Global Harmonic Parameters for Estimation of Power Quality Indices: An Approach for PMUs
Abstract
:1. Introduction
2. Theoretical Background
2.1. Fundamental Phasor Estimation Model
2.2. Power Quality Index
3. HPMU and GHPs
4. Validation and Results
4.1. Study Case 1: Evaluation of PQIs
4.2. Study Case 2: Synthetic Signals
4.3. Study Case 3: Real Signals
5. Conclusions
Funding
Acknowledgments
Conflicts of Interest
Appendix A
Phasor Harmonic Components (Option 1: Magnitude and Phase of Each Harmonic for h = 1 to 50) | |||||
---|---|---|---|---|---|
Stage 1 | Stage 2 | Stage 3 | Stage 4 | Stage 5 | |
Ideal, P-Class, M-Class EP-class, EM-class | Ideal, P-Class, M-Class EP-class, EM-class | Ideal, P-Class, M-Class EP-class, EM-class | Ideal, P-Class, M-Class EP-class, EM-class | Ideal, P-Class, M-Class EP-class, EM-class | |
Mv1 | 127.0, 127.000, 127.001, 4.3 × 10−6, 8.0 × 10−4 | 127.0, 127.000, 127.001, 1.8 × 10−9, 8.0 × 10−4 | 127.0, 127.000, 127.001, 8.7 × 10−11, 8.0 × 10−4 | 127.0, 127.000, 127.001, 6.3 × 10−12, 8.0 × 10−4 | 127.0, 126.989, 127.001, 8.9 × 10−3, 5.2 × 10−4 |
Mv2 | 10.0, 10.000, 10.001, 2.9 × 10−4, 1.3 × 10−2 | 10.0, 10.000, 10.001, 1.7 × 10−7, 1.3 × 10−2 | 10.0, 10.000, 10.001, 8.4 × 10−9, 1.3 × 10−2 | 10.0, 10.000, 10.001, 6.5 × 10−10, 1.3 × 10−2 | 10.0, 9.908, 10.009, 9.2 × 10−1, 8.7 × 10−2 |
Mv3 | 8.0, 8.000, 7.999, 9.6 × 10−4, 8.1 × 10−3 | 8.0, 8.000, 7.999, 7.3 × 10−7, 9.0 × 10−3 | 8.0, 8.000, 7.999, 3.6 × 10−8, 9.0 × 10−3 | 8.0, 8.000, 7.999, 1.8 × 10−9, 9.0 × 10−3 | 8.0, 8.085, 8.000, 1.1, 2.4 × 10−3 |
Mv5 | 6.0, 6.000, 6.000, 7.8 × 10−4, 2.5 × 10−6 | 6.0, 6.000, 6.000, 5.2 × 10−7, 1.4 × 10−6 | 6.0, 6.000, 6.000, 2.5 × 10−8, 1.4 × 10−6 | 6.0, 6.000, 6.000, 1.3 × 10−9, 1.4 × 10−6 | 6.0, 5.912, 6.000, 1.5, 2.1 × 10−3 |
Mv40 | 4.0, 4.000, 4.000, 2.4 × 10−5, 1.5 × 10−4 | 4.0, 4.000, 4.000, 1.1 × 10−9, 6.1 × 10−7 | 4.0, 4.000, 4.000, 1.0 × 10−10, 6.1 × 10−7 | 4.0, 4.000, 4.000, 1.7 × 10−10, 6.1 × 10−7 | 4.0, 4.000, 4.000, 3.9 × 10−3, 5.8 × 10−3 |
Fv1 | 5.0, 5.000, 5.000, 4.3 × 10−3, 2.5 × 10−3 | 5.0, 5.000, 5.000, 2.1 × 10−6, 5.3 × 10−4 | 5.0, 5.000, 5.000, 1.0 × 10−7, 5.3 × 10−4 | 5.0, 5.000, 5.000, 4.9 × 10−9, 5.3 × 10−4 | 139.91, 139.880, 139.91, 2.1 × 10−2, 3.1 × 10−4 |
Fv2 | 30.0, 30.001, 29.997, 3.0 × 10−3, 8.6 × 10−3 | 30.0, 30.000, 29.997, 7.6 × 10−7, 9.0 × 10−3 | 30.0, 30.000, 29.997, 3.9 × 10−8, 9.0 × 10−3 | 30.0, 30.000, 29.997, 1.8 × 10−9, 9.0 × 10−3 | 299.82, 300.024, 299.84, 6.8 × 10−2, 6.2 × 10−3 |
