Abridgment of the reactances of synchronous machines

Abstract

Until somewhat recently, synchronous machine theory has been satisfied with a relatively few characteristic constants, or reactances, in terms of which the behavior of machines has been calculated. Present theory, however, requires many more coefficients. There are now generally recognized two values each of leakage, synchronous, and transient reactance, which correspond to the two symmetrical axes of magnetization of the armature current and which refer to balanced operation. Negative and zero phase-sequence reactances are also employed to determine operation under unbalanced conditions, and it is possible and desirable to distinguish other reactances. In view of the increasing complexity of the subject it is felt that a critical survey of it is in order and the object of the paper has been to provide that survey. The paper has been divided into two parts. Part I describes and treats of the subject with regard to those factors which are important to application or operating engineers, and to designers. In particular, the major types of reactances which include the synchronous, transient, and phase-sequence reactances, are discussed. These quantities are defined and their methods of test outlined. It appears necessary to consider a second type of transient reactance; namely sub-transient reactance. Both reactances may be determined from short-circuit oscillograms as illustrated in the paper. A table is included which gives the numerical range of reactances for the various types of synchronous machines. Part II discusses the theoretical considerations, with a view to broadening and classifying existing conceptions of reactance. It includes the effect of external reactance on negative phase-sequence reactance and the variation in this latter quantity, depending upon whether current or voltage is impressed on the machine. An important aspect of the division of synchronous reactance into armature reaction and leakage reactance is discussed. Transient reactance is shown to be the difference between synchronous reactance and the ratio of the mutual reactance between armature and field and the total field reactance. Calculations are included to show that the short-circuit and open-circuit time constants are related to each other in a simple manner. The appendixes cover the following subjects: a. Application of the Principle of Superposition to Synchronous Machine Analysis. b. Replacing the Effect of Induced Field Currents by Employing Transient Instead of Synchronous Reactances. c. Significant Rotor Circuits in Addition to the Main Field Winding (which effect transient reactances). d. The Negative Phase-Sequence Reactance of a Synchronous Machine with Negative Phase-Sequence Voltage Impressed. e. Construction of Equivalent Circuits: Concept of Field Leakage Reactance. f. Calculation of Total Field Reactance. g. Relation of the Mutual Reactance Between Armature and Field to the No-Load Excitation Current. h. Relation Between Three-Phase and Single-Phase Reactances. i. Discussion of the System of Notation Used in the Paper. j. Per-Unit Representation of Quantities.