Let there be
Φ = Useful flux/pole in Wb
Z = Number of conductor per phase
f = Frequency of induced e.m.f. in c/s
P = Number of poles
N = Speed in r.p.m.
As we know that e.m.f. induced is directly proportional to the rate of change of flux, so the flux cut in one revolution
= Total flux / Time taken
The speed is N r.p.m. so the time taken for one revolution is sec, so the e.m.f. induced per conductor
Obviously
Substituting in the equation, we have, the average e..f. induced
If there are Z conductors per phase then the e.m.f. induced per phase
The r.m.s. value of e.m,f. induced per phase
The winding done, is not always full pitched winding but the fractional pitched winding i.e., long pitch or short pitch windings are also used. The conductors are also concentrated in one slot instead of being distributed in the slots under one pole. Hence two more factors comes into picture the distribution factor (kd) and coil span factor
Now the e.m.f. induced per phase,
Where k the form factor 1.11, k d the distribution factor and
k the coll span factor, : flux in Wb, Zph conductors per phase,
f: frequency in c/s.
The e.m.f. for a single phase alternator is
for three phase alternator.
Eph volts
and as we know that EL Eph • (in star)
volts
Example. Calculate the e.m.f induced (line voltage) in a 3Φ, 8 pole star connected alternator. The Stator has 160 slots with six conductor per slot. Coil span factor being unity and kd 0.85. The speed is 750 r.p.m. and is 19m Wb.
Solution. The frequency of induced e.m.f.
Here coil span factor I and k d
E.m.f. being in star