A sparse and numerically stable implementation of a distribution system state estimator - Hebling, Gustavo Miranda (2022)
The state estimator is the main analysis tool in real-time operation of power systems. It obtains the operating condition of the network given a set of measurements and this is the first step in a series of automated applications in energy management systems. Specialized algorithms have been developed to perform Distribution System State Estimation (DSSE) since the Weighted Least Squares (WLS) estimator, commonly used in transmission systems, faces challenges due to specific characteristics of Distribution Systems (DSs). The WLS estimator requires the solution of a linear system which may be ill-conditioned due to a set of particularities of DSs such as the one, two and three-phase unbalanced branches, large number of nodes and connections between long and short lines, among others. The Gain matrix, the coefficient matrix of the linear system obtained with the WLS estimator, requires factoring and the usual technique, the Cholesky factorization, may create a large number of non-zero elements adding perturbations to an already ill-conditioned system which may impact the solution obtained. Since the Gain matrix is sparse, specialized techniques may be used to extract peak computational performance. In this context, this work evaluates the use of an orthogonal formulation of the WLS state estimator which aims to improve the accuracy of the solution as well as the numerical stability of the estimation process. The QR factorization obtains an upper triangular linear system that can be solved with simple substitutions. Dedicated techniques are used to preserve the sparse structure of the matrices and with a sparse-oriented algorithm to obtain the QR factorization, the state estimation is executed in a very short running time, even for large test systems. This work presents the theoretical background of state estimation, an overview of the sparse techniques that allow for higher computational performance and the orthogonal formulation which improves the numerical stability of the state estimation. Results are presented with performance and accuracy metrics for the proposed estimator and comparisons with a dedicated algorithm for DSs and alternative formulations of the WLS estimator.