An investigation on the numerical ill-conditioning of hybrid state estimators

Convergence problems and loss of accuracy due to numerical ill-conditioning is a frequently encountered problem in power system state estimation. It has been experienced by the researchers that the presence of PMU measurements along with the conventional measurements deteriorates the numerical conditioning of the so-called hybrid state estimator. This paper describes a simple technique to analyze the possible causes of ill-conditioning for different measurement configurations in terms of the condition number of the state estimation gain matrix. Approximate formulation of condition number of the gain matrix in presence of PMU with some simplifying assumptions is applied on a 10-bus radial network. This analysis is further extended for IEEE 14-bus system. The difference in weights assigned to the conventional and PMU measurements has been found to be the main cause of numerical ill-conditioning.