A hybrid method for observability analysis using a reduced network graph theory

This paper presents a hybrid topological-numerical approach for observability analysis in power system state estimation. By partitioning the network in observable areas, a reduced network is formed, where each area is represented by a supernode and each line between areas as a branch. We select as areas the flow islands, being the maximal connected components of flow-measured branches. Only boundary nodes and injections at flow islands are retained for numerical processing. Observability testing and identification of maximal observable islands are accomplished by numerical processing on the echelon form of a rectangular test matrix, which is based on the reduced network graph properties. The method uses a noniterative scheme to select a minimal set of nonredundant pseudo measurements which make an unobservable network barely observable. The existing numerical methods are based on the number of zero pivots obtained during the triangular factorization of the gain matrix. Due to round-off errors, the zero pivots may be misclassified. In the proposed method, the nonzero values of the processed test matrix are + 1 or - 1, resulting in better numerical conditioning and accurate detection of zero pivots. The test matrix is generally sparser than the reduced network gain matrix. As a consequence, the proposed method is faster either for observability testing or multiple measurement placement. Several test results are presented.