). I FS (or K) is the difference between (or the ratio of) the actual excitation and the excitation on the air-gap line of the saturation curve at the operating point. An internal voltage “behind some specific reactance” is usually used to locate the operating point on this saturation curve.