How Space Harmonic in Rotating MMF wave Produces only Fundamental Frequency Voltage in Stator?

It is a well known fact that, space harmonic present in the rotating mmf wave in an uniform air gap Electrical Machine (Non Salient Pole machine) produces or generates only fundamental frequency voltage in the Stator winding of the machine. In this post we will discuss the reason behind this fact.

As we know that flux is given by

Flux = MMF/ Reluctance

Thus, if we neglect the magnetic saturation, the reluctance offered to the magnetic flux is constant for a uniform air gap machine. Therefore, in this case magnetic flux is directly proportional to the mmf. In view of this, the nth space harmonic wave of mmf will produce nth space harmonic in the magnetic flux. Figure below depicts the space distribution of mmf in the machine.

Let us assume that the speed of the fundamental component of rotating mmf wave be Ns1. Then the speed of nth harmonic component of space mmf wave will be (1/n)Ns1. Because of this the poles created by the nth harmonic component of rotating mmf wave will be different than the poles created by the fundamental component.

Let the poles produced by the fundamental component of rotating mmf be P then the poles created by the nth harmonic mmf wave will be nP.

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Now we will find the frequency of emf generated by fundamental flux wave and nth harmonic and will compare them.

Frequency of generated emf in the Stator winding due to fundamental flux,

f = PNs1/120

Frequency of generated emf in the Stator winding due to nth harmonic flux,

fn = [(nP)x{(1/n)Ns1}]/120

     = PNs1/120

Thus from the above two frequencies of generated emf, we observe that nth harmonic component of flux produces only fundamental frequency emf in Stator.