A numerical algorithm for observability analysis based on Gram matrix

This paper presents an efficient numerical method for observability analysis based on the triangular factorization of a Gram matrix corresponding to a reduced size Jacobian matrix. The observable islands are identified in a noniterative manner, by performing back substitutions on the triangular factors of a Gram matrix, associated with the flow islands, which are the connected portions of the network formed by the flow-measured branches. The additional measurements for placement are provided by a direct method, using the triangular factors of the Gram matrix associated with the observable islands. Implementation of the proposed method needs little additional effort, since it uses sparse triangular factorization and forward/backward substitution algorithms common to state estimators. The IEEE 14-bus system is used to illustrate the steps of the proposed method.