Fv3 | 45.0, 45.001, 45.004, 1.2 × 10−3, 9.8 × 10−3 | 45.0, 45.000, 45.004, 1.2 × 10−6, 8.8 × 10−3 | 45.0, 45.000, 45.004, 5.8 × 10−8, 8.8 × 10−3 | 45.0, 45.000, 45.004, 2.8 × 10−9, 8.8 × 10−3 | 89.73, 89.859, 89.726, 1.4 × 10−1, 4.6 × 10−3 |
Fv5 | 315.0, 314.999, 314.998, 2.8 × 10−4, 5.3 × 10−4 | 315.0, 315.000, 314.999, 1.2 × 10−7, 4.3 × 10−4 | 315.0, 315.000, 314.999, 5.9 × 10−9, 4.3 × 10−4 | 315.0, 315.000, 314.999, 2.8 × 10−10, 4.3 × 10−4 | 269.55, 269.265, 269.547, 1.1 × 10−1, 1.2 × 10−3 |
Fv40 | 115.0, 114.992, 114.999, 7.2 × 10−3, 2.0 × 10−3 | 115.0, 115.000, 115.000, 4.5 × 10−6, 1.3 × 10−6 | 115.0, 115.000, 115.000, 4.0 × 10−8, 7.9 × 10−8 | 115.0, 115.000, 115.000, 1.4 × 10−9, 6.5 × 10−8 | 111.4, 111.413, 111.376, 1.2 × 10−2, 2.2 × 10−2 |
Mi1 | 25.0, 25.000, 25.000, 3.6 × 10−5, 4.4 × 10−4 | 25.0, 25.000, 25.000, 1.6 × 10−8, 7.0 × 10−4 | 60.0, 60.000, 60.000, 1.1 × 10−9, 5.6 × 10−4 | 60.0, 60.000, 60.000, 6.3 × 10−11, 1.8 × 10−4 | 60.0, 59.964, 60.001, 6.0 × 10−2, 1.1 × 10−3 |
Mi2 | 0.0, 0.000, 0.000, 4.5 × 10−5, 2.5 × 10−4 | 15.0, 15.000, 15.000, 2.3 × 10−8, 2.4 × 10−3 | 15.0, 15.000, 15.001, 3.5 × 10−9, 4.7 × 10−3 | 15.0, 15.000, 15.001, 2.7 × 10−10, 4.3 × 10−3 | 15.0, 14.998, 15.002, 1.0 × 10−2, 1.4 × 10−2 |
Mi3 | 0.0, 0.000, 0.000, 3.3 × 10−5, 1.9 × 10−4 | 12.5, 12.500, 12.500, 4.7 × 10−8, 2.2 × 10−4 | 12.5, 12.500, 12.500, 8.4 × 10−9, 2.2 × 10−3 | 12.5, 12.500, 12.500, 6.3 × 10−10, 1.9 × 10−3 | 12.5, 12.485, 12.501, 1.2 × 10−1, 7.1 × 10−3 |
Mi5 | 0.0, 0.000, 0.000, 6.6 × 10−6, 1.0 × 10−5 | 10.0, 10.000, 10.000, 3.5 × 10−7, 5.6 × 10−4 | 10.0, 10.000, 10.000, 2.0 × 10−8, 5.8 × 10−4 | 10.0, 10.000, 10.000, 8.8 × 10−10, 5.6 × 10−4 | 10.0, 10.000, 10.000, 2.0 × 10−3, 1.6 × 10−3 |
Mi40 | 0.0, 0.000, 0.000, 2.6 × 10−6, 7.0 × 10−6 | 7.5, 7.500, 7.500, 1.5 × 10−8, 2.2 × 10−7 | 7.5, 7.500, 7.500, 3.3 × 10−10, 2.2 × 10−7 | 7.5, 7.500, 7.500, 2.9 × 10−11, 1.2 × 10−7 | 7.5, 7.500, 7.501, 4.2 × 10−3, 6.1 × 10−3 |
Fi1 | 30.0, 30.000, 30.000, 7.0 × 10−4, 1.5 × 10−3 | 30.0, 30.000, 30.000, 2.7 × 10−7, 1.3 × 10−3 | 30.0, 30.000, 30.000, 1.5 × 10−8, 1.2 × 10−3 | 45.0, 45.000, 45.000, 4.4 × 10−10, 1.0 × 10−3 | 179.91, 179.918, 179.909, 4.6 × 10−3, 8.1 × 10−4 |
Fi2 | 0.0, 141.850, 26.827, 141.850, 26.827 | 25.0, 25.000, 25.000, 3.9 × 10−7, 7.9 × 10−5 | 25.0, 25.000, 25.000, 5.5 × 10−9, 1.5 × 10−4 | 25.0, 25.000, 25.000, 3.3 × 10−10, 1.5 × 10−3 | 294.82, 294.807, 294.832, 4.4 × 10−3, 3.9 × 10−3 |
