EMF Equation of an Alternator or 3 phase AC Generator

EMF Equation of an Alternator

We know Synchronous Machines generates E.M.F.the amount of EMF generated can be calculated using below simple derivation.

Consider following

Φ= flux per pole in wb

P = Number of poles

Ns = Synchronous speed in rpm

f = frequency of induced emf in Hz

Z = total number of stator conductors

Zph = conductors per phase connected in series

Tph = Number of turns per phase

Assuming concentrated winding, considering one conductor placed in a slot

According to Faraday's Law electromagnetic induction,

The average value of emf induced per conductor in one revolution 

eavg = dΦ /dt

eavg = Change of Flux in one revolution/ Time taken for one revolution

Change of Flux in one revolution = p x Φ
Time taken for one revolution = 60/Ns seconds.
Hence eavg = (p x  Φ  ) / ( 60/Ns) = p x   Φ x Ns / 60
We know f = PNs /120
hence PNs /60 = 2f
Hence eavg = 2   Φ f volts
Hence average emf per turn = 2 x 2 Φ f volts = 4Φf volts
If there are Tph, number of turns per phase connected in series, then average emf induced in Tph turns is

Eph,avg = Tph x eavg = 4 f   Φ Tph volts

Hence RMS value of emf induced E = 1.11 x Eph, avg
= 1.11 x 4  Φ f Tph volts
= 4.44 f  Φ Tph volts

Eph,avg= 4.44 f  Φ Tph volts

This is the general emf equation for the machine having concentrated and full pitched winding.In practice, alternators will have short pitched winding and hence coil span will not be  180^o(degrees), but on or two slots short than the full pitch.

***If we assume effect of 
Kd= Distribution factor
Kc or KP = Cos α/2

Eph,avg= 4.44K_c  K_d f  Φ Tph volts

This is the actual available voltage equation of an alternator per phase.If alternator or AC Generator is Star Connected as usually the case, then the Line Voltage is √3 times the phase voltage.

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