Some approaches to approximate the probability density functions of harmonics

Some analytical approaches to approximate the probability density functions (PDFs) of voltage and current harmonics in electric power system are presented. The approaches are due to Johnson, Pearson, Gram-Charlier and Edgeworth and are used to calculate the percentiles and maximum values of the harmonic PDFs, being these quantities the statistical measures of greatest interest in many International Harmonic Standards and Recommendations. The approaches assume as input data the moments or cumulants of the PDFs to be approximated, being these quantities easier and quicker to be obtainable than the PDFs themselves. Several numerical applications are presented and discussed comparing the percentiles and maximum values evaluated with the proposed approaches with the ones obtained starting from the true probability density functions. The main conclusion of the paper is that the best approach to be used for current and voltage harmonic PDF approximation is the one based on the Pearson distributions.