Gaussian modeling of harmonic vectors in power systems

The paper deals with Gaussian modeling of harmonic vectors in power systems. Starting from the bivariate Gaussian distribution of the vector resolved components, the univariate magnitude and phase densities are presented both in closed form solutions, which apply when opportune hypotheses are verified, and by more general empirical models. Reference is made to the results shown in relevant literature also concerning the problem of Cartesian axes rotation to reduce to zero the resolved components correlation coefficient. For the phase distribution a new expression is reported. Applications to both numerical case studies and field measurements on an Italian medium voltage network node are reported allowing comparison among different distributions