General bad data identification and estimation in the presence of critical measurement sets

In power systems state estimation, critical sets are groups of measurements whose normalized residuals are (nearly) equal, so that corresponding bad data are not identifiable. A novel methodology for the identification of critical sets and for the estimation of the bad data is introduced, based on a noisy projection of the residuals correlation matrix on a subspace. The proposed solution takes into account model and data uncertainty and is able to detect cases of nearly-critical sets, missed by traditional methods, including higher-order critical k-tuples. A convenient interpretation of the estimated bad data as the total error within the sets is also proposed.