Robust Mahalanobis distances in power system state estimation

The paper describes a fast method for calculating robust distances of the data points in the factor space of a linearized power system state estimation model. The coordinates of these points are the entries of the associated row vectors of the weighted Jacobian matrix. The developed method makes use of a new version of the projection algorithm that accounts for the sparsity of the Jacobian matrix. The method is implemented through an algorithm that assigns to each data point the maximum of the standardized projections of the point cloud on some directions passing through the origin. Statistical tests applied to the projection distances allow us to identify the outliers in the factor space and thereby to single out the so-called leverage points. By deleting these outliers, robust Mahalanobis distances can be calculated and used to derive weights for robustifying the one-step GM-estimators starting from a robust state estimate