Statistical Characterization of Harmonic Emissions in Power Supply Systems
This paper deals with the derivation of the statistics of some quantities defined in the Standard IEC 61000-4-7 to describe the harmonic emissions of power supply systems. This is clearly a crucial point with respect to the assessment of compliance with emission limits. In particular, the quantities analyzed in the paper are the rms values of harmonic components, harmonic subgroups, and harmonic groups. A complete statistical characterization of such quantities are derived in the paper in terms of probability density functions, cumulative distribution functions, and statistical moments. The statistical properties are provided as functions of the additive input noise superimposed to the voltage/current waveform under analysis, including the noise added by the measurement system. The most challenging issue is the statistical analysis of the harmonic group, since in this case the Standard foresees a proper smoothing of several spectral lines. Rigorous analytical results are derived also in this case, and an approximate and much simpler approach based on the central limit theorem is proposed. Analytical results are validated by means of numerical simulations.
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