Transients in 2-Phase Synchronous Machines

The analytical study of 3-phase synchronous machines has been well covered by man authors,^1,2,3,4 Not so much attention has been devoted to the 2-phase machine because much of the development of the methods of analysis occurred after the trend away from 2-phase systems was well established. Although the present use of 2-phase generators represents a small percentage of total generation, it is believed that there is some justification for analytical study of 2-phase machine performance. Such a study has value for the 2-phase systems now in use, and it has value in an analytical sense by showing how the relations developed for 3-phase generators may be adapted to generators with a different number of phases. The discussion in this paper is confined to L-connected, or quarter-phase machines with salient poles and without damper windings. It is limited to short-circuit or transient conditions. The inductances are defined and the relations expressing the variations of the several inductances of the windings are developed. The general fluxlinkage equations for all windings are determined in terms of stator and rotor currents. With this basis the operation of the machine under all possible short-circuit conditions is considered with the object of determining the transient and steady-state currents. The possible short-circuit conditions for the L-connected quarter-phase machine are the double line-to-neutral fault, the line-to-line fault, and the single line-to-neutral fault. The equations developed are compared with similar relations for 3-phase machines to show the similarities and the differences.