<abstract xmlns="http://www.w3.org/1999/xhtml"><p>This work deals with the statistical characterization of real-time digital measurement of the amplitude of harmonics affected by frequency instability. In fact, in modern power systems both the presence of harmonics and frequency instability are well-known and widespread phenomena mainly due to nonlinear loads and distributed generation, respectively. As a result, real-time monitoring of voltage/current frequency spectra is of paramount importance as far as power quality issues are addressed. Within this framework, a key point is that in many cases real-time continuous monitoring prevents the application of sophisticated algorithms to extract all the information from the digitized waveforms because of the required computational burden. In those cases only simple evaluations such as peak search of discrete Fourier transform are implemented. It is well known, however, that a slight change in waveform frequency results in lack of sampling synchronism and uncertainty in amplitude estimate. Of course the impact of this phenomenon increases with the order of the harmonic to be measured. In this paper an approximate analytical approach is proposed in order to describe the statistical properties of the measured magnitude of harmonics affected by frequency instability. By providing a simplified description of the frequency behavior of the windows used against spectral leakage, analytical expressions for mean value, variance, cumulative distribution function, and probability density function of the measured harmonics magnitude are derived in closed form as functions of waveform frequency treated as a random variable.</p></abstract>

This work deals with the statistical characterization of real-time digital measurement of the amplitude of harmonics affected by frequency instability. In fact, in modern power systems both the presence of harmonics and frequency instability are well-known and widespread phenomena mainly due to nonlinear loads and distributed generation, respectively. As a result, real-time monitoring of voltage/current frequency spectra is of paramount importance as far as power quality issues are addressed. Within this framework, a key point is that in many cases real-time continuous monitoring prevents the application of sophisticated algorithms to extract all the information from the digitized waveforms because of the required computational burden. In those cases only simple evaluations such as peak search of discrete Fourier transform are implemented. It is well known, however, that a slight change in waveform frequency results in lack of sampling synchronism and uncertainty in amplitude estimate. Of course the impact of this phenomenon increases with the order of the harmonic to be measured. In this paper an approximate analytical approach is proposed in order to describe the statistical properties of the measured magnitude of harmonics affected by frequency instability. By providing a simplified description of the frequency behavior of the windows used against spectral leakage, analytical expressions for mean value, variance, cumulative distribution function, and probability density function of the measured harmonics magnitude are derived in closed form as functions of waveform frequency treated as a random variable.

Statistical Properties of Real–Time Amplitude Estimate of Harmonics Affected by Frequency Instability

Department of Electronics, Information and Bioengineering, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milan,

Journal of Electrical Engineering

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

This work deals with the statistical characterization of real-time digital measurement of the amplitude of harmonics affected by frequency instability. In...

Statistical Properties of Real–Time Amplitude Estimate of Harmonics Affected by Frequency Instability

Published Online: Sep 18, 2016

Page range: 292 - 298

Received: Mar 05, 2016

DOI: https://doi.org/10.1515/jee-2016-0043

Keywords
digital measurements, discrete Fourier transform, frequency-domain analysis, frequency instability, harmonics, statistical analysis

© 2016 Faculty of Electrical Engineering and Information Technology, Slovak University of Technology

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Statistical Properties of Real–Time Amplitude Estimate of Harmonics Affected by Frequency Instability

Published Online: Sep 18, 2016

Page range: 292 - 298

Received: Mar 05, 2016

DOI: https://doi.org/10.1515/jee-2016-0043

Keywordsdigital measurements, discrete Fourier transform, frequency-domain analysis, frequency instability, harmonics, statistical analysis

© 2016 Faculty of Electrical Engineering and Information Technology, Slovak University of Technology

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
digital measurements, discrete Fourier transform, frequency-domain analysis, frequency instability, harmonics, statistical analysis