Assessment of Errors of Fundamental Frequency Estimation Methods in the Presence of Voltage Fluctuations and Distortions

TL;DR

The paper addresses accurate fundamental frequency estimation in power systems under voltage fluctuations and distortions, where short measurement windows are needed for diagnostics and compliance. It compares the IEC 61000-4-30 method with Autocorrelation, Hilbert, and ESPRIT-based approaches using a Matlab-generated disturbance-rich test signal. Findings show IEC and Modified ESPRIT offer the best accuracy but none meet the ±10 mHz requirement, with errors increasing as modulation speed and frequency deviation grow and with notable outliers. The work highlights the need for new estimation methods and for metrological validation of equipment using the proposed test signal to ensure robust power quality assessment.

Abstract

The fundamental frequency is one of the parameters that define power quality. Correctly determining this parameter under the conditions that prevail in modern power grids is crucial. Diagnostic purposes often require an efficient estimation of this parameter within short time windows. Therefore, this article presents the results of numerical simulation studies that allow the assessment of errors in various fundamental frequency estimation methods, including the standard IEC 61000-4-30 method, when the analyzed signal has a form similar to that found in modern power grids. For the purposes of this study, a test signal was adopted recreating the states of the power grid, including the simultaneous occurrence of voltage fluctuations and distortions. Conclusions are presented based on conducted research.

Figures (7)

• Figure 1: An example of the fundamental frequency $f_0$ over time characteristic in a power network recorded using PQA, where the red line shows the fundamental frequencies $f_0$(10s) measured at a 10-second interval, and the blue and green lines show the maximum $f_0$(max) and minimum $f_0$(min) fundamental frequencies measured at successive 200 ms intervals within a 10-second window.
• Figure 2: An example of the characteristic fundamental frequency $f_0$ over time on board a passenger train recorded using PQA, where the red line shows the fundamental frequencies $f_0$(10s) measured at a 10-second interval, and the blue and green lines show the maximum fundamental frequencies $f_0$(max) and minimum $f_0$(min) measured at successive 200 ms intervals within a 10-second window.
• Figure 3: The dispersion of fundamental frequency estimation errors $\delta f_0$ in the form of boxplot grouped by the modulating frequency $f_m$ for the individual methods considered, where the top plot shows the dispersion with outliers, while the middle and bottom plots show the dispersion without the outlier with an appropriate zoom.
• Figure 4: The dispersion of fundamental frequency estimation errors $\delta f_0$ in the form of boxplot grouped by the deviation of fundamental frequency $\Delta f_0$ for the individual methods considered, where the top plot shows the dispersion with outliers, while the middle and bottom plots show the dispersion without the outlier with an appropriate zoom.
• Figure 5: The dispersion of fundamental frequency estimation errors $\delta f_0$ in the form of boxplot grouped by the fundamental frequency of the carrier signal $f_0$ (this value is approximately equal to the average value of the fundamental frequency of the test signal determined for a 10-second window) for the individual methods considered, where the top plot shows the dispersion with outliers, while the middle and bottom plots show the dispersion without the outlier with an appropriate zoom.