E.M.F. Equation of an Alternator
E.M.F. Equation of an Alternator:
Let Z = No. of conductors or coil sides in series/ phase
= 2T - where T is the no. of coils or turns per phase
(One turn or coil has two sides)
P = No. of poles
F = Frequency of induced e.m.f in Hz
Φ = flux/pole in webers
In one revolution of the rotor (i.e. in 60/N second) each stator conductor is cut by a flux of ΦP webers.
Therefore, dΦ = ΦP and dt = 60/N second
Average e.m.f. induced per conductor =
Now, we know that f = PN/120 or N = 120 f/P
Substituting this value of N above, we get
Average e.m.f. per conductor
If there are Z conductors in series/phase, then Average e.m.f./phase = 2f ΦZ volt = 4 fΦT volt
R.M.S. value of e.m.f./phase = 1.11 × 4f ΦT = 4.44f ΦT volt
This would have been the actual value of the induced voltage if all the coils in a phase were (i) full-pitched and (ii) concentrated or bunched in one slot (instead of being distributed in several slots under poles). But this not being so, the actually available voltage is reduced in the ratio of these two factors.
Therefore, actually available voltage/phase = 4.44 kc kd f Φ T = 4 kf kckd f Φ T volt.
If the alternator is star-connected (as is usually the case) then the line voltage is 3 times the phase voltage (as found from the above formula).