Accuracy analysis of generalized discrete Fourier transform‑based harmonics extraction in presence of background harmonics

Shuo Zhang; Yuzheng Xia; Tao Yang; Xiang Li; Daorong Lu; Haibing Hu

Accuracy analysis of generalized discrete Fourier transform‑based harmonics extraction in presence of background harmonics

Vol. 22, No. 1, pp. 72-83, Jan. 2022

10.1007/s43236-021-00338-1

Harmonics extraction

Generalized discrete Fourier transform

Background harmonics

Frequency feature analysis

Abstract

The generalized discrete Fourier transform (GDFT) realizes the rapid extraction of specific order harmonics, and shortens the extraction time to 1/3 of a fundamental cycle (6.7 ms at 50 Hz grid) for 6r ± 1 order harmonics. However, the GDFT becomes less accurate when the system presents background harmonics other than specific-order harmonics in the inputs. Therefore, this paper analyzes the influence introduced by these background harmonics on the GDFT. First, the frequency feature of the GDFT is derived by a geometric method based on the z-domain unit circle. Then, the extraction of the 6r ± 1 order harmonics is taken as an example to show the extraction accuracy of the GDFT. The Accuracy of Harmonic Extraction (AHE) index, is also given to evaluate the accuracy of the extraction. Simulation and experimental results confirmed the correctness of the theoretical analysis by showing that the GDFT has the same accuracy as the RDFT when only 6r ± 1 order harmonics are involved. However, if there are other background harmonics in the inputs, the extraction accuracy is affected greatly. Therefore, when the background harmonics cannot be ignored, it is necessary to analyze the AHE of the GDFT. When AHE > 95%, the GDFT has good accuracy and is applicable to real applications.

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Cite this article

[IEEE Style]

S. Zhang, Y. Xia, T. Yang, X. Li, D. Lu, H. Hu, "Accuracy analysis of generalized discrete Fourier transform‑based harmonics extraction in presence of background harmonics," Journal of Power Electronics, vol. 22, no. 1, pp. 72-83, 2022. DOI: 10.1007/s43236-021-00338-1.

[ACM Style]

Shuo Zhang, Yuzheng Xia, Tao Yang, Xiang Li, Daorong Lu, and Haibing Hu. 2022. Accuracy analysis of generalized discrete Fourier transform‑based harmonics extraction in presence of background harmonics. Journal of Power Electronics, 22, 1, (2022), 72-83. DOI: 10.1007/s43236-021-00338-1.