Distribution factor is also known as the breadth factor or winding factor. The distribution factor is concerned with the winding type, nature and the induced e.m.f. of the alternator. If the coil sides of any one phase under one pole are concentrated in one slot, the total e.m.f. induced will be equal to the arithmetic sum of the e.m.f. induced in all the coils of one phase under one pole. But in order to obtain a sinusoidal wave of alternating e.m.f., the coils are spread into a number of slots under each pole forming a polar group in Fig. 17.6. In what case the resultant e.m.f. will not be the arithmetic sum of the individual coil side e.m.f. but it will be the vector sum of the e.m.f.s induced in different slots under one pole as shown in Fig. 17.7.
Fig. 17.7 Distribution factor.
Hence the distribution factor is defined as the ratio of the vector sum of the e.m.f. induced in all the coils under one pole to the arithmetic sum of the induced e.m.f. if the winding would have been in one slot.
kd = (Vector sum of the c. m, f, s in all the coils under one pole)/(Arithmetic sum of induced e.m.f. if the winding would have been in one slot)
Let there be
n = Number Of slots per pole per phase.
E = E.m.f. induced in each coil side.
α = Angular displacement between the adjacent slots
Obviously
Here
and
Substituting we have,