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 induce in the rotor conductor ( according to the faraday's law  ). Eventually, this emf circulates currents the rotor conductors. Let us see the expression for induced emf in the rotor conductors.



E.M.F Equation :


Let,

    Zph  =  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

  Kc or Kp  =  Pitch or chrding or coil span factor 

                      =  Cos α/2

  Kd or Kb = Distribution factor / breadth factor

EMF Equation of a Synchronous Generator or Alternator

  Kf = 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 

EMF Equation of a Synchronous Generator or Alternator

Average emf induced / phase = 2 f ϕ Zph = 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 Kc and distribution factor Kd  are considered then the actual emf induced will reduce.

Actually induced emf / ph  =  4.44 Kc Kd f ϕ T volt 


Eph = 4 Kf Kc Kd f ϕ T volt



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