In this paper we discuss the power of a pivoting transformation introduced by Castillo, Cobo, Jubete, and Pruneda [Orthogonal Sets and Polar Methods in Linear Algebra: Applications to Matrix Calculations, Systems of Equations and Inequalities, and Linear Programming, John Wiley, New York, 1999] and its multiple applications. The meaning of each sequential tableau appearing during the pivoting process is interpreted. It is shown that each tableau of the process corresponds to the inverse of a row modified matrix and contains the generators of the linear subspace orthogonal to a set of vectors and its complement. This transformation, which is based on the orthogonality concept, allows us to solve many problems of linear algebra, such as calculating the inverse and the determinant of a matrix, updating the inverse or the determinant of a matrix after changing a row (column), determining the rank of a matrix, determining whether or not a set of vectors is linearly independent, obtaining the intersection of tw...

This paper provides a technique to determine the minimum required measurement set to ensure observability in state estimation even if any meters fail. The technique relies on solving a nonlinear integer programming problem. The proposed procedure is illustrated through a simple example and three case studies based on the IEEE Test Systems. Conclusions are finally drawn.

An efficient and robust technique for observability checking in power system state estimation based on Gaussian elimination and binary arithmetic is provided. Since the proposed technique uses binary arithmetic, no rounding error, numerical instability or zero identification problems occur. In some cases, the technique may not identify all observable state variables, requiring an additional numerical analysis over a matrix of dimension that is highly reduced. An illustrative example of small size and a realistic case study are used to demonstrate the features of the proposed technique. Adequate conclusions are finally drawn.