Optimal Selection of Sampling Rates and Mother Wavelet for an Algorithm to Classify Power Quality Disturbances
Abstract
:1. Introduction
2. Discrete Wavelet Transform
3. Support Vector Machine
- Linear:
- Polynomial:
- Sigmoid:
4. Materials and Methods
4.1. Data Generation
4.2. Processing and Feature Extraction
4.3. Training and Prediction
5. Results
6. Discussion
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Abbreviations
PQ | Power Quality |
PQD | Power Quality Disturbance |
FFT | Fast Fourier Transform |
DWT | Discrete Wavelet Transform |
ST | Stockwell Transform |
TTT | Time-Time Transform |
DT | Decision Tree |
SVM | Support Vector Machine |
RFC | Random Forest Classifier |
ELM | Modular Probabilistic Neural Network |
STFT | Short-Time Fourier Transform |
LSTM | Long Short-Term Memory |
OAA | One-Against-All |
OAO | One-Against-One |
SNR | Signal-to-Noise Ratio |
Sampling Rate | |
WGN | White Gaussian Noise |
GAN | Generative Adversarial Network |
WT | Wavelet Transform |
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Name | Class | Mathematical Model | Parameters |
---|---|---|---|
Normal | C1 | ||
Sag | C2 | ||
Transient Oscillation | C3 | ||
Swell | C4 | ||
Flicker | C5 | ||
Interruption | C6 | ||
Notch | C7 | ||
Feature | Equation | Feature | Equation |
---|---|---|---|
Mean (1) | Root Mean Square (2) | ||
Standard Deviation (3) | Symmetry (4) | ||
Kurtosis (5) | Variance (6) | ||
Energy (7) |
(kHz) | DWT Level | Levels Removed | Noise Level (SNR) | Comb. | Success % | DWT Level | Levels Removed | Noise Level (SNR) | Comb. | Success % |
---|---|---|---|---|---|---|---|---|---|---|
3.2 | 5 | - | - | 1, 3, 4, 5, 6 | 97.44 | 7 | 1 | 50 | 2, 4, 5, 6 | 94.02 |
5 | 6 | - | - | 1, 2, 3, 4, 5, 6 | 96.18 | 7 | 1 | 50 | 1, 3, 5, 6 | 93.14 |
6.4 | 6 | - | - | 3, 4, 5, 6 | 98.95 | 7 | 1 | 50 | 1, 2, 3, 4, 5, 6 | 95.42 |
8 | 7 | - | - | 1, 2, 3, 4, 5, 6 | 97.49 | 4 | 2 | 50 | 3, 5, 6 | 94.85 |
9.6 | 5 | - | - | 1, 5, 6 | 99.90 | 5 | 2 | 50 | 3, 5, 6 | 95.79 |
15 | 7 | - | - | 1, 3, 4, 5, 6 | 97.39 | 5 | 1 | 50 | 1, 3, 4, 5, 6 | 94.49 |
20 | 7 | - | - | 1, 2, 3, 5, 6 | 97.04 | 5 | 2 | 50 | 3, 4, 5, 6 | 95.11 |
30 | 7 | - | - | 4, 5, 6 | 97.54 | 6 | 1 | 50 | 3, 5, 6 | 96.00 |
3.2 | 7 | - | 30 | 3, 4, 5, 6 | 91.58 | 7 | 1 | 40 | 1, 2, 4, 5, 6 | 93.55 |
5 | 6 | - | 30 | 2, 4, 5, 6 | 90.02 | 7 | - | 40 | 2, 3, 4, 5, 6 | 91.89 |
6.4 | 7 | - | 30 | 1, 2, 3, 5, 6 | 92.56 | 7 | - | 40 | 1, 2, 3, 4, 5, 6 | 94.49 |
8 | 7 | 1 | 30 | 1, 2, 3, 5, 6 | 93.66 | 7 | 2 | 40 | 1, 3, 5, 6 | 94.49 |
