Extensions and singularities in compensated network solution applicable to security monitoring

Compensation methods are computationally simple methods of quickly finding changes to an existing nodal-voltage solution of a linear network when changes are made to the network topology or parameters [1]. This paper investigates the efficient detection of `singular¿¿ networks and computational instabilities, which can occur during a compensation process, in order to prevent physical maloperations and the propagation of computation errors. These singular networks include those which have no solution, multiple solutions or an island (totally disconnected subnetwork). Efficient methods are given for the detection and identification of an island, for continuing the compensation process both in the main network and in the island, and for reconnecting the main network to the island so that compensation methods can continue as usual for the reconnected network. Extensions of the method efficiently deal with the removal of a short circuit of a branch (opening a switch), for which case the standard method always fails because of the singularity of the nodal impedance matrix when there is a short circuit.