An Iterative Hybrid Harmonics Detection Method Based on Discrete Wavelet Transform and Bartlett–Hann Window
Abstract
:1. Introduction
2. Principles of Improved Harmonic Detection Methods
2.1. Mallat Algorithm
2.2. Bartlett–Hann Algorithm Principle
2.3. Comparison of Bartlett–Hann Windows and Common Windows
2.4. Comparison of Bartlett–Hann Windows and Common Windows
3. Design of Improved Harmonic Detection Method
3.1. Hybrid Harmonic Detection Method Based on Bartlett–Hann Window DFT and DWT
- (1)
- Analysis of the reconstructed waveform from the wavelet transform shows that there is no attenuating signal in the high frequency part, but only the steady-state signal. In view of this situation, the parameters extracted from the data obtained by windowed interpolation DFT are used to restore the high frequency harmonics. The obtained is the result of harmonic analysis.
- (2)
- The high frequency part contains only time-varying signals with a tendency to decay. In view of this situation, the reconstruction result of the wavelet transform is used as the result of the final harmonic analysis.
- (3)
- There are both time-varying harmonic signals and steady-state harmonic signals in the high frequency part. In view of this situation, the parameters extracted from the data obtained by the windowed interpolation DFT are used to restore the high frequency harmonics to obtain , and sequentially perform difference processing with the high frequency signal reconstructed by the wavelet. After each , the attenuation rate is recalculated. When the attenuation rate shows a decreasing trend or reaches a minimum or even a negative value, this indicates that is an attenuation harmonic signal and is recorded as . According to , it can restore time-varying harmonic signals.
4. Simulation Test Analysis
4.1. Modeling and Analysis of Power Signals
4.2. Simulation Results of Low Frequency Part of Power Data
4.3. Simulation Results of High Frequency Part of Power Data
4.3.1. High Frequency Steady-State Component Simulation Results
4.3.2. High Frequency Steady-State and Attenuation Component Simulation Results
4.3.3. High Frequency Attenuation Component Simulation Results
5. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
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Number of Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
Content(%) | 0.5 | 5 | 0.4 | 3 | 0.6 | 2 | 0.2 | 3 | 0.5 |
Number of Harmonic | Relative Frequency Error (%) | Relative Amplitude Error (%) | ||
Common DFT | Bartlett–Hann Window Interpolation DFT | Common DFT | Bartlett–Hann Window Interpolation DFT | |
Fundamental | −2.34 | −1.86 | −14.52 | −3.43 |
2 | 0.12 | 0.098 | 254.05 | −1.02 |
3 | 0.9 | −0.73 | −27 | −2.36 |
4 | 0.098 | 0.1 | 63.75 | 2.64 |
5 | −0.39 | −0.3906 | −36.64 | 3.37 |
6 | 0.097 | 0.097 | 10.83 | −0.83 |
7 | 0.035 | 0.034 | −28.5 | −4.28 |
8 | 0.098 | 0.098 | 38.25 | −2.44 |
9 | −0.0482 | −0.0484 | −21.67 | −3.67 |
10 | 0.097 | 0.0976 | 8.4 | −3 |
Number of Harmonic | Fundamental | 3 | 5 | 7 |
Theory Frequency (Hz) | 50 | 150 | 250 | 350 |
Actual Frequency (Hz) | 50.78 | 148.44 | 250 | 351.56 |
Theory Amplitude (V) | 220 | 21 | 15 | 13 |
Hanning Window Function Interpolation DFT Algorithm Amplitude (V) | 218.68 | 20.87 | 14.59 | 10.43 |
Bartlett–Hann Window Function Interpolation DFT Algorithm Amplitude (V) | 219.24 | 20.94 | 14.63 | 10.98 |
Number of Harmonic | Fundamental | 3 | 5 | 7 | Average Value | |
Amplitude Accuracy(%) | Hanning Window Function Interpolation DFT Algorithm | 99.4 | 98.38 | 97.27 | 80.23 | 93.82 |
Bartlett–Hann Window Function Interpolation DFT Algorithm | 99.65 | 99.71 | 97.53 | 84.46 | 95.3375 | |
Relative Amplitude Error (%) | Hanning Window Function Interpolation DFT Algorithm | −0.6 | −0.619 | −2.73 | −19.77 | −5.93 |
Bartlett–Hann Window Function Interpolation DFT Algorithm | −0.345 | −0.286 | −2.46 | −15.53 | −4.655 |
Number of Harmonic | Theory Frequency (Hz) | Actual Frequency (Hz) | Theory Amplitude (V) | Actual Amplitude (V) | Accuracy (%) |
11 | 550 | 549.13 | 8 | 7.71 | 96.365 |
13 | 650 | 650.32 | 5 | 4.77 | 95.4 |
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Wang, G.; Wang, X.; Zhao, C. An Iterative Hybrid Harmonics Detection Method Based on Discrete Wavelet Transform and Bartlett–Hann Window. Appl. Sci. 2020, 10, 3922. https://doi.org/10.3390/app10113922
Wang G, Wang X, Zhao C. An Iterative Hybrid Harmonics Detection Method Based on Discrete Wavelet Transform and Bartlett–Hann Window. Applied Sciences. 2020; 10(11):3922. https://doi.org/10.3390/app10113922
Chicago/Turabian StyleWang, Guishuo, Xiaoli Wang, and Chen Zhao. 2020. "An Iterative Hybrid Harmonics Detection Method Based on Discrete Wavelet Transform and Bartlett–Hann Window" Applied Sciences 10, no. 11: 3922. https://doi.org/10.3390/app10113922
APA StyleWang, G., Wang, X., & Zhao, C. (2020). An Iterative Hybrid Harmonics Detection Method Based on Discrete Wavelet Transform and Bartlett–Hann Window. Applied Sciences, 10(11), 3922. https://doi.org/10.3390/app10113922