Fi3 | 0.0, 136.730, 210.995, 136.730, 210.995 | 20.0, 20.000, 20.000, 5.8 × 10−7, 7.4 × 10−4 | 20.0, 20.000, 20.000, 5.7 × 10−9, 1.2 × 10−3 | 20.0, 20.000, 19.999, 8.7 × 10−11, 3.7 × 10−3 | 64.73, 64.714, 64.731, 2.5 × 10−2, 8.7 × 10−4 |
Fi5 | 0.0, 135.180, 168.677, 135.180, 168.677 | 270.0, 270.000, 269.999, 1.8 × 10−7, 3.8 × 10−4 | 270.0, 270.000, 269.999, 9.5 × 10−9, 4.1 × 10−4 | 270.0, 270.000, 269.999, 4.8 × 10−10, 4.0 × 10−4 | 224.55, 224.586, 224.548, 1.6 × 10−2, 1.0 × 10−3 |
Fi40 | 0.0, 174.440, 49.656, 174.440, 49.656 | 0.0, 0.000, 0.001, 5.4 × 10−7, 6.4 × 10−4 | 0.0, 0.000, 0.001, 2.7 × 10−8, 6.9 × 10−4 | 0.0, 0.000, 0.001, 1.4 × 10−9, 7.1 × 10−4 | 356.4, 356.418, 356.3797, 5.0 × 10−3, 5.7 × 10−3 |
frec | 60.0, 59.999, 59.999, 1.0 × 10−3, 1.0 × 10−3 | 60.0, 60.000, 60.000, 9.6 × 10−7, 9.6 × 10−7 | 60.0, 60.000, 60.000, 4.7 × 10−8, 4.7 × 10−8 | 60.0, 60.000, 60.000, 2.2 × 10−9, 2.2 × 10−9 | 61.50, 61.502, 61.502, 3.4 × 10−3, 3.4 × 10−3 |
Global harmonic parameters (Option 2: GHP with fundamental parameters Mv1, Mi1, Fv1 and Fi1) | |||||
RMSHV | 14.697, 14.697, 14.697, 3.3 × 10−4, 3.8 × 10−3 | 14.697, 14.697, 14.697, 2.3 × 10−7, 3.4 × 10−3 | 14.697, 14.697, 14.697, 1.1 × 10−8, 3.4 × 10−3 | 14.697, 14.697, 14.697, 6.8 × 10−10, 3.4 × 10−3 | 14.697, 14.629, 14.703, 4.6 × 10−1, 4.1 × 10−2 |
RMSHI | 0.0, 0.000, 0.000, 5.7 × 10−5, 3.2 × 10−4 | 23.184, 23.184, 23.184, 5.9 × 10−8, 1.0 × 10−3 | 23.184, 23.184, 23.184, 6.1 × 10−9, 1.4 × 10−3 | 23.184, 23.184, 23.184, 4.0 × 10−10, 1.4 × 10−3 | 23.184, 23.175, 23.186, 3.8 × 10−2, 8.3 × 10−3 |
HAPF | 0.0, −0.250, 0.198, 2.5 × 10−1, 2.0 × 10−1 | 0.792, 0.792, 0.792, 2.2 × 10−7, 4.3 × 10−4 | 0.792, 0.792, 0.792, 9.5 × 10−9, 5.2 × 10−4 | 0.792, 0.792, 0.792, 5.3 × 10−10, 4.0 × 10−4 | 0.792, 0.792, 0.792, 3.9 × 10−2, 1.1 × 10−2 |
PQIs for Both Option | |||||
---|---|---|---|---|---|
Stage 1 | Stage 2 | Stage 3 | Stage 4 | Stage 5 | |
Ideal, P-Class, M-Class EP-class, EM-class | Ideal, P-Class, M-Class EP-class, EM-class | Ideal, P-Class, M-Class EP-class, EM-class | Ideal, P-Class, M-Class EP-class, EM-class | Ideal, P-Class, M-Class EP-class, EM-class | |
RMSV | 127.848, 127.848, 127.849, 6.5 × 10−8, 8.4 × 10−4 | 127.848, 127.848, 127.849, 1.3 × 10−9, 8.4 × 10−4 | 127.848, 127.848, 127.849, 6.5 × 10−11, 8.4 × 10−4 | 127.848, 127.848, 127.849, 3.1 × 10−12, 8.4 × 10−4 | 127.848, 127.828, 127.849, 1.5 × 10−2, 1.1 × 10−3 |
