Characteristic Function of Fundamental and Harmonic Active Power in Digital Measurements Under Nonsinusoidal Conditions

Abstract

This work provides the analytical derivation of the characteristic function of noisy digital measurements of fundamental and harmonic active power in electrical systems. Knowledge of the characteristic function, in fact, allows a complete statistical description of the measured active power since both the probability density function and the distribution function can be readily derived. Moreover, from the characteristic function all the statistical moments can be evaluated, whereas in the existing literature only the first- and second-order moments of the fundamental component were provided. More specifically, it is well known that voltage and current waveforms in electrical systems under non-sinusoidal conditions are digitized through analog-to-digital conversion and transformed into the frequency domain. Each waveform spectral line is processed to evaluate active power at the corresponding frequency. Since spectral lines are affected by additive noise the measured active power can be properly treated as a random variable. In particular, harmonic active power is more sensitive to additive noise since it is given by low-magnitude spectral lines. In the paper, the probability density function corresponding to the derived characteristic function is validated through numerical simulation of the whole measurement process and the impact of waveform and sampling parameters is investigated.
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