Abridgment of synchronous machines — IV

The special case of cylindrical rotor machine has been treated previously by Boucherot and others. The present paper solves the general case, including salient pole machines. The cylindrical rotor type thus becomes merely a limiting case. The principle assumption which distinguishes the present theory from the extensively studied cylindrical rotor theory is that the total armature self-inductance is here taken as variable with respect to rotor position, whereas the previous theory of short circuits, as represented by Boucherot, for instance, assumes this inductance to be constant — in other words, that the air-gap is uniform. Expressions are derived for the short-circuit currents in the armature and field, for voltage induced in the open phase, and for voltages across external reactances in the armature and field circuits. Comparison of calculated and test curves for these quantities are shown in Figs. 5 to 8, for a 7000-kv-a., 385-rev. per min., salient pole alternator, and in Figs. 11 to 25 for a 20-hp., 1800-rev. per min. induction machine (cylindrical rotor). These show satisfactory agreement. The mathematical work and definitions are in Appendixes as follows: A. Summary of Equations. B. Armature Current. C Field Current. D. Voltage Across External Reactance in Armature Circuit. E. Voltage Across the Open Phase. F. Voltage Across the Open Phase. G. Variation of Armature Inductance with Position. H. Decrement Factors. I. Reactances — Definitions and Relations.