EMF Equation of a Synchronous Generator or Alternator


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


EMF Equation of Synchronous Generator :

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 K p = Pitch or chrding or coil span factor = Cos α/2
  • Kd or Kb = Distribution factor / breadth factor
    EMF Equation of a Synchronous Genertor or Alternator
  • Kf = Form factor = 1.11 for sinusoidal emf.



Total flux cut to complete one revolution = P φ 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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