A 500-kVa, 3.3-kV, 3-phase star-connected alternator is found to give a short-circuit current of 110√3 A at normal field current. Estimate the magnitude of synchronous reactance if the effective winding resistance per phase is 1 ohm.
A 500-kVa, 3.3-kV, 3-phase star-connected alternator is found to give a short-circuit current of 110√3 A at normal field current. Estimate the magnitude of synchronous reactance if the effective winding resistance per phase is 1 ohm.
Right Answer is:
Xs = √99Ω
SOLUTION
Per phase Synchronous impedance is given by
Zs = Voc/Isc
Where,
Zs = Per phase Synchronous impedance
Voc = Per phase Open circuit voltage of the alternator
Isc = Per phase Short circuit current of the alternator
Given:
Rating of alternator = 500 KVA
Terminal voltage of alternator Vt L-L = 3.3 KV = 3300 V
Short circuit current Isc = 110√3 A
Winding Resistance = 1 Ω
Voc = 3300/√3 V
Isc = 110√3 A ( assume star connected)
Therefore,
${Z_s} = \dfrac{{\dfrac{{3300}}{{\surd 3}}}}{{110\surd 3}}$ = 10 Ω
$\begin{array}{l} {Z_s} = \sqrt {{R^2} + X_s^2} \\ \\ 10 = \sqrt {{1^2} + X_s^2} \end{array}$
100 = 1 + Xs2
Xs = √99Ω