RMSI | 25.0, 25.000, 25.000, 3.6 × 10−5, 4.4 × 10−4 | 34.095, 34.095, 34.096, 3.6 × 10−8, 8.6 × 10−4 | 64.323, 64.323, 64.324, 1.7 × 10−9, 6.8 × 10−4 | 64.323, 64.323, 64.324, 1.1 × 10−10, 3.4 × 10−4 | 64.323, 64.287, 64.325, 5.7 × 10−2, 2.1 × 10−3 |
THDV | 11.572, 11.572, 11.573, 3.3 × 10−4, 3.0 × 10−3 | 11.572, 11.572, 11.573, 2.3 × 10−7, 2.6 × 10−3 | 11.572, 11.572, 11.573, 1.2 × 10−8, 2.6 × 10−3 | 11.572, 11.572, 11.573, 6.8 × 10−10, 2.6 × 10−3 | 11.572, 11.520, 11.577, 4.6 × 10−1, 4.1 × 10−2 |
THDI | 0.0, 0.000, 0.001, 2.3 × 10−4, 1.3 × 10−3 | 92.736, 92.736, 92.737, 4.3 × 10−8, 3.5 × 10−4 | 38.640, 38.640, 38.640, 5.1 × 10−9, 8.7 × 10−4 | 38.640, 38.640, 38.641, 3.3 × 10−10, 1.2 × 10−3 | 38.640, 38.649, 38.643, 2.2 × 10−2, 7.1 × 10−3 |
ST | 3196.189, 3196.188, 3196.230, 3.6 × 10−5, 1.3 × 10−3 | 4359.021, 4359.021, 4359.095, 3.4 × 10−8, 1.7 × 10−3 | 8223.590, 8223.590, 8223.715, 1.6 × 10−9, 1.5 × 10−3 | 8223.590, 8223.590, 8223.687, 1.0 × 10−10, 1.2 × 10−3 | 8223.590, 8217.705, 8223.846, 7.2 × 10−2, 3.1 × 10−3 |
PF | 2877.527, 2877.526, 2877.570, 4.4 × 10−5, 1.5 × 10−3 | 2877.527, 2877.527, 2877.579, 3.5 × 10−8, 1.8 × 10−3 | 6906.065, 6906.065, 6906.179, 1.6 × 10−9, 1.6 × 10−3 | 5837.259, 5837.259, 5837.354, 1.4 × 10−10, 1.6 × 10−3 | 5837.259, 5830.016, 5837.442, 1.2 × 10−1, 3.1 × 10−3 |
QF | −1341.813, −1341.813, −1341.814, −2.2 × 10−5, −4.5 × 10−5 | −1341.813, −1341.813, −1341.815, −6.4 × 10−8, −1.5 × 10−4 | −3220.351, −3220.351, −3220.354, −1.0 × 10−9, −9.6 × 10−5 | −4898.042, −4898.042, −4898.045, −2.8 × 10−11, −7.3 × 10−5 | −4898.042, −4898.561, −4898.019, −1.1 × 10−2, −4.6 × 10−4 |
SF | 3175, 3174.999, 3175.039, 4.0 × 10−5, 1.2 × 10−3 | 3175.0, 3175.000, 3175.048, 1.8 × 10−8, 1.5 × 10−3 | 7620.0, 7620.000, 7620.104, 1.1 × 10−9, 1.4 × 10−3 | 7620.0, 7620.000, 7620.075, 6.9 × 10−11, 9.9 × 10−4 | 7620.0, 7614.787, 7620.126, 6.8 × 10−2, 1.6 × 10−3 |
SN | 367.423, 367.425, 367.439, 2.9 × 10−4, 4.2 × 10−3 | 2986.710, 2986.710, 2986.767, 5.3 × 10−8, 1.9 × 10−3 | 3092.416, 3092.416, 3092.491, 4.7 × 10−9, 2.4 × 10−3 | 3092.416, 3092.416, 3092.488, 3.1 × 10−10, 2.3 × 10−3 | 3092.416, 3089.610, 3092.787, 9.1 × 10−2, 1.2 × 10−2 |
