Equivalent Circuit of the Primitive Rotating Machine With Asymmetrical Stator and Rotor

The equations and equivalent circuits of all standard types of rotating electric machinery operating under arbitrary conditions may be derived as special cases of a single generalized rotating machine, the so-called primitive machine. This paper derives the steady-state equivalent circuit of the primitive machine having unbalanced rotor as well as stator. That is, the load or transmission line connected to a salient-pole synchronous machine is assumed to be unbalanced (due to faults, short circuits, and so forth), or the load connected to the slip rings of an induction motor is assumed to be unbalanced. The single-phase alternator, instrument Selsyns, and also sudden short-circuit studies are cases that require an infinite series of time harmonics in the stator and rotor windings in addition to the fundamental. It is assumed that these time harmonics are due to space waves with fundamental pairs of poles rotating at different speeds. The effect of the harmonic space waves is not considered. A paper by A. W. Rankin
¹
shows network analyzer studies made of the harmonic currents and torques of a single-phase alternator.