Geometrical approaches for gross errors analysis in power systems state estimation

Abstract

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.

A two steps procedure in state estimation gross error detection, identification, and correction

“…Second step: the measurement gross error correction and the state estimation Once a gross error has been detected and also the measurements with errors identified, they should have their magnitudes corrected, using the measurement's CNE as in (11). The reason for using that correction is because the CNE's subspace is obtained from a space of dimension m, the measurement space, going to a subspace of smaller dimension, the residual subspace, of dimension (m À N); as a consequence, the computation in residual space is accurate.…”

“…More recently, using topological and geometrical approaches Bretas et al [10][11][12][13][14][15][16][17][18][19][20], have proposed methodologies that beyond having the classical SE functions it also composes the error and then correct the magnitude of the measurements in error.…”

Application of the undetectability index to design reliable metering systems for bad data processing

“…Figures 2 and 3 show the UI for the measurements of metering system 1. Observe that, because the UI does not depend only on the measurement redundancy [13] [14], even considering a highly redundant metering system, with all possible power and voltage magnitude measurements, some measurements present high UI, as, for example, measurements P:5 (UI >5), P:2 (UI >3), Q:5 (UI >3), and Q:4-9(UI >2). …”

“…Recently, through a geometric analysis of the WLS Estimator, some works [13], [14] have shown that even for highly redundant metering system the WLS Estimator, endowed with the largest normalized residual test, is not able to process single bad data. In order to demonstrated this statement, in those works was developed an index, called Undetectability Index (UI), to classify the measurements according to their characteristics of not reflecting their errors into the residuals of the WLS Estimator.…”

Análise de observabilidade e de redundância de medidas no contexto de estimação de estado trifásica

“…Trabalhos publicados nessa área (THORP et al, 1985. PHADKE et al, 1986ZHOU et al, 2006;LONDON JR. et al, 2009) demonstram que quando as medidas fasoriais são adicionadas às medidas convencionais, no processo de EESEP, a precisão do estimador é aumentada. …”