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EMF Equation of a Synchronous Generator

05/27/2025

Synchronous Generator and EMF Equation Derivation
A generator operating at synchronous speed is termed a synchronous generator, which converts mechanical power into electrical energy for grid integration. The derivation of the EMF equation for a synchronous generator is as follows:
Notation:
  • P = number of poles
  • ϕ = flux per pole (Weber)
  • N = rotational speed (revolutions per minute, r.p.m)
  • f = frequency (Hertz)
  • Zph = number of series-connected conductors per phase
  • Tph = number of series-connected turns per phase
  • Kc = coil span factor
  • Kd = distribution factor
Derivation: The flux cut by each conductor in one revolution is Pϕ Weber. The time to complete one revolution is 60​/N seconds. The average EMF induced per conductor is given by:
Average EMF induced per phase will be given by the equation shown below:
Average EMF Equation Assumptions
The derivation of the average EMF equation is based on the following assumptions:
  • Coils exhibit full pitch configuration.
  • All conductors are concentrated within a single stator slot.
The root mean square (RMS) value of the induced EMF per phase is expressed as:Eph = Average Value×Form Factor Thus,
EMF Equation and Winding Factors
Equation (1) above represents the EMF equation of a synchronous generator.
Coil Span Factor (Kc)
The coil span factor is defined as the ratio of the induced EMF in a short-pitched coil to that in an identical full-pitched coil.
Distribution Factor (Kd)
The distribution factor is the ratio of the induced EMF in a distributed coil group (wound across multiple slots) to that in a concentrated coil group (wound in a single slot).
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