Multiple gross errors detection, identification and correction in three-phase distribution systems WLS state estimation: A per-phase measurement error approach

•Three-phase WLS-SE formulation considering both measurements and pseudo measurements simultaneously with different load models.•Three-phase model for WLS-SE solution minimizing the composed measurement errors.•Multiple per-phase gross error detection based on Chi-square Hypothesis Testing of composed measurement errors.•Multiple per-phase normalized composed measurement error test to identify gross errors.•Multiple per-phase gross error correction for both measurement and pseudo measurements. This paper presents an analytical methodology for multiple measurement gross error detection, identification and correction for three-phase distribution systems weighted least square (WLS) state estimation. Initially, a three-phase WLS state estimator, considering the inherent distribution systems characteristics, as unbalance operation and different load types, is presented. Extended formulations for Jacobian matrix elements calculation, relating to different load models are proposed. Detection, identification and correction of gross errors are performed considering hypothesis testing in a per-phase component approach. Gross error detection is made through a Chi-square (χ2) Hypothesis Testing (HT) applied to the phase composed measurement error (CME). Composed errors are estimated with measurements’ phase innovation index (II). Gross error identification is made through the Largest Normalized Error Test property. Gross error correction is made considering the phase composed normalized error (CNE). A method to correct pseudo measurements identified as having gross errors is proposed. Validation is made with the IEEE 123 bus test system. Comparative tests with the state of art are presented. Test results are encouraging, indicating potential aspects for real-life applications.