Least Median Of Squares Estimation In Power Systems

Static state estimators currently in use in power systems are prone to masking by multiple bad data. This is mainly because the power system regression model contains many leverage points; typically they have a cluster pattern. As reported recently in the statistical literature, only high breakdown point estimators are robust enough to cope with gross errors corrupting such a model. This paper deals with one such estimator, the least median of squares estimator, developed by Rousseeuw in 1984. The robustness of this method is assessed while applying it to power systems. Resampling methods are developed, and simulation results for IEEE test systems discussed. © 1991 IEEE.

Stability Problems in Inverse Diffraction

Inverse diffraction consists in determining the field distribution on a boundary surface from the knowledge of the distribution on a surface situated within the domain where the wave propagates. This problem is a good example for illustrating the use of least-squares methods (also called regularization methods) for solving linear ill-posed inverse problem. We focus on obtaining error bounds For regularized solutions and show that the stability of the restored field far from the boundary surface is quite satisfactory: the error is proportional to ∊(ðŗ‚ ≃ 1) ,ðŗœ being the error in the data (Hölder continuity). However, the error in the restored field on the boundary surface is only proportional to an inverse power of │In∊│ (logarithmic continuity). Such a poor continuity implies some limitations on the resolution which is achievable in practice. In this case, the resolution limit is seen to be about half of the wavelength. Copyright © 1981 by The Institute of Electrical and Electronics Engineers, Inc.