A blocked sparse matrix formulation for the solution of equality-constrained state estimation

A block-partitioned (blocked) sparse formulation for the solution of equality-constrained power system static-state estimation is presented. The blocked structure is formed based on a new formulation of Hachtel's augmented matrix method, which preserves several desired features of the conventional normal equations with equality constraints approach. The proposed formulation treats the constraints by the method of Lagrange multipliers, but allows triangular factorization to proceed in a positive-definite manner. A mixed-size blocked structure is proposed for the internal solution, while a formulation composed exclusively of (2*2) blocks is proposed for the external solution. The method is well suited to the implementation of regulation schemes and limit enforcement, necessary in the state-emission-based external solution. The pairing of equations with state variables in the observable state-estimation solution is tightly linked to the results of a topological observability algorithm.>