Synchronous Reactance and Impedance

 The sum of fictitious armature reaction reactance accounted for considering armature reaction effect and the leakage reactance of the armature called synchronous reactance of the alternator demoted as X_s.

So          X_s = X_L + X_ar   Ω/ph  

       As both X_L and X_ar   are ohmic values per phase, synchronous reactance is also specified as ohms per phase.

       Now from this, it is possible to define an impedance of the armature winding. Such an impedance obtained by combining per phase values of synchronous reactance and armature resistance is called synchronous impedance of the alternator denoted as Z_s.

So         Z_s = R_a + j X_s   Ω/ph  

And       | Z_s | = √ (R_a² + j (Xs)² )

        For getting a standard frequency, alternator is to be driven at synchronous speed. So word synchronous used in specifying the reactance and impedance is referred to the working speed of the alternator. Generally impedance of the winding is constant but in case of alternator, synchronous reactance depends on the load and its power factor condition, hence synchronous impedance also varies with the load and its power factor conditions.