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Analysis of Ill‐conditioning of hybrid state estimators in the presence of PMU measurements

It has been observed by the practicing engineers that the inclusion of measurements from phasor measurement units (PMUs), current measurements in particular, into the conventional state estimators (SEs), may deteriorate the numerical performance of the SEs in terms of convergence and accuracy. This paper analyzes the reason for such possible ill-conditioning of the hybrid SEs that use both conventional and PMU measurements. It presents simpliﬁed analytical approaches to identify what causes such ill-conditioning when PMU measurements are used. The condition number of SE gain matrix may vary depending on the number of the PMUs and its placement in the network. It has been identiﬁed that the large difference in weights that are allocated to the traditional measurements and PMU measurements is the main reason of the ill-conditioning of the hybrid SEs.