In the paper it is verified heuristically and experimentally (via simulation) that instability in power systems due to a fault occurs when one machine or a group of machines, called the critical group, loses synchronism with the remaining machines. Using energy functions associated with a critical group (rather than system-wide energy functions), transient stability results which are less conservative than other existing results, have recently been obtained.
The multimachine power system is represented by a special class of Lagrange’s equations. Specifically, dynamic systems with n degrees of freedom are considered. Some general stability results are established by means of La Salle’s invariance principle and of the notion of partial stability. Next, the paper shows that these stability results can be used to establish analytically the existence and the identity of the critical group of machines in a power system due to a given fault. Furthermore, it also shows that stability results can be used to obtain an estimate of the domain of attraction of an asymptotically stable equilibrium of a power system. The results of the presented paper can potentially be used on-line to determine which machines belong to a critical group, and to use this information for corrective action.