On the Statistics of Noisy Space Vector in Power Quality Analysis

Abstract—This work deals with the analysis of the impact of additive noise on the geometrical features of the space vector shape on the complex plane. The space vector shape is of great importance in the power quality analysis of modern three-phase power systems since its geometrical features are closely related to the voltage supply quality. In case of voltage sag or swell the space vector shape changes accordingly. In case of additive noise the geometrical parameters of the space vector shape can be treated as random variables. In the paper, the mean values and the variances of such parameters are derived in closed form as functions of the noise level and of the sampling conditions. Analytical results are validated through numerical simulation of the whole measurement process. Keyword-Discrete Fourier transform, Noise propagation, Power quality, Power system analysis, Space vector, Statistical analysis