Using linear and non-parametric regression models to describe the contribution of non-linear loads on the voltage harmonic distortions in the electrical grid

This study addresses the problem of determining which non-linear loads can be considered potential harmonic sources to the voltage harmonic distortions observed in the utility grid voltages. Statistical regression models are used to establish correlations between the simultaneously measured harmonic voltages, in the grid, and harmonic currents, at each non-linear individual load. First, the R-squared statistic is used to decide the goodness of fit of the developed models, giving indication on the relevance of the model. In order to overcome the limitation of the linear regression model based on voltage and current magnitudes measurements only, that imposes a constant behaviour for the background harmonic sources, a non-parametric regression model is suggested and a comparison between the performances of the two models is carried out. Field data from two real electrical systems, one having a 138 kV substation in which a large industrial load and a 34.5 kV rural long feeder are connected; and the other having four urban 13.8 kV feeders supplying industrial and commercial loads, were used to develop and validate the statistical models used in the application.