Electrical Power Systems

Synchronous Machine: Steady State and Transient Operations 91
ig. 4.9: Equivalent circuit for the subtransient condition.
Subtransient reactance x d² can be given as,
xd ² = xl
HG
a f dKJ
-1
1 1 1
+ + +
x x x
I
...(4.32)
The direct axis subtransient reactance x d ² is only used if the initial current is important, for
example to determine the short-circuit rating of circuit breaker.
The short-circuit subtransient time constant of damper winding is very small (about 0.03 to
0.04 seeads) and this component of current decays very quickly.
Therefore, one can ignore the branch of the equivalent circuit which takes into account the
damper winding. Equivalent circuit is shown in ig. 4.10.
ig. 4.10: Equivalent circuit for the transient condition.
The equivalent reactance of ig. 4.10 is known as short circuit transient reactance and is
given by
x d ¢ = xl
HG
a fKJ
-1
1 1
+ +
x x
inally, when the disturbance is over, there will
not be any transformer action between the stater and
roter windings and the equivalent circuit is shown in
ig. 4.11.
The equivalent reactance of ig. 4.11 is known as
direct axis synchronous reactance and is given by
x d = x l + x a
I
ig. 4.11: Equivalent circuit for
the steady-state condition.
...(4.33)
...(4.34)