Abstract
This work deals with the statistical analysis of additive noise impact on the space-vector ellipse parameters used to detect and classify three-phase voltage sags. In fact, since voltage waveforms are always corrupted by additive noise and harmonics, the space vector is pre-processed through the Discrete Fourier Transform to extract the power frequency components. Thus, harmonics can be readily discarded, but additive noise can still have significant impact on the elliptical trajectory of the space vector on the complex plane. Therefore, by modeling the ellipse parameters (i.e., the shape index and the inclination angle) as random variables, the related statistical characterization is derived in the paper. In particular, the main results and the novelty of the paper are given by the analytical derivation in closed-form of the probability density function, cumulative distribution function, mean value, and variance of the ellipse parameters as functions of the additive noise variance. Since the ellipse shape index and inclination angle are commonly used to detect and classify voltage sags, the results derived in the paper are useful for both uncertainty propagation analysis, and assessment of detection capability in case of voltage dips close to the minimum value defined in the IEEE Standard 1159. Analytical results are validated through numerical simulation of noisy voltage sags.
Highlights
The voltage space vector is corrupted by harmonics and additive noise
Since the ellipse parameters refer to the power frequency component only, pre-processing of space vector is required
In case of lack of synchronization, windowing of voltage samples (e.g., Hann window) is required to minimize spectral leakage. In this case the analytical results derived in the paper hold provided that the variance (13) is multiplied by the equivalent noise bandwidth (ENBW) of the selected window (e.g., ENBW = 1.50 for the Hann window) [29]
Summary
As the most frequent power quality disturbance, voltage sags can have severe consequences spanning from malfunctioning of control system equipment, to disconnection or loss of efficiency in electric machines For this reason, many researchers have focused on the analysis, classification and characterization of voltage sags (e.g., [4]–[10]). When an unbalanced voltage sag occurs (i.e., when the voltage drop is not the same for all the phases), the space vector trajectory becomes elliptical [11]–[18]
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