Synchronous, Stepper and AC Motors Formulas and Equations
AC Machine Formulas & Equations for Stepper and Synchronous Motors
Following are the useful equations and AC motors formulas while designing and analyzing synchronous motors, stepper motors and other related AC machines.
Synchronous Machine:
Speed of Synchronous Machine:
Synchronous machine are designed to be operated at synchronous speed, which is given by:
Where
- Ns is the synchronous speed
- f is the line voltage frequency
- P is the number of poles in a machine
Synchronous Motor:
Voltage Equation of Synchronous Motor:
V = Eb + Ia(Ra + jXs)
Where
- V = voltage applied
- Eb = Back emf
- Ia = Armature current
- Ra = Armature resistance
- Xs = synchronous reactance
Resultant Voltage:
The difference between the voltage applied V and back EMF is known as resultant voltage ER
ER = V – Eb
ER = Ia(Ra + jXs)
Internal Angle:
It is the angle by which the armature current Ia lags behind the resultant voltage in armature ER, and it is given by;
Back EMF Generated:
Eb = KaφaNs
Where
- Ka = constant of the armature winding
- φa = magnetic Flux per pole of the rotor
- Ns = synchronous speed of the rotor
Related Posts:
- Single-Phase Induction Motor – Construction, Working, Types & Applications
- Three-Phase Induction Motor – Construction, Working, Types & Applications
Different Excitations:
- Eb = V Normal Excitation Lagging Power Factor
- Eb < V Under-Excitation Lagging Power Factor
- Eb > V Over- Excitation Leading Power Factor
Input Power:
The input power of synchronous motor is given by:
Where
Φ is the angle between V and Ia
Mechanical Power In Rotor:
Where
- α is the load angle between Eb & V
- Φ is the angle between V & Ia
- Tg is gross torque produced
- Ns is the synchronous speed
Related Posts:
- Servo Motor – Types, Construction, Working, Controlling & Applications
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Stepper Motors Formulas
Step Angle:
Where
- β = step angle, the angle of rotation of the shaft with each pulse.
- Ns = number of stator poles or teeth
- Nr = number of rotor poles or teeth
Resolution Of Stepper Motor:
The number of steps required to complete one revolution, its given by;
The higher the resolution, the higher the accuracy of the stepper motor.
Motor Speed:
Where
- n = motor speed in revolution per second
- f = stepping pulse frequency
Related Formulas and Equations Posts:
- Induction Motor & Linear Induction Motors Formulas & Equations
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- 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
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