Estimation of harmonics emission level by the probability density function

Because of the changes in system harmonic sources, many international rules and standards use the data of no more than 95% probability as standard level of the random harmonic. It is difficult to get the probability density functions of the random harmonic sources. This paper introduced several classic methods of obtaining the probability density functions (pdf) of the random harmonic vectors (voltage or current). The probability density functions were obtained by three kinds of methods (Gram-Charlier and Edgeworth expansion, Pearson Transform and Johnson Transform) to compare with those obtained by true data of arc furnace of 110 kV node power system. A conclusion is drawn that the probability density functions of the random harmonic vectors (voltage or current) got with Pearson Transform are more exact than others. The error of the no more than 95% probability using Pearson Transform within 10% compared with true data. It can be used in practice and only needs 1-3th cumulants.