FPGA-Based Online PQD Detection and Classification through DWT, Mathematical Morphology and SVD
Abstract
:1. Introduction
2. Mathematical Framework
2.1. Discrete Wavelet Transform
2.2. Mathematical Morphology
2.3. Dilation
2.4. Erosion
2.5. Singular Value Decomposition SVD
2.6. Jacobi Rotations
2.7. Hestenes–Jacobi Algorithm
2.8. Artificial Neural Networks
- (a)
- Since the output can be computed using parallel operations, MLP can be suitable for real-time applications.
- (b)
- MLP can produce coherent results for distinct combinations of inputs for which the network has not been trained (surveillance applications).
- (c)
- Their implementation in hardware is straightforward in terms of conventional pattern recognition methods.
2.9. ANN Architecture
3. Proposed Methodology
4. Experiment Setup
4.1. Numerical Simulation of PQDs
4.2. Benchmark for Real PQD
5. Results
5.1. Hardware Implementation
5.2. Validation of Classification Results
5.3. Numerical Simulation Results
5.4. Experimental Results
5.5. Discussion of Results
6. Conclusions
Acknowledgments
Author Contributions
Conflicts of Interest
References
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Disturbances | Model T ≤ t2 − t1 ≤ 9T | Parameters | Class |
---|---|---|---|
Pure Sine | A | ||
Sag | 0.1 ≤ α ≤ 0.9 | B | |
Swell | 0.1 ≤ α ≤ 0.8. | C | |
Outage | 0.9 ≤ α ≤ 1 | D | |
Harmonic | 0.1 ≤ α3 ≤ 0.2 0.05 ≤ α5 ≤ 0.1 0.1 ≤ α ≤ 0.9 | E | |
Harmonic with sag | F | ||
Harmonic with swell | 0.1 ≤ α3 ≤ 0.2 0.05 ≤ α5 ≤ 0.1 0.1 ≤ α ≤ 0.8 | G | |
High frequency transient | 20 ≤ b ≤ 80 0.1 ≤ λ ≤ 0.2 0.1 ≤ α ≤ 0.9 | H | |
Low frequency transient | 5 ≤ b ≤ 20 0.1 ≤ λ ≤ 0.2 0.1 ≤ α ≤ 0.9 | I |
Resource Utilization | Xilinx Virtex 6 | Altera DE3 |
---|---|---|
Programmable logic | 33% | 34% |
Memory | 43% | 32% |
Multipliers | 36% | 37% |
Max. Oper. frequency | 66 MHz | 77 MHz |
Xilinx Virtex 6 | Altera Stratix-III | Software Implementation Intel Core i7 | |
---|---|---|---|
Feature Extraction | 2.34 ms | 2.01 ms | 4667.30 ms |
ANN Classification | 0.65 ms | 0.56 ms | 12.68 ms |
Total | 2.99 ms | 2.57 ms | 4679.98 ms |
True Class | A | B | C | D | E | F | G | H | I | Accuracy (%) |
---|---|---|---|---|---|---|---|---|---|---|
A | 300 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 100 |
B | 0 | 299 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 99.7 |
C | 0 | 0 | 300 | 0 | 0 | 0 | 0 | 0 | 0 | 100 |
D | 0 | 0 | 0 | 300 | 0 | 0 | 0 | 0 | 0 | 100 |
E | 0 | 0 | 0 | 0 | 299 | 0 | 0 | 0 | 0 | 99.7 |
F | 0 | 0 | 0 | 0 | 0 | 300 | 0 | 0 | 0 | 100 |
G | 0 | 0 | 0 | 0 | 0 | 0 | 300 | 0 | 0 | 100 |
H | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 300 | 0 | 100 |
I | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 300 | 100 |
Overall Success Rate | 99.9 |
True Class | SNR | |||
---|---|---|---|---|
20 dB | 30 dB | 40 dB | 50 dB | |
A | 100 | 100 | 100 | 100 |
B | 99.3 | 100 | 100 | 100 |
C | 100 | 100 | 100 | 100 |
D | 100 | 100 | 100 | 100 |
E | 99.3 | 100 | 100 | 100 |
F | 100 | 100 | 100 | 100 |
G | 100 | 100 | 100 | 100 |
H | 100 | 100 | 100 | 100 |
I | 100 | 100 | 100 | 100 |
Overall | 99.8 | 100 | 100 | 100 |
Class | A | B | C | D | E | F | G | H | I |
