SHORT CIRCUIT OF A SYNCHRONOUS MACHINE (ON NO-LOAD)

When a fault occurs in a power system network, the current flowing is determined by the internal emfs of the machines in the network, their impedances and the impedances between the machines and the fault.

Figure shown below represents “the short circuit current as a function of time” when a sudden short circuit (three-phase) occurs for a synchronous generator operating under open circuit condition. The machine undergoes a transient in all the three phases finally ending up in steady state condition. The circuit breaker must interrupt the current much before steady state is reached.

The short circuit current sustained in the synchronous generator can be divided into three periods namely:

(i) initial subtransient period (when the current is large and the machine offers subtransient reactance)
(ii) the middle transient period (where the machine offers transient reactance) and
(iii) the steady state period (when the machine offers synchronous reactance).

There are three types of reactances for synchronous machines:

• Synchronous reactance (Xd): When the armature reactance (Xa) is combined with the leakage reactance (Xl) of the machine then, it is called “synchronous reactance (Xd)” (or direct axis synchronous reactance in case of salient pole machine). The steady state short circuit model of a synchronous machine is shown below in fig. (a).

where, Xd=(Xa + Xl)

• Subtransient reactance (X″d): The reactance presented by the machine in the initial period of the short circuit is called “subtransient reactance (Xd)”. During the initial period of the short circuit, the damper and field windings have transformer current’s induced in them so that in the circuit model their reactances – Xf of field winding and Xdw of damper winding appear in parallel with Xa as shown below in fig. (b). Hence, the subtransient reactance using fig. (b) is given by

• Transient reactance (X′d): The reactance effective after the damper winding current have died out is called the transient reactance of the machine ( X′d ).

From below fig. (c), the transient reactance of machine is given by

X′d =Xl + (Xa || Xf )

Using the plot of symmetrical short circuit armature current, the various current during short circuit are given by :