Convergence property of the measurement gross error correction in power system state estimation, using geometrical background

In this paper it is shown that once the measurements with gross errors are detected and identified, the geometrical approach to recover gross errors in power system state estimation, as we have previously proposed, is a convergent process. For the purpose of correcting the measurement gross errors, the measurement residuals are computed, and then the measurement gross errors are composed. For the detection and identification of the measurements with gross errors, the composed measurement error in the normalized form (CMEN) is used. The measurement magnitude corrections otherwise are performed using the composed normalized error (CNE). To support the thesis that, after the detection and identification of the measurements containing gross errors, the measurement correction is a convergent procedure, the generalization of the largest normalized error test is also provided. A two-bus power network is used to show in a didactic way the behavior of the gross error correction. The IEEE 14-bus system and the 45-bus equivalent of Brazil south are used to perform the tests for the multiple measurement gross errors case. Many gross error scenarios with different redundancy levels, for multiple gross error situations, have been tested. The measurement correction is made one at a time.