Generators
are the active elements in the network.They
are connected by a shaft to turbines in any type of power plants - to have
the same speed and the same torque.
Its
speed must be constant and not to vary with load variation. It can be
determined by the law:
W=(120 f / P)
where:
W
(r.p.m) : revolution per minute.
P (poles) : number of generator poles.
f
(Hz) : frequency .
Modeling of Synchronous Generator :
The model of
synchronous generator is shown in the following figure:
where:
Vt : Terminal
voltage.
Eeff : Effective emf.
d : Power angle
(rotor angle)
Ra : Armature resistance.
Xs : Synchronous
reactance
Xa : Armature
reactance
XL : Leakage
reactance.
Ia : Armature current
Cos j : Power factor.
Noting that:
1 - Xs
>> Ra , (Xs / Ra > 10)
2 - Xs = Xa + XL
3
- Emf. is always constant (neglecting any change in If).
4
- In some times, (Ra) is neglected w.r.t (Xs).
Mathematical model:
The
mathematical model of synchronous generator is indicated in the following
equation :
- Where f is the angle between the voltage and the current (the
power factor angle).
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