DI | 0.0, 0.007, 0.040, 7.2 × 10−3, 4.0 × 10−2 | 2944.374, 2944.374, 2944.428, 6.1 × 10−8, 1.8 × 10−3 | 2944.374, 2944.374, 2944.440, 6.2 × 10−9, 2.2 × 10−3 | 2944.374, 2944.374, 2944.438, 4.0 × 10−9, 2.2 × 10−3 | 2944.374, 2943.005, 2944.633, 4.6 × 10−2, 8.8 × 10−3 |
DV | 367.423, 367.425, 367.439, 2.9 × 10−4, 4.2 × 10−3 | 367.423, 367.423, 367.439, 2.2 × 10−7, 4.1 × 10−3 | 881.816, 881.816, 881.852, 1.0 × 10−8, 4.0 × 10−3 | 881.816, 881.816, 881.848, 6.2 × 10−10, 3.6 × 10−3 | 881.816, 877.196, 882.189, 5.2 × 10−1, 4.2 × 10−2 |
SH | 0.0, 0.001, 0.005, 8.3 × 10−4, 4.7 × 10−3 | 340.735, 340.735, 340.750, 1.7 × 10−7, 4.5 × 10−3 | 340.735, 340.735, 340.751, 5.3 × 10−9, 4.9 × 10−3 | 340.735, 340.735, 340.751, 2.9 × 10−10, 4.8 × 10−3 | 340.735, 339.024, 340.903, 5.0 × 10−1, 4.9 × 10−2 |
PH | 0.0, 0.000, 0.001, 2.1 × 10−4, 9.2 × 10−4 | 269.808, 269.808, 269.821, 4.9 × 10−8, 4.9 × 10−3 | 269.808, 269.808, 269.822, 4.1 × 10−9, 5.4 × 10−3 | 269.808, 269.808, 269.822, 2.4 × 10−10, 5.2 × 10−3 | 269.808, 268.558, 269.971, 4.6 × 10−1, 6.1 × 10−2 |
DH | 0.0, 0.001, 0.005, 8.1 × 10−4, 4.6 × 10−3 | 208.095, 208.095, 208.103, 5.5 × 10−7, 3.8 × 10−3 | 208.095, 208.095, 208.104, 2.1 × 10−8, 4.0 × 10−3 | 208.095, 208.095, 208.104, 1.2 × 10−9, 4.1 × 10−3 | 208.095, 206.914, 208.159, 5.7 × 10−1, 3.0 × 10−2 |
P | 2877.527, 2877.526, 2877.571, 5.1 × 10−5, 1.5 × 10−3 | 3147.335, 3147.335, 3147.400, 3.6 × 10−8, 2.1 × 10−3 | 7175.873, 7175.873, 7176.001, 1.7 × 10−9, 1.8 × 10−3 | 6107.066, 6107.066, 6107.176, 1.4 × 10−10, 1.8 × 10−3 | 6107.066, 6098.574, 6107.413, 1.4 × 10−1, 5.7 × 10−3 |
N | 1391.209, 1391.209, 1391.212, 3.1 × 10−5, 2.0 × 10−4 | 3015.849, 3015.849, 3015.888, 3.2 × 10−8, 1.3 × 10−3 | 4016.750, 4016.750, 4016.776, 1.5 × 10−9, 6.5 × 10−4 | 5507.375, 5507.375, 5507.398, 5.5 × 10−11, 4.2 × 10−4 | 5507.375, 5508.001, 5507.373, 1.1 × 10−2, 3.2 × 10−5 |
PF1 | 0.906, 0.906, 0.906, 3.9 × 10−6, 2.6 × 10−4 | 0.906, 0.906, 0.906, 1.8 × 10−8, 2.9 × 10−4 | 0.906, 0.906, 0.906, 4.7 × 10−10, 2.8 × 10−4 | 0.766, 0.766, 0.766, 6.8 × 10−11, 6.4 × 10−4 | 0.766, 0.766, 0.766, 5.6 × 10−2, 1.5 × 10−3 |
PF | 0.900, 0.900, 0.900, 1.6 × 10−5, 2.5 × 10−4 | 0.722, 0.722, 0.722, 1.9 × 10−9, 3.7 × 10−4 | 0.873, 0.873, 0.873, 5.8 × 10−11, 2.7 × 10−4 | 0.743, 0.743, 0.743, 3.9 × 10−11, 6.1 × 10−4 | 0.743, 0.742, 0.743, 6.8 × 10−2, 2.6 × 10−3 |
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Classical Formulation | GHPs-Based Formulation |
---|---|
True RMS value of Voltage (RMSV) and Current (RMSI) | |
