Reducing cluster size for computing remedial adjustments for voltage and loading violations on the power system

A technique was earlier proposed by the authors [1], [2] for solving sectional outbreaks of voltage and overload violations on large electric power transmission systems by finding relatively small size clusters of controls and violated as well as nonviolated network elements to which they react sensitively. Since the clusters are as much as two orders of magnitude smaller than the entire system, immense savings of computation are possible. Unfortunately the size of the clusters can not be well regulated a priori so that there is a possibility for oversize clusters. This paper introduces an effective algorithm for splitting up such undesirably large clusters by inactivating a few well chosen controls. It was necessary to develop some new results in graph theory to develop the new algorithm.