DETECTION OF GROSS ERROR BY MODIFIED RELAXATION STATE ESTIMATION IN POWER SYSTEM Leonardo Geo MANESCU LEG / INPG - UJF - UMR 5529, France; manescu@leg.ensieg.inpg.fr GIE – IDEA France; manescu_adi@yahoo.fr Abstract − This paper proposes a modified relaxation- based method for gross error identification. Toward this end,a participation matrix is defined. It consists of the elements of the residue sensitivity matrix and the corresponding measurements. The sum of row elements of the participation matrix constitutes the residues. The column elements of the participation matrix are also a source of information of masking which sum is quantified as distortion. Large distortion and large residues are proposed to indicate the quality of measurements. The measurement corresponding to the poorest quality is then corrected using the modified form of relaxation. The above procedure is repeated sequentially until all residues are within a particular tolerance. The method gives a measurement set very near to true measurement set. Keywords: state estimation, error filtering, relaxation methods 1. INTRODUCTION Power system state estimation is an important algorithm used in monitoring and control the power system. The presence of gross errors in measurements tends to bias the estimated state of the system. Hence, it is essentially to eliminate grossly erroneous measurements. Measurement residuals are conventionally used for this purpose. However, the measurement residuals suffer from the phenomenon of smearing, [1 … 4]. Different strategies could be employed for grouped search, as given by [5]...[9]. All of them have acknowledged the importance of measurement correction. Slutsker, [10], has exploited the best of both the ordered and the grouped search techniques. The method comes up with the unique proposition of unmasking of the residuals with the help of measurement compensation. The selection of the initial suspected set is done using the unmasking property of measurement compensation. This unmasking property is due to the partial neutralization of the errors. The method estimates the error in the measurements in an optimal way, [8_…_9]), and identification of gross error is carried out using hypothesis testing. The advantages of ordered search for extraction of gross error over the optimal error estimation in brought out clearly in [11]. The role of the column elements of the residue sensitivity matrix in the formation of the residues is well illustrated by [12] . The importance of the sequential correction of measurements for better identification has been highlighted in [7], [10] and [13]. In [2] and [14] it was confirmed that the interaction of measurements takes place in its neighborhood only. Slusker, [15] discusses the requirement of localized search. A study of repeated application of measurement correction using a modified form of relaxation technique to the identified grossly erroneous measurements revealed that it is possible to correct the identified measurements toward their true values. In [16] it was applied the relaxation for the estimation of large power systems. This paper makes an attempt to formulate a scheme for gross error identification using a modified form of relaxation. It tries to make the best use of the rich knowledge available in the above literature to formulate the scheme. Toward this end it s proposed a new approach of the error residue equation related through the residual sensitivity matrix " W ". In the proposed method the error vector is viewed as a set of objects. Each element of the residue sensitivity matrix W is considered as a filter. When the objects are seen through the filters, the images are obtained. The images are in form of a matrix called image matrix " IM ". The sum of the row elements of the image matrix is called the residual image vector RIM . The column elements represent the quantum of image transmission of an error into the residual image vector, [12]. The sum of the column elements of the image matrix is therefore defined as the image distortion vector DIM . Image distortion is defined as the cause of masking. Computation of RIM and DIM vectors cannot actually be carried out because e is an unknown vector. The residues and distortions are therefore defined using the elements of measurement vector as objects. The matrix consisting of the product of elements of W matrix and the corresponding measurement is defined as the participation matrix. The sum of the row elements of the participation matrix then gives the residue vector. The sum of the magnitude of the column elements of participation matrix is defined as the distortion vector. 275 Annals of the University of Craiova, Electrical Engineering series, No. 30, 2006 _________________________________________________________________________________________________