Total Harmonic Distortion of Voltage (THDV) and Current (THDI) | |
Total Apparent Power (ST) | |
Fundamental Real Power (PF) | |
Fundamental Active Power (QF) | |
Fundamental Apparent Power (SF) | |
Non-60 Hz or Nonfundamental Apparent Power (SN) | |
Current Distortion Power (DI) | |
Voltage Distortion Power (DV) | |
Harmonic Apparent Power (SH) | |
Harmonic Real Power (PH) | |
Harmonic Distortion Power (DH) | |
Active Power Total (PT) | |
Non Active Power (N) | |
Power Factor (PFF) | |
Total Power Factor (PFT) | |
Voltage Components | Current Components | ||
---|---|---|---|
V1 /θ1 | √2·100 V/0° | I1 /φ1 | √2·100 A/30° |
V3 /θ3 | √2·8 V/−70° | I3 /φ3 | √2·20 A/165° |
V5 /θ5 | √2·15 V/140° | I5 /φ5 | √2·15 A/233° |
V7 /θ7 | √2·5 V/20° | I7 /φ7 | √2·10 A/−72° |
PQI | Option 1 | Option 2 | PQI | Option 1 | Option 2 |
---|---|---|---|---|---|
RMSV | 101.56 V | 101.56 V | DI | 2692.6 VAR | 2692.6 VAR |
RMSI | 103.56 A | 103.56 A | DV | 1772.0 VAR | 1772.0 VAR |
THDV | 17.72 % | 17.72 % | SH | 477.13 VA | 477.13 VA |
THDI | 26.93 % | 26.93 % | PH | −27.47 W | −27.47 W |
ST | 10517.5 VA | 10517.5 VA | DH | 476.34 VAR | 476.34 VAR |
PF | 8660.3 W | 8660.3 W | PT | 8632.8 W | 8632.8 W |
QF | 5000 VAR | 5000 VAR | N | 6007.7 VAR | 6007.7 VAR |
SF | 10000 VA | 10000 VA | PFF | 0.87 | 0.87 |
SN | 3258.5 VA | 3258.5 VA | PFT | 0.82 | 0.82 |
Stages for v(t) | f | V1/θ1 | V2/θ2 | V3/θ3 | V5/θ5 | V40/θ7 |
---|---|---|---|---|---|---|
1,2,3,4 | 60 Hz | 127 V/5° | 10 V/30° | 8 V/45° | 6 V/−45° | 4 V/115° |
5 | 61.5 Hz | |||||
Stages for i(t) | F | I1 /ϕ1 | I2 /ϕ2 | I3 /ϕ3 | I5 /ϕ5 | I40 /ϕ7 |
1 | 60 Hz | 25A/35° | 0 | |||
2 | 25A/35° | 15 A/25° | 12.5 A/20° | 10 A/−90° | 7.5 A/0° | |
3 | 60A/35° | |||||
4 | 60A/115° | |||||
5 | 61.5 Hz | 60A/115° |
© 2020 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
Share and Cite
Granados-Lieberman, D. Global Harmonic Parameters for Estimation of Power Quality Indices: An Approach for PMUs. Energies 2020, 13, 2337. https://doi.org/10.3390/en13092337
Granados-Lieberman D. Global Harmonic Parameters for Estimation of Power Quality Indices: An Approach for PMUs. Energies. 2020; 13(9):2337. https://doi.org/10.3390/en13092337
Chicago/Turabian StyleGranados-Lieberman, David. 2020. "Global Harmonic Parameters for Estimation of Power Quality Indices: An Approach for PMUs" Energies 13, no. 9: 2337. https://doi.org/10.3390/en13092337