The actual generated voltage consists of the summation of two component voltages. One of these components voltages is the voltage that would be generated if there were no armature reaction. it is the voltage that would be generated because of only field excitation. This component of the generated voltage is called the excitation voltage, Eexc.

The other component of the generated voltage is called armature reaction voltage , EAR. This is the voltage that must be added to the excitation voltage to take care of the effect of armature reaction upon the generated voltage .

Ea = Eexc + EAR

Since armature reaction results, in a voltage effect in circuit caused bu change in flux by current in the same circuit, its effect is of the nature of an inductive reactance .therefore EAR is equivalent to a voltage of inductive reactance and

EAR = -

*j*XAR Ia
The inductive Reactance XAR is a fictitious reactance which will result in a voltage in armature circuit to account for the effect of armature reaction upon the voltage relations of the armature circuit. Therefore armature reaction voltage can be modelled as in inductor in series with internal generated voltage .

In additionato the effect of armature reaction , the stator winding also has a self inductance and resistance.

Let La = self inductance of stator
winding.

Xa = self reactance of stator winding.

Ra =
armature (stator) resistance.

The terminal voltage V is given by

V = Ea -

*j*XAR Ia -*j*Xa Ia - RaIa
where

RaIa = armature resistance drop

Xa Ia = armature leakage reactance drop

XAR Ia = armature reaction voltage

the armature reaction effect
and the leakage flux effect in the machine are both represented by inductive
reactance . therefore, it is customary to combine them into a single reactance,
is called the synchronous reactance of the machine, Xs.

Xs = Xa + XAR

V =

**Ea**- j*Xs Ia - RaIa*
V =

**Ea**- ( Ra +*j*Xs) Ia**V = Ea - Zs Ia**

**Zs =**Ra +

*j*Xs

**Zs**is called

**synchronous impedance.**

The synchronous Reactance Xs is the fictitious reactance employed to account for voltage effects in the armature circuit produced by the actual armature leakage reactance and by the change in air gap flux caused by the armature reaction.

similarly ,synchronous impedance Zs is a fictitious impedance employed to account for voltage effects in the armature circuit produced by the actual armature resistance, the actual armature leakage reactance, and the change in air gap flux produced by armature reaction.

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