Abstract
With the development of smart substations and the promotion of 61850 standards, sampling values based on IEC61850-9-2 have become an important part of smart substation construction. With the popularization and application of the sample value (SV), the interpolation algorithm has been increasingly used in protection, measurement, control, wave recorder and power quality applications. However, the error in the interpolation algorithm poses a challenge to its use. This paper describes the basic methods of linear Lagrange and parabolic Lagrange interpolation and presents maximum theoretical values for the interpolation error when Lagrange linear and second-order approximations of sinusoidal signals are performed. The single-point error of each sampling point is analyzed using the remainder equation, and the harmonic error of the Fourier transform after interpolation is strictly mathematically derived. Finally, the accuracy of the theory is verified by real measurement data, and suggestions for the application of the interpolation method are introduced.
Highlights
Harmonic measurement and vector calculation are important tasks in substations, utilities and users [1]
To reduce the effect of asynchronous sampling on fast Fourier transform (FFT) to improve the accuracy of harmonic analysis in motor testing, this paper improves the original algorithm by adding windows and interpolation
This paper aims to analyze the effect of the first- and secondorder Lagrange interpolation algorithms on the results of the FFT algorithm, present maximum theoretical values for the interpolation error when Lagrange linear and secondorder approximations of sinusoidal signals are performed, estimate the maximum error, provide a theoretical basis for VOLUME 9, 2021 the monitoring and measurement of intelligent substations, and verify the accuracy of the analysis with a practical case
Summary
Harmonic measurement and vector calculation are important tasks in substations, utilities and users [1]. Reference [18] proposed a new method for the harmonic analysis of industrial power systems based on a windowed FFT with high accuracy, fast calculation speed and easy implementation. To reduce the effect of asynchronous sampling on FFT to improve the accuracy of harmonic analysis in motor testing, this paper improves the original algorithm by adding windows and interpolation. This paper aims to analyze the effect of the first- and secondorder Lagrange interpolation algorithms on the results of the FFT algorithm, present maximum theoretical values for the interpolation error when Lagrange linear and secondorder approximations of sinusoidal signals are performed, estimate the maximum error, provide a theoretical basis for VOLUME 9, 2021 the monitoring and measurement of intelligent substations, and verify the accuracy of the analysis with a practical case
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