Page 301 - Solutions Manual to accompany Electric Machinery Fundamentals

Appendix B: Coil Pitch and Distributed Windings

B-1. A 2-slot three-phase stator armature is wound for two-pole operation. If fractional-pitch windings are to
be used, what is the best possible choice for winding pitch if it is desired to eliminate the fifth-harmonic
component of voltage?
SOLUTION The pitch factor of a winding is given by Equation (B-19):


k  sin
p
2
5
To eliminate the fifth harmonic, we want to select  so that sin  0 . This implies that
2

5   180 n , where n = 0, 1, 2, 3, …
2

2  180 n
or    72 , 144 , ...
5
These are acceptable pitches to eliminate the fifth harmonic. Expressed as fractions of full pitch, these
pitches are 2/5, 4/5, 6/5, etc. Since the desire is to have the maximum possible fundamental voltage, the
best choice for coil pitch would be 4/5 or 6/5. The closest that we can approach to a 4/5 pitch in a 24-slot
winding is 10/12 pitch, so that is the pitch that we would use.
At 10/12 pitch,
150
k  sin  . 0 966 for the fundamental frequency
p
2
150 5  
k  sin  . 0 259 for the fifth harmonic
p
2

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