9.6 | 7 | 2 | 30 | 1, 2, 4, 5, 6 | 91.78 | 7 | 2 | 40 | 3, 4, 5, 6 | 92.98 |
15 | 7 | 3 | 30 | 1, 4, 5, 6 | 92.82 | 7 | 3 | 40 | 1, 2, 4, 5, 6 | 94.23 |
20 | 5 | 3 | 30 | 1, 3, 5, 6 | 92.67 | 7 | 3 | 40 | 1, 3, 5, 6 | 94.02 |
30 | 6 | 3 | 30 | 1, 2, 3, 4, 5, 6 | 94.23 | 6 | 3 | 40 | 3, 4, 5, 6 | 95.11 |
(kHz) | SNR | Mother Wavelet | DWT Level | Levels Removed | Comb. | Success Rate | Run-Time (s) | |||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
AVG | C1 | C2 | C3 | C4 | C5 | C6 | C7 | |||||||
3.2 | - | dmey | 5 | - | 1, 3, 4, 5, 6 | 97.4 | 94.7 | 96.7 | 99.7 | 98.6 | 100 | 91.8 | 100 | 239 |
5 | - | db28 | 6 | - | 1, 2, 3, 4, 5, 6 | 96.2 | 93.1 | 93.9 | 100 | 97.6 | 100 | 88.4 | 99.7 | 277 |
6.4 | - | dmey | 6 | - | 3, 4, 5, 6 | 98.9 | 100 | 97.5 | 100 | 100 | 100 | 95 | 99.7 | 294 |
8 | - | bior4.4 | 7 | - | 1, 2, 3, 4, 5, 6 | 98.3 | 95.1 | 96.5 | 99.7 | 100 | 100 | 96.8 | 100 | 212 |
9.6 | - | dmey | 5 | - | 1, 5, 6 | 99.9 | 100 | 100 | 100 | 100 | 100 | 99.6 | 99.7 | 323 |
15 | - | dmey | 7 | - | 1, 3, 4, 5, 6 | 97.4 | 93.7 | 96.2 | 99.7 | 100 | 100 | 91.5 | 100 | 445 |
20 | - | dmey | 7 | - | 1, 2, 3, 5, 6 | 97 | 91.6 | 97.3 | 100 | 100 | 99.3 | 90.8 | 100 | 527 |
30 | - | db28 | 7 | - | 4, 5, 6 | 99.6 | 98.6 | 100 | 100 | 100 | 100 | 98.8 | 99.7 | 661 |
3.2 | 50 | bior4.4 | 7 | 1 | 2, 4, 5, 6 | 94.3 | 80.6 | 94.7 | 100 | 97.9 | 100 | 90.3 | 100 | 314 |
5 | rbio3.1 | 7 | 1 | 1, 3, 5, 6 | 93.9 | 82.3 | 97.3 | 100 | 99.3 | 97.7 | 85.7 | 99.3 | 306 | |
6.4 | dmey | 7 | 1 | 1, 2, 3, 4, 5, 6 | 95.4 | 84.8 | 96.7 | 100 | 97.9 | 100 | 90.6 | 100 | 544 | |
8 | dmey | 4 | 2 | 3, 5, 6 | 94.9 | 86.9 | 97 | 100 | 97.2 | 96.9 | 88.3 | 100 | 387 | |
9.6 | dmey | 5 | 2 | 3, 5, 6 | 95.8 | 86.7 | 97.5 | 100 | 99.3 | 99.2 | 89.9 | 100 | 401 | |
15 | dmey | 5 | 1 | 1, 3, 4, 5, 6 | 94.5 | 83.7 | 95.4 | 100 | 97.5 | 98.8 | 88.8 | 100 | 477 | |
20 | dmey | 5 | 2 | 3, 4, 5, 6 | 95.1 | 86.8 | 98.3 | 100 | 97.9 | 96.2 | 89.1 | 100 | 399 | |
30 | dmey | 6 | 1 | 3, 5, 6 | 96 | 88.4 | 97.2 | 100 | 98 | 98.5 | 91.4 | 100 | 482 | |
3.2 | 40 | dmey | 7 | 1 | 1, 2, 4, 5, 6 | 93.6 | 76.6 | 95.4 | 100 | 99.6 | 98.5 | 90.7 | 100 | 566 |
5 | rbio3.1 | 7 | - | 2, 3, 4, 5, 6 | 93.2 | 80.1 | 97.2 | 100 | 99.3 | 96.3 | 85.7 | 99.3 | 435 | |
6.4 | db28 | 7 | - | 1, 2, 3, 4, 5, 6 | 94.7 | 83.4 | 95 | 100 | 98.6 | 100 | 88.6 | 100 | 698 | |
8 | rbio3.1 | 7 | 2 | 1, 3, 5, 6 | 95.4 | 86.8 | 96.6 | 100 | 97.4 | 99.6 | 89.5 | 99.6 | 233 | |
9.6 | dmey | 7 | 2 | 3, 4, 5, 6 | 93 | 85 | 92.2 | 100 | 91.8 | 97 | 86.8 | 99.6 | 477 | |
