Question

Derive an expression for the e.m.f induced in a a.c. generator.

Equation of Induced E.M.F.

Let

Z=No. of conductors or coil sides in series/phase

= 2T— where T is the No. of coils or turns per phase (remember 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

K_d =distribution factor=sinmβ/2/msinβ/2

K_e or K_p=pitch or coil span factor=cosα/2

K_c=form factor=1.l —if e.m.f. is assumed sinusoidal N= rotative speed of the rotor in r.p.m.

In one revolution of the rotor (i.e. in 60/N second) each stator conductor is cut by a flux of ΦP webers.

dΦ=ΦP and dt=60/N second

.*. average e.m.f. induced per conductor = dΦ/ dt = Φ p / 60N = ΦNP / 60 volt

Now we know that f = PN /120 or

N = 120f / P

Substituting this value of N above, we get

Average e.m.f. / phase = 2fΦZ volt = 4fΦT = 4.44fΦT volt.

This would have been the actual value of the voltage induced if all the coils in a phase were (1) full-pitched and (2) 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.

Actually available voltage/phase

= 4.44 K_e K_d f Φ T = 4 K_f K_e K_d 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).