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,

• Z_ph = Number of conductors in series per phase = 2T (T = Number of turns per 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 is given by,

= P Φ weber

Time taken to complete one revolution is,

= 60/N sec

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

Average emf induced per phase is given by,

= 2 f Φ Z_ph volts

= 4 f Φ T volts

RMS value of emf induced per phase is given by,

= Average value of emf per 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 per phase is given by,

= 4.44 K_c K_d f Φ T volts

E_ph = 4 K_f K_c K_d f Φ T volts