A numerically stable decomposition based power system state estimation algorithm

This paper proposes a new approach for solving the equality constrained power system state estimation (PSSE) problem. The proposed approach decomposes the linear least squares with the linear equality constraints (LSE) problem encountered at each PSSE iteration into two unconstrained linear least squares (LS) problems. The solution of the LSE problem is the sum of the solutions of the individual LS problems. The proposed approach avoids giving large weights to equality constraints and hence results in a more stable formulation, that can be solved within the framework of unconstrained least squares. Based on the proposed decomposition, a Givens rotations based PSSE algorithm is proposed and developed It is shown that the proposed implementation is numerically more stable than the conventional NE, normal equations with constraints (NE/C), Givens rotations and Hachtel's methods for PSSE. The first LS problem to be solved in the proposed implementation is identical to that encountered in conventional constrained weighting approaches like NE approach and Givens rotations approach, except for the fact that equality constraints (Zero injection constraints) are not assigned large weights. The resulting error due to the lack of large weights for equality constraints is corrected by the solution obtained from the second LS problem. Simulation results on 23, 89 and 319 node systems show the desirable stability characteristics of the proposed implementation in comparison with NE, Givens rotations, NE/C, Hachtel's approach and NE based decomposition (DNE). The proposed approach has better speed characteristics compared to NE/C and Hachtel's approaches. (C) 1997 Elsevier Science Ltd.