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An analysis of subsynchronous resonance problems requires a clear understanding of the physical relationships that produce the phenomenon. This paper presents these relationships and uses them to derive a number of useful formulas for studying the problems. The mathematical basis of these formulas is shown and the approximations required for their derivation are described. These formulas are most useful in planning a series capacitor compensated transmission system to avoid or minimize subsynchronous resonance problems, This application is the subject of a companion paper.

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Early investigations were conducted with the machine operating as a 3 phase generator with delta connected capacitors. To simplify the work an at tempt was made later to operate the machine as a single phase generator. Experimentation and com parison showed that the characteristics for either are identical. This fact is brought out clearly by the curves of figure 2 where both the 3 phase and single phase curves correspond exactly as to shape. Furthermore, the bottom curve of figure 2 is for both 3 phase and single phase operation. It was discovered further that the constants or values of capacitance for either case could be translated quite easily to the other. In the single phase method, the wye connected machine was operated with 2 of the phases in series. As a result, in compensating, the series capacitive reactance must be approximately twice the 3 phase value, since it must balance out the inductive reactance of 2 of the phases. In re gard to the shunt capacitance, remembering that to operate at the same voltage (either single or 3 phase) the iron of the machine must be at the same saturation, it might be supposed that the same kilovolt-ampere value of capacitance would be re quired for either single or 3 phase operation. This relation checked quite closely experimentally.To obtain large values of capacitance for series use, series transformers may be used with small-ca pacitance high-voltage capacitors. The operation of a capacitor through a transformer gives the capaci tor an effective reactance equal to its actual reac tance multiplied by the square of the transformation ratio. Operation in this manner is satisfactory so long as the transformers are operated well below the knee of their saturation curves.The effects of magnetic saturation on the various types of reactances used in calcula tions on synchronous machines are con sidered in this paper. Saturation factors for the important constants used in transient and unbalanced load calculations are presented in curve form. These data are taken from short-circuit tests on a large number of ma chines. The saturation factor for transient reactance under conditions encountered in stability calculations is difficult to test di rectly so the test data are supplemented by theoretical calculations.HE new methods of analyzing syn chronous machine performance under transient or unbalanced load conditions have introduced a large number of new constants. 58 The method of sym-A paper recommended for publication by the A.I.E.E. committee oq( electrical machinery, and tentatively scheduled for discussion at the A.I.E.E. summer convention, Ithaca, Ν. Y.

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