Answer MET Question 53
Question: Explain distribution factor and pitch factor for alternator windings. Answer: Distribution or breadth or winding factor
When
the coils comprising a phase of the winging are distributed in two or
more slots per pole, the emfs in the adjacent coils will be out of phase
with respect to one another and their resultant will be less than their
algebric sum. The ratio of the vactor sum of the emfs induced in all
the coils distributed in a number of slots under one pole to arithmatic
sum of the emfs induced (or to the resultant of the emfs induced in all
the coils concentrated in one slot under one pole) is known as
distributed factor Kd.
$\displaystyle \small \mathrm{K_d = \frac{emf\ induced\ in\ a\ distributed\ winding}{emf\ induced\ if\ the\ winding\ would\ have\ been\ concentrated} }$
$\displaystyle \small \mathrm{K_d = \frac{Vector\ sum}{arithmatic\ sum} }$
The distribution factor is always less than unity
let, n= number of slots/pole
q = number of slots/pole/phase
β = angular displacement between the slots = $\displaystyle \small \mathrm{ \frac{180^o}{n} }$
Then distribution factor,
$\displaystyle \small \mathrm{K_d =\frac{sin(\frac{q\beta }{2})}{q\times sin\frac{\beta }{2}} }$
qβ is also known as the phase spreader and is expressed in electrical radians.
$\displaystyle \small \mathrm{K_d = \frac{emf\ induced\ in\ a\ distributed\ winding}{emf\ induced\ if\ the\ winding\ would\ have\ been\ concentrated} }$
$\displaystyle \small \mathrm{K_d = \frac{Vector\ sum}{arithmatic\ sum} }$
The distribution factor is always less than unity
let, n= number of slots/pole
q = number of slots/pole/phase
β = angular displacement between the slots = $\displaystyle \small \mathrm{ \frac{180^o}{n} }$
Then distribution factor,
$\displaystyle \small \mathrm{K_d =\frac{sin(\frac{q\beta }{2})}{q\times sin\frac{\beta }{2}} }$
qβ is also known as the phase spreader and is expressed in electrical radians.
Value of the distribution factor for nth harmonics is,
$\displaystyle \small \mathrm{K_d =\frac{sin(\frac{qn\beta }{2})}{q\times sin\frac{n\beta }{2}} }$
$\displaystyle \small \mathrm{K_d =\frac{sin(\frac{qn\beta }{2})}{q\times sin\frac{n\beta }{2}} }$
In a full pitch coil, the emfs in the two coil sides are in phase and therefore the coil emf is twice the emf of each coil side. In a short pitch coil the emfs of the two coil sides are not in phase and must be added vectorially to give the coil emf. The factor by which the emf per coil is reduced, because of the pitch being less, is known as pitch factor (or coil span factor). Thus,
$\displaystyle \small \mathrm{K_p =\frac{Vector\ or\ Phasor\ sum\ of\ induced\ emfs\ per\ coil}{Arithmetic\ sum\ of\ the\ induced\ emfs\ per\ coil} }$
It is always less than unity
Pitch factor can be caluated by using the relation,
$\displaystyle \small \mathrm{K_p = cos\frac{\alpha }{2} }$
where α is angle by which coil falls short pitched.
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