On the Statistics of IEC 61000-4-7 Distortion Factors in Power Supply Systems

This work deals with the analytical derivation of the statistical properties of the distortion factors defined in the Standard IEC 61000-4-7 regarding harmonics and interharmonics measurements and instrumentation for power supply systems and equipment connected thereto. The statistical characterization is provided in terms of probability density function, cumulative distribution function, and statistical moments by exploiting the properties of noise propagation through the discrete Fourier transform. The paper concerns an ongoing research activity, therefore the main novelty is a further step towards the generalization of previously obtained results. In particular, the paper presents an explicit closed-form representation of the statistics of the THDS distortion factor instead of the implicit integral representation provided in a previous paper. The presented methodology can be further extended to other distortion factors. The analytical results are validated by means of numerical simulations.