Short Circuit of a Synchronous Machine on No Load | Power Systems - Electrical Engineering (EE) PDF Download

Short Circuit of a Synchronous Machine on No Load
Under steady state short circuit conditions, the armature reaction of a synchronous generator produces a demagnetizing flux. In terms of a circuit this effect is modelled as a reactance X_a in series with the induced emf. This reactance when combined with the leakage reactance X_l of the machine is called synchronous reactance X_d (direct axis synchronous reactance in the case of salient pole machines). Armature resistance being small can be neglected. The steady state short circuit model of a Synchronous Machine on No Load is shown in Figure on per phase basis.

Consider now the sudden short circuit (three-phase) of a synchronous generator initially operating under open circuit conditions. The machine undergoes a transient in all the three phase finally ending up in steady state conditions described above.

The circuit breaker must, of course, interrupt the current much before steady conditions are reached. Immediately upon short circuit, the DC off-set currents appear in all the three phases, each with a different magnitude since the point on the voltage wave at which short circuit occurs is different for each phase. These DC off-set currents are accounted for separately on an empirical basis and, therefore, for short circuit studies, we need to concentrate our attention on symmetrical (sinusoidal) short circuit current only.

Immediately in the event of a short circuit, the symmetrical short circuit current is limited only by the leakage reactance of the machine. Since the air gap flux cannot change instantaneously (theorem of constant flux linkages), to counter the demagnetization of the armature short circuit current, currents appear in the field winding as well as in the damper winding in a direction to help the main flux. These currents decay in accordance with the winding time constants.

The time constant of the damper winding which has low leakage inductance is much less than that of the field winding, which has high leakage inductance. Thus during the initial part of the short circuit, the damper and field windings have transformer currents induced in them so that in the circuit model their reactances—X_f of field winding and X_dw of damper winding—appear in parallel with X_a as shown in Figure 1(b). As the damper winding currents are first to die out, X_dw effectively becomes open circuited and at a later stage X_f becomes open circuited. The machine reactance thus changes from the parallel combination of X_a, X_f and X_dw during the initial period of the short circuit to X_a and X_f in parallel (Figure 1(c)) in the middle period of the short circuit, and finally to X_a in steady state (Figure 1(a)). The reactance presented by the machine in the initial period of the short circuit, i.e.
is called the subtransient reactance of the machine. While the reactance effective after the damper winding currents have died out, i.e.
is called the transient reactance of the machine. Of course, the reactance under steady conditions is the synchronous reactance of the machine. Obviously X″_d < X′_d < X_d. The machine thus offers a time-varying reactance which changes from X″_d to X′_d and finally to X_d.

If we examine the oscillogram of the short circuit current of a Synchronous Machine on No Load after the DC off-set currents have been removed from it, we will find the current wave shape as given in Fig. 2(a). The envelope of the current wave shape is plotted in Fig. 2(b). The short circuit current can be divided into three periods—initial subtransient period when the current is large as the machine offers subtransient reactance, the middle transient period where the machine offers transient reactance, and finally the steady state period when the machine offers synchronous reactance.