Comparison of different methods for state estimation

Ill-conditioning in the gain matrix of the classical normal-equations-approach for state estimation has created a numerical stability problem for large power systems. Several methods have been proposed to circumvent the problem. A comparative study of five methods, namely, the normal equations method, the orthogonal transformation method, the hybrid method, normal equations with constraints, and Hachtel´s augmented matrix method for state estimation has been conducted. The comparison is made in terms of their (i) numerical stability, (ii) computational efficiency, and (iii) implementation complexity. A theoretical analysis indicates that the orthogonal transformation method is numerically most stable. But the orthogonal transformation method cannot be implemented in the efficient fast decoupled version. It is shown that the hybrid method and Hachtel´s method are both good compromises between numerical stability and computational efficiency