Network observability: a factorization path formulation in equality-constrained state estimation

A factorization path approach for network observability in equality-constrained state estimation is presented. The factorization path formulation of observability applied to the conventional normal equations (NE), are extended to the hybrid approach of state estimation. Many of the desired features of the observability for NE are preserved. The constraints are treated in a way that allows the triangular factorization to proceed as in the positive-definite manner. No block partitioned formulation is required, as well as no pairing of equations with state variables. In case there exist observable subnetworks, obtained from the factorization of the quadratic part of the gain matrix, the constraint equations relating variables of the same island are incorporated into the estimation process. The others constraints otherwise will be incorporated into the estimation if they relate, in a sequential way, variables of a group of islands typing them all together in the same island. The others constraints will be discardable measurements in the state estimation sense. The algorithm as developed does not require the solving of any algebraic equations. Representative networks were tested in order to show the aforementioned properties and advantages of the algorithm.