Geometrical approach on masked gross errors for power systems state estimation

In this paper, a geometrical based-index, called undetectability index (UI), that quantifies the inability of the traditional normalized residue test to detect single gross errors is proposed. It is shown that the error in measurements with high UI is not reflected in their residues. This masking effect is due to the ldquoproximityrdquo of a measurement to the range of the Jacobian matrix associated with the power system measurement set. A critical measurement is the limit case of measurement with high UI, that is, it belongs to the range of the Jacobian matrix, has an infinite UI index, its error is totally masked and cannot be detected in the normalized residue test at all. The set of measurements with high UI contains the critical measurements and, in general, the leverage points, however there exist measurements with high UI that are neither critical nor leverage points and whose errors are masked by the normalized residue test. In other words, the proposed index presents a more comprehensive picture of the problem of single gross error detection in power system state estimation than critical measurements and leverage points. The index calculation is very simple and is performed using routines already available in the existing state estimation software. Two small examples are presented to show the way the index works to assess the quality of measurement sets in terms of single gross error detection. The IEEE-14 bus system is used to show the efficiency of the proposed index to identify measurements whose errors are masked by the estimation processing.