A frequency-domain transient stability criterion for normal contingencies

In a previous paper, a simple frequency-domain stability criterion was proposed for networks near the stability limit subjected to a 3-phase fault with no loss of line. The criterion can be summarized as follows: if a system is stable, the phase angle of the Fourier transform of a network´s transient voltage response exhibits a clockwise polar plot behaviour at all buses (i.e. for increasing frequency); if the system is unstable, it exhibits a counter-clockwise behaviour in at least one location. Though these results are of interest, the criterion would be of greater practical use in mechanizing dynamic security analysis if it could be extended to the types of contingencies actually used in security analysis, namely “normal contingencies”. Normal contingencies are commonly defined as the loss of any element in a power system, either spontaneously or preceded by a fault, and such changes in topology impact post-contingency steady-state voltages in addition to their transient behaviour. The paper shows how such cases can be treated, thereby extending the applicable range of the criterion to normal contingencies