A Real-Time Smart Sensor for High-Resolution Frequency Estimation in Power Systems
Abstract
:1. Introduction
2. Theoretical Background
2.1. Chirp-Z Transform
2.2. Power Spectrum Analysis
2.3. CZT Computation Unit
2.4 Computational Complexity Comparison between CZT, FFT, and Zoom-FFT
3. Simulation Results
3.1. Pure periodic signal
3.2. Periodic Signal with White-Noise Contamination
3.3. Periodic Signal plus Harmonic Contamination
3.4. Periodic Signal plus White Noise and Harmonic Contamination
3.5. Simulation of an Instantaneous Jump on the Power Line Frequency
4. Experimental Results
4.1. Power Supply Frequency Measurement
4.2. Frequency Estimation of Digitally Synthesized Functions
4.3. Smart Sensor Linearity
5. Discussion
6. Conclusions
Acknowledgments
References and Notes
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Parameter | FFT | Zoom-FFT | CZT |
---|---|---|---|
N | 65,536 | 65,536 | 512 |
L | -- | 512 | 512 |
Op | 1,048,576 | 655,360 | 262,144 |
Tacq (s) | 100 | 100 | 1 |
Signal + white noise at SNR (dB) | Frequency estimation (Hz) | Error (Hz) | ||
---|---|---|---|---|
Mean (μ) | Standard deviation (σ) | Mean (μ) | Standard deviation (σ) | |
17.0 | 59.9997 | 0.0040 | 0.0003 | 0.0040 |
11.0 | 59.9992 | 0.0066 | 0.0008 | 0.0066 |
7.4 | 60.0007 | 0.0106 | 0.0007 | 0.0106 |
Signal + harmonic | Frequency estimation (Hz) | Error (Hz) | ||
---|---|---|---|---|
Mean (μ) | Standard deviation (σ) | Mean (μ) | Standard deviation (σ) | |
2nd | 60.0000 | 0.0000 | 0.0000 | 0.0000 |
3rd | 60.0000 | 0.0000 | 0.0000 | 0.0000 |
3rd + 5th | 60.0000 | 0.0000 | 0.0000 | 0.0000 |
Signal + white noise and harmonic | Frequency estimation (Hz) | Error (Hz) | ||
---|---|---|---|---|
Mean (μ) | Standard deviation (σ) | Mean (μ) | Standard deviation (σ) | |
2nd | 60.0002 | 0.0042 | 0.0002 | 0.0042 |
3rd | 59.9996 | 0.0032 | 0.0004 | 0.0032 |
3rd + 5th | 59.9999 | 0.0038 | 0.0001 | 0.0038 |
Signal + white noise at SNR (dB) | Frequency estimation (Hz) | Error (Hz) | ||
---|---|---|---|---|
Mean (μ) | Standard deviation (σ) | Mean (μ) | Standard deviation (σ) | |
17.0 | 60.0007 | 0.0034 | 0.0007 | 0.0034 |
11.0 | 60.0001 | 0.0064 | 0.0001 | 0.0064 |
7.4 | 60.0020 | 0.0091 | 0.0020 | 0.0091 |
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Granados-Lieberman, D.; Romero-Troncoso, R.J.; Cabal-Yepez, E.; Osornio-Rios, R.A.; Franco-Gasca, L.A. A Real-Time Smart Sensor for High-Resolution Frequency Estimation in Power Systems. Sensors 2009, 9, 7412-7429. https://doi.org/10.3390/s90907412
Granados-Lieberman D, Romero-Troncoso RJ, Cabal-Yepez E, Osornio-Rios RA, Franco-Gasca LA. A Real-Time Smart Sensor for High-Resolution Frequency Estimation in Power Systems. Sensors. 2009; 9(9):7412-7429. https://doi.org/10.3390/s90907412
Chicago/Turabian StyleGranados-Lieberman, David, Rene J. Romero-Troncoso, Eduardo Cabal-Yepez, Roque A. Osornio-Rios, and Luis A. Franco-Gasca. 2009. "A Real-Time Smart Sensor for High-Resolution Frequency Estimation in Power Systems" Sensors 9, no. 9: 7412-7429. https://doi.org/10.3390/s90907412