New Facts in Regression Estimation under Conditions of Multicollinearity

This paper considers the approaches and methods for reducing the influence of multi-collinearity. Great attention is paid to the question of using shrinkage estimators for this purpose. Two classes of regression models are investigated, the first of which corresponds to systems with a negative feedback, while the second class presents systems without the feedback. In the first case the use of shrinkage estimators, especially the Principal Component estimator, is inappropriate but is possible in the second case with the right choice of the regularization parameter or of the number of principal components included in the regression model. This fact is substantiated by the study of the distribution of the random variable , where b is the LS estimate and β is the true coefficient, since the form of this distribution is the basic characteristic of the specified classes. For this study, a regression approximation of the distribution of the event based on the Edgeworth series was developed. Also, alternative approaches are examined to resolve the multicollinearity issue, including an application of the known Inequality Constrained Least Squares method and the Dual estimator method proposed by the author. It is shown that with a priori information the Euclidean distance between the estimates and the true coefficients can be significantly reduced.

Low Impedance Fault Identification and Classification Based on Boltzmann Machine Learning for HVDC Transmission Systems

Identification and classification of DC faults are considered as fundamentals of DC grid protection.A sudden rise of DC fault current must be identified and classified to immediately operate the corresponding interrupting mechanism.In this paper,the Boltzmann machine learning(BML)approach is proposed for identification and classification of DC faults using travelling waves generated at fault point in voltage source converter based high-voltage direct current(VSC-HVDC)transmission system.An unsupervised way of feature extraction is performed on the frequency spectrum of the travelling waves.Binomial class logistic regression(BCLR)classifies the HVDC transmission system into faulty and healthy states.The proposed technique reduces the time for fault identification and classification because of reduced tagged data with few characteristics.Therefore,the faults near or at converter stations are readily identified and classified.The performance of the proposed technique is assessed via simulations developed in MATLAB/Simulink and tested for pre-fault and post-fault data both at VSC1 and VSC2,respectively.Moreover,the proposed technique is supported by analyzing the root mean square error to show practicality and realization with reduced computations.