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

V_RMS = 1.11 x 4fΦT

V_RMS = 4.44fΦT Volts

Actual generated voltage per phase

V_PH = 4.44 K_c K_d f ΦT_PH

V_PH = 4.44 K_f K_c K_d f 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

Related Posts

• EMF Equation of an Alternator & Synchronous Generator
• Equation of a DC Motor
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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.

Related Formulas and Equations Posts:

• DC Generator Formulas and Equations
• Power, Voltage and EMF Equation of a DC Motor – Formulas
• Synchronous, Stepper and AC Motors Formulas and Equations
• Induction Motor & Linear Induction Motors Formulas & Equations
• Transformer Formulas and Equations
• Basic Electrical Engineering Formulas and Equations
• Basic Electrical Quantities Formulas
• Power Formulas in DC and AC Single-Phase & Three-Phase Circuits
• Electrical & Electronics Engineering Formulas & Equations
• Generator and Alternator Symbols