  An analytic approximation for the critical clearing time (CCT) metric is
derived from direct methods for power system stability. The formula has been
designed to incorporate as many features of transient stability analysis as
possible such as different fault locations and different post-fault network
states. The purpose of this metric is to analyse trends in stability (in terms
of CCT) of power systems under the variation of a system parameter. We
demonstrate the performance of this metric to measure stability trends on an
aggregated power network, the so-called two machine infinite bus network, by
varying load parameters in the full bus admittance matrix using numerical
continuation. Our metric is compared to two other expressions for the CCT which
incorporate additional non-linearities present in the model.
