Vectorial summation of probabilistic current harmonics in power systems: From a bivariate distribution model towards a univariate probability function

Abstract

AbstractThis paper extends the investigation into the bivariate normal distribution (BND) model which has been widely used to study the asymptotic behaviour of the sum of a sufficiently large number of randomly‐varying harmonic phasors (of the same frequency). Although the BND model is effective and applicable to most problems involving harmonic summation, its main drawback resides in the computation time required to extract the probability density function of the harmonic magnitude from the two‐dimensional BND model. This paper proposes a novel approach to the problem by assimilating the generalized Gamma distribution (GGD) model to the marginal distribution (the magnitude) of the BND using the method of moments. The proposed method can accurately estimate the parameters of the GGD model without time‐consuming calculation. A power system containing ten harmonic sources is taken as an example where the comparison of the Monte‐Carlo simulation, the BND model and the GGD model is given and discussed. The comparison shows that the GGD model approximates the BND model very well.