EMF Equation of a Synchronous Generator or Alternator

     We know that in a synchronous generator or alternator when the conductor of the rotor cuts the alternating magnetic flux lines produced by the stator or field winding an EMF will induced in the rotor conductor ( according to the faraday's law  ). Eventually this emf circulates an currents the rotor conductors. Let us see the expression for induced emf in the rotor conductors.

E.M.F Equation :

Let,

    Z_ph  =  Number of conductors in series / phase

             =  2 T, where T is the number of turns / phase

      P  =  Number of poles

      ϕ  =  Useful flux per pole in weber

      f  =  Frequency of the induced emf equal to NP / 120 Hz

      N  =  Rotational speed in rpm

  K_c or K_p  =  Pitch or chrding or coil span factor 

                      =  Cos α/2

  K_d or K_b = Distribution factor / breadth factor

  K_f = Form factor = 1.11 for sinusoidal emf.

Total flux cut to complete one revolution = Pϕ Wb

Time taken to complete one revolution = 60 / N sec

     According to faraday's law of electromagnetic induction average emf induced / conductor 

Average emf induced / phase = 2 f ϕ Z_ph = 4 f ϕ T volt

RMS value of emf / phase = Average value of emf / phase * Form factor

= 1.11 × 4 f ϕ T

= 4.44 f ϕ T volt

     If pitch factor K_c and distribution factor K_d  are considered then the actual emf induced will reduce.

Actually induced emf / ph  =  4.44 K_c K_d f ϕ T volt 

E_ph = 4 K_f K_c K_d f ϕ T volt