روش تجزیه و تحلیل حساسیت برای محاسبه ماتریس کواریانس باقی مانده

In state estimation, the covariance matrix of residuals is used to compute the normalized residuals and to detect erroneous measurements. This paper describes a method based on sensitivity analysis that allows computing the residual covariance matrix. The proposed method is estimator-independent, i.e., it is suitable for most solution approaches based on mathematical programming procedures. Several case studies illustrate the technique proposed. Relevant conclusions are finally drawn.

State estimation consists in processing a given set of measurements to obtain the optimal estimate of the power system state. Several state estimation methods are proposed in the technical literature. Most of them are based on solving an optimization problem, such as the following methods: the Weighted Least Squares (WLS), the Least Absolute Value (LAV), the Least Median of Squares (LMS), the Least Trimmed of Squares (LTS), the Quadratic-Constant Criterion (QCC), and the Quadratic-Linear Criterion (QLC). Measurements may contain gross errors due to various reasons. Thus, an essential feature of any state estimator is to detect those gross measurement errors, and, if possible, to identify and eliminate them. In general, bad measurement identification procedures rely on the residual covariance matrix and on the subsequent residual normalization. However, residual covariance matrix computation techniques differ across the methods. Moreover, these techniques usually compute an approximate residual covariance matrix using a first-order approximation and generally disregarding constraints. To overcome these drawbacks is the aim of this paper; i.e., to propose a novel estimator-independent procedure to compute accurately the residual covariance matrix.

This paper proposes a novel technique to compute the residual covariance matrix and normalized residuals for a state estimator based on a mathematical programming formulation (e.g., WLS or LAV), considering constraints. This technique relies on the sensitivities of the state variables with respect to the measurements at the optimal solution of the estimation problem. The sensitivities are calculated through the solution of a linear system of equations, which results from the perturbation of the optimality conditions of the estimation problem. Detailed numerical simulations show that the proposed method is an efficient and accurate technique to estimate the residual covariance matrix regardless of the considered estimator. The proposed technique that is estimator-independent is superior or similar to the estimator-dependent techniques proposed in the technical literature. Within a multi-regional electric energy system, future research will focus on the decentralized computation of the residual covariance matrix.