In ac machines, the stator windings are intended to have a sinusoidally distributed conductor density in order to produce a sinusoidally distributed field distribution in the air gap. In the squirrel-cage rotor of induction machines, the bar density is uniform. Yet the currents in the rotor bars produce a magnetomotive force (mmf) that is sinsuoidally distributed. Therefore, it is possible to replace the squirrel-cage with an equivalent wound rotor with three sinsuoidally distributed windings.

In this chapter, we will briefly review the sinusoidally distributed windings and then calculate their inductances for developing equations for induction machines in phase (*a-b-c*) quantities. The development of these equations is assisted by space vectors, which are briefly reviewed. The analysis in this chapter establishes the framework for the *dq* winding-based analysis of induction machines under dynamic conditions carried out in the next chapter.

In the following analysis, we will also assume that the magnetic material in the stator and the rotor is operated in its linear region and has an infinite permeability.

In ac machines of Fig. 2-1a, windings for each phase ideally should produce a sinusoidally distributed radial field (*F*, *H*, and *B*) in the air gap. Theoretically, this requires a sinusoidally distributed winding in each phase. If each phase ...

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