 # 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. ### 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

Where:

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

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### Output Electrical Frequency & Speed: Where

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

### Voltage Generated:

E= KΦaNs

Where

• 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

Where

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

#### Three Phase Terminal Voltage: ### Power of Synchronous Generator: Where

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

### Voltage Regulation: Where

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

### Efficiency:

η = (POUT / PIN) * 100%

PIN = POUT + PCu + PIron + P­Mech ­+ PStray

Where:

• 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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