# The Speed Of Rotation On Electric Machines

The Speed Of Rotation On Electric Machines

Synchronous generators are by definition synchronous,  meaning that the electrical frequency produced is locked in or synchronous with the mechanical rate of rotation or the generator.

The rate or rotation of the magnetic field

nsyn = ns = ( 120 * fc ) / p

fc → electrical frequency, in Hz

nsyn → ns → synchronous speed, rpm

p → H of poles

if the speed of rotor n, for synchronous machine

nsyn = ns = nm

The Internal Generated Voltage

The magnitude of the voltage induced in a give stator phase

Ea = 2 * 𝜋 * Nc * ⲫ * f

Ea = K * ⲫ * ⍹

if ⍹  is expressed in electrical radians per second

K = Nc /2

if ⍹ is expressed in mechanical radians per second

K = Nc * p /2

The Equivalent circuit of a synchronous generator

Ea is the internet generates voltage

Vⲫ is the terminal voltage of the generator
There are a number of factors that cause the difference between Ea and Vⲫ

1. The distortion of the air gap magnetic field by the current flowing in the stator, called armature reaction – AR
2. The self inductance of the armature coils
3. The resistance of the armature coils
4. The effect of salient pole rotor shapes

Vⲫ = Ea – jXs*Ia – Ra*Ia

Ra -> winding resistance

Xs -> synchronous reactance

Xs = XAR + XAl

XAR → inductance due to AR

XAl →self inductance

The Speed Of Rotation On Electric Machines