State Estimation, Numerical Instability, Ill-conditioning, Lagrangian, QR Factorization
Abstract
The traditional formulation of the State Estimator (SE) in Power Systems (PS) using Weighted Least Squares is susceptible to numerical instability. Several mechanisms have been presented in the literature as causes of such problems, and some solutions have been suggested to address this issue. However, most of these mechanisms are pointed out empirically or using simplified numerical conditioning estimates. As this is an expected problem in modern networks, this study aims to evaluate the various causes of numerical ill-conditioning in state estimators, evaluating two numerically stable methods, namely, the Normal Equation via QR (NeQR) factorization and Lagrangian Equation Method (LaE) in a fair simulation environment. Towards validating the discussions, computational simulation results are presented in IEEE14, IEEE30, and IEEE118 systems. The results indicate that ill-conditioning is connected to measurement weighting network parameters, and NeQR demonstrates superior numerical stability.
