1.3 Short Circuit Phenomenon
Consider a two pole elementary single phase alternator with concentrated stator winding as shown in Fig. 4.
Fig. 4 |
The corresponding waveforms for stator and rotor currents are shown in the Fig. 5.
Fig. 2 |
Let short circuit occurs at position of rotor shown in Fig. 4(a)
when there are no stator linkages. After 1/4 Rev as shown Fig. 4(b), it
tends to establish full normal linkage in stator winding. The stator
opposes this by a current in the shown direction as to force the flux in
the leakage path. The rotor current must increase to maintain its flux
constant. It reduces to normal at position (c) where stator current is
again reduces to zero. The waveform of stator current and field current
shown in the Fig. 5. changes totally if the position of rotor at the
instant of short circuit is different. Thus the short circuit current is
a function of of relative position of stator and rotor.
Using the theorem of constant linkages a three phase short
circuit can also be studied. After the instant of short circuit the flux
linking with the stator will not change. A stationary image of main
pole flux is produced in the stator. Thus a d.c. component of current is
carried by each phase. The magnitude of d.c. component of current is
different for each phase as the instant on the voltage wave at which
short circuit occurs is different for each phase. The rotor tries to
maintain its own poles. The rotor current is normal each time when rotor
poles occupy the position same as that during short circuit and the
current in the stator will be zero if the machine is previously
unloaded. After one half cycle from this position the stator and rotor
poles are again coincident but the poles are opposite. To maintain the
flux linkages constant, the current in rotor reaches to its peak value.
The stationary field produced by poles on the stator induces a
normal frequency emf in the rotor. Thus the rotor current is fluctuating
whose resultant a.c. component develops fundamental frequency flux
which rotates and again produces in the stator winding double frequency
or second harmonic currents. Thus the waveform of transient current
consists of fundamental, a.c. and second harmonic components of
currents.
Thus whenever short circuit occurs in three phase generator then
the stator currents are distorted from pure sine wave and are similar to
those obtained when an alternating voltage is suddenly applied to
series R-L circuit.
1.4 Stator Currents during Short Circuit
If a generator having negligible resistance, excited and running
on no load is suddenly undergoing short circuit at its terminals, then
the emf induced in the stator winding is used to circulate short circuit
current through it. Initially the reactance to be taken into
consideration is not the synchronous reactance of the machine. The
effect of armature flux (reaction) is to reduce the main field flux. But
the flux linking with stator and rotor can not change instantaneously
because of the induction associated with the windings. Thus at the short
circuit instant, the armature reaction is ineffective. It will not
reduce the main flux. Thus the synchronous reactance will not come into
picture at the moment of short circuit. The only limiting factor for
short circuit current at this instant is the leakage reactance.
After some time from the instant of short circuit, the armature
reaction slowly shows its effect and the alternator then reaches to
steady state. Thus the short circuit current reaches to high value for
some time and then settles to steady value.
It can be seen that during the initial instant of short circuit
is dependent on induced emf and leakage reactance which is similar to
the case which we have considered previously of voltage source suddenly
applied to series R-L circuit. The instant in the cycle at which short
occurs also affects the short circuit current. Near zero e.m.f. (or
voltage) it has doubling effect. The expressions that we have derived
are applicable only during initial conditions of short circuit as the
induced emf also reduces after some tome because of increased armature
reaction.
The short circuit currents in the three phases during short circuit are as shown in the Fig. 6
Fig. 6 Short circuit current waveforms in the three phases of alternator |
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