The truth about airgap leakage reactance in polyphase squirrel-cage induction motors

The paper examines the validity of the theory arrived at by some authors, notably Alger, that the airgap leakage reactance of a polyphase squirrel-cage induction motor consists of two separate entities, namely, the `zig-zag¿ reactance and `belt¿ leakage reactance. The paper shows that not only the lower-order primary airgap m.m.f. harmonics have equal and opposing m.m.f.s induced in the secondary, but also the stator harmonics of pole-pair pitch smaller than the rotor slot pitch, which Alger calls `zig-zag¿ leakage harmonics. This fact thus disproves that the `zig-zag¿ leakage is a separate entity from the so-called `belt leakage reactance¿, which Alger suggests should be disregarded for squirrel-cage motors. Further analysis reveals that the alternative theory of `differential leakage reactance¿, as also derived by Alger, but on the assumption of vanishingly narrow slot-openings, is also valid for slot-opening which are not so. This, provided that the magnetising reactance, (with which the differential leakage coefficient must be multiplied to obtain the differential leakage reactance) incorporates the Carter airgap coefficient, as in fact it does in practice. The effect of slot-openings which are not infinitesimally narrow on the mean permeance and the permeance harmonics produced are also dealt with. The theory set forth in this paper is supported by locked-rotor tests on a number of machines. machines.