---|---|---|---|---|---|---|---|---|---|
FPGA | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 |
% of Effectiveness | Proposed Method | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
True Class | [8] | [19] | [21] | [22] | [45] | [49] | [50] | [51] | [52] | [53] | Numerical | FPGA |
A | --- | 100 | 100 | --- | 100 | 100 | 90 | 100 | --- | 100 | 100 | 100 |
B | 93 | 98 | 88 | 100 | 99 | 100 | 98 | 93 | 93 | 99 | 99 | 100 |
C | --- | 96 | 98 | 98 | 97 | 100 | 99 | 100 | 96 | 100 | 100 | 100 |
D | --- | 100 | 100 | 98 | 100 | 100 | 100 | 99 | 98 | 100 | 100 | 100 |
E | --- | 98 | 93 | --- | 100 | 100 | 90 | 99 | 98 | 100 | 99 | 100 |
F | --- | 98 | 95 | --- | 100 | 83 | 89 | 97 | 95 | 100 | 100 | 100 |
G | --- | 99 | 98 | --- | 99 | 83 | 88 | 98 | 96 | 100 | 100 | 100 |
H | --- | --- | --- | 96 | 100 | 100 | 86 | --- | 94 | 100 | 100 | 100 |
I | --- | --- | --- | --- | 100 | --- | --- | --- | --- | 99 | 100 | 100 |
Overall | 93 | 98 | 96 | 98 | 99 | 96 | 93 | 98 | 96 | 99 | 99 | 100 |
Methodology | Applied Techniques | Analysis Window | Implementation | Elapsed Time |
---|---|---|---|---|
Biscaro et al. [8] | Wavelet transform, multiresolution analysis, signal energy, and fuzzy ANN | 100 ms | PC | 30 ms |
Deokar & Wghmare [19] | Multiresolution signal decomposition, fast Fourier transform, DWT, energy entropy, and decision tree | Not provided | PC | Not Provided |
Dehghani et al. [21] | DWT, and hidden Markov model | Not provided | PC | 1 s |
Liu et al. [22] | Spectral kurtosis, and ANN | Not Provided | PC | Not provided |
Lopez-Ramirez et al. [45] | Empirical mode decomposition, and ANN | 200 ms | PC | 10 ms |
Manikandan et al. [49] | Sparse signal decomposition, and decision tree | 200 ms | PC | 20 ms |
Valtierra-Rodriguez et al. [50] | Fast Fourier transform, ANN, and decision tree | 200 ms | PC | 46.5 ms per analyzed cycle |
Eristi et al. [51] | Wavelet transform, and support vector machine | 266 ms | PC | Not Provided |
Borges et al. [52] | Smart meter signals, decision tree, and ANN | 166 ms | PC | 10 ms |
Khokhar et al. [53] | Wavelet transform, probabilistic neural network, and artificial bee colony | 200 ms | PC | 76.5 ms |
Proposed | DWT, mathematical morphology, SVD, and ANN | 200 ms | Hardware (FPGA) | 2.99 ms |
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Lopez-Ramirez, M.; Cabal-Yepez, E.; Ledesma-Carrillo, L.M.; Miranda-Vidales, H.; Rodriguez-Donate, C.; Lizarraga-Morales, R.A. FPGA-Based Online PQD Detection and Classification through DWT, Mathematical Morphology and SVD. Energies 2018, 11, 769. https://doi.org/10.3390/en11040769
Lopez-Ramirez M, Cabal-Yepez E, Ledesma-Carrillo LM, Miranda-Vidales H, Rodriguez-Donate C, Lizarraga-Morales RA. FPGA-Based Online PQD Detection and Classification through DWT, Mathematical Morphology and SVD. Energies. 2018; 11(4):769. https://doi.org/10.3390/en11040769
Chicago/Turabian StyleLopez-Ramirez, Misael, Eduardo Cabal-Yepez, Luis M. Ledesma-Carrillo, Homero Miranda-Vidales, Carlos Rodriguez-Donate, and Rocio A. Lizarraga-Morales. 2018. "FPGA-Based Online PQD Detection and Classification through DWT, Mathematical Morphology and SVD" Energies 11, no. 4: 769. https://doi.org/10.3390/en11040769