Equation of Induced EMF in Alternator

EQUATION OF INDUCED EMF

Let,

Z_ph = number of conductors or coils sides in series/phase

Z_ph = 2T_ph, where T_p is the number of coils or turns per phase

P = number of poles

f = frequency of induced emf in Hz

φ = flux/pole in webers

K_c or K_p = pitch factor or coil span factor = cos (α/2)

K_f = form factor = 1.11 (If e.m.f is assumed sinusoidal)

N = rotor speed in r.p.m.

For one revolution of the rotor, each stator conductor is cut by a flux of φP webers

dφ = φР

dt = 60/N Second.

Average emf induced per conductor = dφ/dt = φР / (60/N) = φΡΝ / 60

We know that f = PN / 120 (or) N = 120f / P

Substituting this value of N, we get average emf per conductor as

If there are Z_ph conductors in series/phase, then

Average e.m.f / Phase = 2fφ Z_ph volts = 4fφ T_ph volts

RMS value of e.m.f / Phase = 1.11 × 4fφ T_ph = 4.44fφ T_ph Volts.

The above equation is true only if the winding concentrated in one slot. But practically it is not true, as the winding for each phase under each pole is distributed and for such cases k_p and k_d must be considered.

Actually available voltage/phase = 4.44 k_p k_d fφ T_ph Volts

K_p k_d = k_w = winding factor.

If the alternator is star connected, then the line voltage is √3 times the phase voltage.