15 | dmey | 7 | 3 | 1, 2, 4, 5, 6 | 94.2 | 81.2 | 96 | 100 | 98.9 | 100 | 87.6 | 100 | 448 | |
20 | dmey | 7 | 3 | 1, 3, 5, 6 | 94 | 82.6 | 96.4 | 100 | 98.2 | 98.5 | 86.3 | 100 | 449 | |
30 | dmey | 6 | 3 | 3, 4, 5, 6 | 95.1 | 84 | 98.7 | 100 | 98.2 | 99.2 | 88.9 | 100 | 384 | |
3.2 | 30 | db4 | 7 | - | 3, 4, 5, 6 | 91.9 | 76.4 | 91.2 | 100 | 97.8 | 97 | 86.1 | 100 | 443 |
5 | rbio3.1 | 6 | - | 2, 4, 5, 6 | 93 | 79.8 | 96.4 | 100 | 97.9 | 98.1 | 86.4 | 97.4 | 429 | |
6.4 | rbio3.1 | 7 | - | 1, 2, 3, 5, 6 | 93.7 | 79.9 | 99.5 | 100 | 97.9 | 99.2 | 86.4 | 98.5 | 434 | |
8 | rbio3.1 | 7 | 1 | 1, 2, 3, 5, 6 | 94.6 | 84.4 | 95 | 100 | 97.6 | 99.2 | 88.5 | 99.6 | 300 | |
9.6 | bior4.4 | 7 | 2 | 1, 2, 4, 5, 6 | 93.2 | 79.8 | 91.2 | 99.6 | 97.1 | 99.2 | 89.6 | 99.3 | 256 | |
15 | dmey | 7 | 3 | 1, 4, 5, 6 | 92.8 | 78.3 | 92.1 | 100 | 98.6 | 98.9 | 86.5 | 99.6 | 439 | |
20 | db4 | 5 | 3 | 1, 3, 5, 6 | 93.9 | 86.8 | 94.1 | 100 | 95.3 | 96.6 | 86.7 | 100 | 146 | |
30 | bior4.4 | 6 | 3 | 1, 2, 3, 4, 5, 6 | 95.2 | 86.4 | 97.9 | 100 | 99.3 | 97.7 | 88.2 | 99.6 | 208 |
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Medina-Molina, J.A.; Reyes-Archundia, E.; Gutiérrez-Gnecchi, J.A.; Rodríguez-Herrejón, J.A.; Chávez-Báez, M.V.; Olivares-Rojas, J.C.; Guerrero-Rodríguez, N.F. Optimal Selection of Sampling Rates and Mother Wavelet for an Algorithm to Classify Power Quality Disturbances. Computers 2025, 14, 138. https://doi.org/10.3390/computers14040138
Medina-Molina JA, Reyes-Archundia E, Gutiérrez-Gnecchi JA, Rodríguez-Herrejón JA, Chávez-Báez MV, Olivares-Rojas JC, Guerrero-Rodríguez NF. Optimal Selection of Sampling Rates and Mother Wavelet for an Algorithm to Classify Power Quality Disturbances. Computers. 2025; 14(4):138. https://doi.org/10.3390/computers14040138
Chicago/Turabian StyleMedina-Molina, Jonatan A., Enrique Reyes-Archundia, José A. Gutiérrez-Gnecchi, Javier A. Rodríguez-Herrejón, Marco V. Chávez-Báez, Juan C. Olivares-Rojas, and Néstor F. Guerrero-Rodríguez. 2025. "Optimal Selection of Sampling Rates and Mother Wavelet for an Algorithm to Classify Power Quality Disturbances" Computers 14, no. 4: 138. https://doi.org/10.3390/computers14040138
APA StyleMedina-Molina, J. A., Reyes-Archundia, E., Gutiérrez-Gnecchi, J. A., Rodríguez-Herrejón, J. A., Chávez-Báez, M. V., Olivares-Rojas, J. C., & Guerrero-Rodríguez, N. F. (2025). Optimal Selection of Sampling Rates and Mother Wavelet for an Algorithm to Classify Power Quality Disturbances. Computers, 14(4), 138. https://doi.org/10.3390/computers14040138