Equation of Induced EMF - Synchronous Generator or Alternator

Equation of Induced EMF

Let          Φ = Flux per pole, in Wb

P = Number of poles

N_s = Synchronous speed in r.p.m.

f = Frequency of induced e.m.f. in Hz

Assume full pitch winding for simplicity i.e. this conductor is connected to a conductor which is 180^o electrical apart. So there two e.m.f.s will try to set up a current in the same direction i.e. the two e.m.f. are helping each other and hence resultant e.m.f. per turn will be twice the e.m.f. induced in a conductor.

.^.. E.m.f. per turn = 2 x (e.m.f. per conductor)

= 2 x (2 f Φ)

= 4 f Φ volts

Let T_ph be the total number of turn per phase connected in series. Assuming concentrated winding, we can say that all are placed in single slot per pole per phase. So induced e.m.f.s in all turns will be in phase as placed in single slot. Hence net e.m.f. per phase will be algebraic sum of the e.m.f.s per turn.

Average E_ph = T_ph x (Average e.m.f. per turn)

Average Eph = T_ph x 4 f Φ

But in a.c. circuits R.M.S. value of an alternating quantity is used for the analysis. The form factor is 1.11 of sinusoidal e.m.f.

K_f = (R.M.S.)/Average = 1.11     ......... for sinusoidal

.^..  R.M.S. value of E_ph   = K x Average value