Masked errors in power systems state estimation and measurement gross errors detection and identification

In this paper, a topological and geometrical based approach is used to define an index, undetectability index (UI), which provides the distance of a measurement from the range space of the Jacobean matrix of the power system. The higher the value of this index, for a measurement, the closer it will be to the range space of that matrix, that is, the error in measurements with high UI is not reflected in their residuals, thus masking a possible gross error those measurements might have. Using the UI of a measurement, the possible gross error the state estimation process might mask is recovered; then the total gross error of that measurement is composed and used to the gross error detection and identification test. A two bus system is used to show how this geometrical view of gross error analysis works. The classical three bus system used in many papers of the state estimation field is used as an example of a small application of the proposed methodology.