Geometrical approaches for gross errors analysis in power systems state estimation

In this paper, a geometrical based approach is used to define the undetectability index (UI) that gives the distance of a measurement from the range of the jacobian matrix. The higher the value of this index the closer this measurement will be to the range of that matrix; the error in measurements with high UI is not reflected in their residues. A critical measurement has infinite UI, belongs to the range of the Jacobian matrix, and its error is totally masked. Using the UI, it is shown measurements not classified as leverage points, and having large masked gross errors in the state estimation process. As example to illustrate the way that UI index works, a two bus power system will be used; to test the index efficiency in identifying the measurements that have the gross errors masked by the state estimation process the IEEE-14 bus system will be used.