Field-harmonic theory of slip-ring motor taking multiple armature reaction into account

The voltage equations of the slip-ring motor including the multiple armature reaction, i.e. the primary, secondary and tertiary armature reaction, are derived and presented in matrix notation. The theory put forward is valid for integral-and fractional-slot windings. With integral-slot windings and equal numbers of phases in the stator and the rotor, the current and field harmonics are neither influenced by delta connection nor by parallel branches of the winding (unlike the squirrel-cage motor). A system of n complex equations, for which, in general, n = 14, ¿, 30 suffices, is used to determine the n unknown stator-and rotor-current harmonics. The field harmonics, losses, torques etc. are obtained from the current harmonics. As an illustrative example, the system of simultaneous equations with n = 18 is solved for a 4-pole 70kW motor having 48 stator 36 rotor slots. The magnitudes and frequencies of the stator-and rotor-current harmonics for several coil pitches and slot skewings are given, and the resulting flux-density harmonics in the air gap are determined. The results are compared with measurements and are in agreement with them.