Synchronous Generator and Alternator Formulas & Equations

Electrical Technology

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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.

Table of Contents

EMF Equation of Synchronous Generator

RMS value of generated EMF per phase

V_RMS = 1.11 x 4fΦT

V_RMS = 4.44fΦT Volts

Actual generated voltage per phase

V_PH = 4.44 K_c K_df ΦT_PH

V_PH = 4.44 K_fK_c K_df ΦT Volts

Where:

V = Generated voltage per phase
K_C = Pitch Factor or Coil Span Factor
K_D = Distribution Factor
K_f = Form Factor
T = Number of turns per Phase
f = Frequency

Output Electrical Frequency & Speed:

Where

f_e = Electrical frequency
N_r = speed of rotor in RPM
P = Number of poles

Voltage Generated:

E_a= KΦ_aN_s

Where

K = constant representing the construction of machine
_Φa= magnetic Flux per pole of the rotor
N_s= synchronous speed of the rotor

Total Phase Voltage:

V_Φ = E_a – jX_sI_a – R_aI_a

Where

X_s = Synchronous reactance of machine
I_a = Armature current
R_a = Armature resistance

Three Phase Terminal Voltage:

Power of Synchronous Generator:

Where

T_app = Torque applied
T_ind = Torque induced in rotor
ω_r = mechanical speed of rotor

Voltage Regulation:

Where

V_nl= Voltage at no load
V_fl = Voltage at full load

Efficiency:

η = (P_OUT / P_IN) * 100%

P_IN = P_OUT + P_Cu + P_Iron + P_Mech+ P_Stray

Where:

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

Synchronous Generator and Alternator Formulas & Equations