Robustification of the least absolute value estimator by means of projection statistics

This paper describes a fast and robust method for identifying the leverage points of a linearized power system state estimation model. These are measurements whose projections on the space spanned by the row vectors of the weighted Jacobian matrix, the so-called factor space, do not follow the pattern of the bulk of the point cloud. In other words, their projections are outliers in the factor space. The proposed method is implemented through a new version of the projection algorithm that accounts for the sparsity of the Jacobian matrix. It assigns to each data point a projection statistic defined as the maximum of the standardized projections of the point cloud on some directions passing through the origin. By comparing these projection statistics to cutoff values, we can identify the outliers in the factor space and thereby pinpoint the leverage points. The projection statistics are also used to derive weights for robustifying the weighted least absolute value estimator. The computational efficiency and the robustness of the method are demonstrated on the IEEE-14 bus and 118-bus systems.