Stochastic evaluation of harmonics at network buses

Evaluation of harmonic distortion and power quality in electrical networks cannot neglect the stochastic approach, which takes into account the random nature of harmonics injected in the network by distorting loads. In this paper, procedures are proposed to evaluate the resultant probability density and cumulative functions of the sum of harmonic currents at buses of electrical networks. These procedures are applied to the results of long-term measurements performed on MV networks, which supply both residential and industrial loads. It is shown that the time series associated to real and imaginary components of harmonic currents are, in general, nonstationary, so that the statistical tools proposed in literature to evaluate the probability function of the magnitude of the sum of random vectors may give inaccurate results. On the contrary, the proposed procedures allow accurate estimates of the sum of harmonics, associated to given probabilities, to be achieved