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Assume that a 3 phase symmetrical short circuit occurs at the terminals of a synchronous machine working at no load and constant speeed. The machine is characterised by a field winding fed with a DC current and no damper windings. Neglect saturation.

It is possible to obtain the following equivalent circuit for the moment immediately after the short circuit and the equivalent reactance (neglecting resistive components) is the transient reactance to be used for short circuit peak current calculation.

schematic

simulate this circuit – Schematic created using CircuitLab

where Xa is the stator leakage reactance, Xr the reaction reactance and Xc the field winding leakage reactance.

Why does this equivalent circuit holds? My lecture notes say that the total flux linked with the field winding is a state variable and therefore is conserved right before (t=0-) and after (t=0+) the short circuit. Due to the short circuit, a current in the armature winding arises, therefore the field winding current increases to keep the flux constant.

Mainly (but not exclusively), what is not clear at all in my mind is:

  1. If the flux is a state variable in this case, then the current should not change at t=0+. In other words, i(t=0+)=0. So what is the point of saying that both the armature and field winding current change? They must not change at t=0+.

Almost all the texts I read just explain what the transient and subtransient reactances are needed for but they do not explain how they can be derived, i.e. why this equivalent circuit holds.

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