Robust and distributed state estimation for power systems - Chen, Tengpeng (2017)
Power system state estimation (PSSE) plays an important role in power system operation. The Gaussian noise assumption is commonly made in PSSE. However, this assumption is only an approximation to reality. Outliers that are far away from the expected Gaussian distribution function can give rise to erroneous estimation results. Robust estimators such as Quadratic-Constant (QC), Quadratic-Linear (QL), Square-Root (SR), Multiple-Segment (MS) and Schweppe-Huber Generalized-M (SHGM) have been introduced in the literature to solve the outlier problem in power systems. In this thesis, an analytical equation is derived using the Influence Function (IF), a tool from robust statistics, to calculate approximately the variances of the estimates of these robust estimators. This variance formula has many advantages: (i) It can be used to express the variance of state estimate as a function of measurement variances thus enabling the selection of sensors for specified estimator precision; (ii) It can be used to design an optimal estimator; (iii) Although numerical methods can also be used to find variance, the derived equation as a mathematical function is more insightful and requires less computational effort.