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Synchronous Generator and Alternator Formulas & Equations

Alternator and Synchronous Generator Formulas & Equations

The following synchronous generator & alternator formulas and equations can be used to design, simplify, and analyze the basic AC generators circuits to determine the generated voltage and EMF, speed & frequency, efficiency, voltage & current, generated power and losses etc.

Synchronous Generator and Alternator Formulas & Equations

EMF Equation of Synchronous Generator

RMS value of generated EMF per phase

VRMS = 1.11 x 4fΦT

VRMS = 4.44fΦT Volts

Actual generated voltage per phase

VPH = 4.44 Kc Kd f ΦTPH

VPH = 4.44 Kf Kc Kd f ΦT Volts


  • V = Generated voltage per phase
  • KC = Pitch Factor or Coil Span Factor
  • KD = Distribution Factor
  • Kf = Form Factor
  • T = Number of turns per Phase
  • f = Frequency

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Output Electrical Frequency & Speed:

Output Electrical frequency of synchronous generator


  • f = Electrical frequency
  • Nr = speed of rotor in RPM
  • P = Number of poles

Voltage Generated:

E= KΦaNs


  • K = constant representing the construction of machine
  • Φa = magnetic Flux per pole of the rotor
  • N= synchronous speed of the rotor

Total Phase Voltage:

VΦ = Ea – jXsIa – RaIa


  • Xs = Synchronous reactance of machine
  • Ia = Armature current
  • Ra = Armature resistance

Three Phase Terminal Voltage:

Three Phase Terminal voltage of synchronous generator

Power of Synchronous Generator:

Power of synchronous generator


  • Tapp = Torque applied
  • Tind = Torque induced in rotor
  • ωr = mechanical speed of rotor

Voltage Regulation:

Voltage Regulation of synchronous generator


  • Vnl ­­= Voltage at no load
  • Vfl = Voltage at full load


η = (POUT / PIN) * 100%

PIN = POUT + PCu + PIron + P­Mech ­+ PStray


  • η = Generator effeminacy
  • PIN = Input power
  • POUT = Output power
  • Cu + Iron + Mech + Stray = copper, iron, mechanical & stray losses in a generator.

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