Page 303 - Solutions Manual to accompany Electric Machinery Fundamentals

1 E 1 E
2  2 A
  n
sin sin
2 2
 n
sin
E A  2
E 
sin
2
Finally,

 n
sin
E 2
k  A 
d
nE 
n sin
2
since k d is defined as the ratio of the total voltage produced to the sum of the magnitudes of each

component voltage.
B-3. A three-phase four-pole synchronous machine has 96 stator slots. The slots contain a double-layer
winding (two coils per slot) with four turns per coil. The coil pitch is 19/24.
(a) Find the slot and coil pitch in electrical degrees.

(b) Find the pitch, distribution, and winding factors for this machine.
(c) How well will this winding suppress third, fifth, seventh, ninth, and eleventh harmonics? Be sure to
consider the effects of both coil pitch and winding distribution in your answer.
SOLUTION

(a) The coil pitch is 19/24 or 142.5. Note that these are electrical degrees. Since this is a 4-pole
machine, the coil pitch would be 71.25 mechanical degrees.

There are 96 slots on this stator, so the slot pitch is 360/96 = 3.75 mechanical degrees or 7.5 electrical
degrees.

(b) The pitch factor of this winding is
 142 5 . 
k p  sin  sin  . 0 947
2 2

The distribution factor is
 n
sin
k  2 
d
n sin
2
The electrical angle  between slots is 7.5, and each phase group occupies 8 adjacent slots. Therefore,
the distribution factor is
 n 158  
sin sin
2
k d  2   15  . 0 956
n sin 8 sin
2 2

297