Page 306 - Solutions Manual to accompany Electric Machinery Fundamentals

. 0 342
th
7 :  . 0 347
. 0 985
th
th
In other words, the 5 harmonic is suppressed by 34.7% relative to the fundamental, and the 7 harmonic
is suppressed by 65.3% relative to the fundamental frequency.
B-7. What coil pitch could be used to completely eliminate the seventh-harmonic component of voltage in ac
machine armature (stator)? What is the minimum number of slots needed on an eight-pole winding to
exactly achieve this pitch? What would this pitch do to the fifth-harmonic component of voltage?
SOLUTION To totally eliminate the seventh harmonic of voltage in an ac machine armature, the pitch factor
for that harmonic must be zero.
7
k  0  sin
p
2
7
   180 n , n = 0, 1, 2, …
2
2  180 n
 
7
In order to maximize the fundamental voltage while canceling out the seventh harmonic, we pick the
value of n that makes  as nearly 180 as possible. If n = 3, then  = 154.3, and the pitch factor for the
fundamental frequency would be
154 3 . 
k  sin  . 0 975
p
2
This pitch corresponds to a ratio of 6/7. For a two-pole machine, a ratio of 6/7 could be implemented
with a total of 14 slots. If that ratio is desired in an 8-pole machine, then 56 slots would be needed.

The fifth harmonic would be suppressed by this winding as follows:
154 5 3 .  
k  sin  . 0 434
p
2
B-8. A 13.8-kV Y-connected 60-Hz 12-pole three-phase synchronous generator has 180 stator slots with a
double-layer winding and eight turns per coil. The coil pitch on the stator is 12 slots. The conductors
from all phase belts (or groups) in a given phase are connected in series.
(a) What flux per pole would be required to give a no-load terminal (line) voltage of 13.8 kV?
(b) What is this machine’s winding factor k w ?

SOLUTION

(a) The stator pitch is 12/15 = 4/5, so   144 , and
144
k  sin  . 0 951
p
2
Each phase belt consists of (180 slots)/(12 poles)(6) = 2.5 slots per phase group. The slot pitch is 2
mechanical degrees or 24 electrical degrees. The corresponding distribution factor is
 n   5 . 2  24
sin sin
k d  2   2 24  . 0 962
n sin 2 .5 sin
2 2

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