The Air Gap Reactance of Polyphase Machines

This paper presents some new formulas for the differential leakage reactance of distributed polyphase windings, such as those of induction motors and voltage regulators. Previous authors have used two distinct methods for evaluating the differential reactance, but the results obtained by these two methods have been inconsistent, particularly for open slot machines. The overlap method is based on calculating the average overlap of the teeth on the primary and secondary, and then calculating the leakage through the zig-zag flux path under the combined influence of the primary and secondary ampere turns. The ``differential method´´ is that of calculating the leakage by taking the difference between the total flux produced by the primary or the secondary, and the fundamental sine wave of the flux. When the effects of flux fringing with open slots are included, the results obtained by the two methods are shown to be entirely consistent. The new formulas derived in this way are believed to be more general in application than any heretofore published. They show that the slot openings decrease the differential leakage reactance much more rapidly than they decrease the magnetizing reactance.