Electrical Power Systems

90 Electrical Power Systems
ig. 4.8: Schematic representation of synchronous machine.
4.7 SIMPLIIED REPRESENTATION O SYNCHRONOUS
MACHINE OR TRANSIENT ANALYSIS
or steady state operation, the synchronous generator was represented with a constant emf
behind a synchronous reactance x s. or salient pole machine, because of the nonuniformity of
the air gap, it was modeled with direct axis reactance x d and the quadrature axis reactance x q.
Under short circuit conditions, the circuit resistance is much smaller than the reactance and
hence the stator current lags nearly 90º behind the driving voltage and the armature reaction
mmf is centered almost on the direct axis. Therefore, under short circuit conditions, the
effective reactance of the machine may be assumed only along the direct axis.
At the instant, prior to short circuit condition, there must be some flux on the direct axis
linking both the stator and rotor, due to rotor mmf only if the machine on open circuit or due
to the resultant of rotor and stator mmf, if some stator current is flowing. Under short circuit
condition, there will be sudden increase of stator current and the flux linking the stator and
rotor cannot change immediately due to eddy currents flowing in the rotor and damper circuits,
which oppose this change. The reactance of armature reaction is negligible because stator mmf
is unable at first to establish any armature reaction and value of initial reactance is same as the
leakage reactance when the eddy current in the damper circuit and eventually in the field
circuit decays, the armature reaction will be fully established.
or the purpose of explanation, imagine that the field and damper windings are the
secondaries of a transformer where primary is the armature winding. Under normal steady
state operations there is no transformer action between stator and rotor windings as the
resultant field produced by both the stator and rotor revolve with the same synchronous speed.
During short circuit conditions, rotor speed is not the same as that of the revolving field
produced by stator windings resulting in the transformer action. Therefore, damper and field
circuits resemble much more nearly as short-circuited secondaries. The equivalent circuit for
this condition is shown in ig. 4.9 and equivalent reactance is known as direct axis subtransient
reactance.