Improved Performance of M-Class PMUs Based on a Magnitude Compensation Model for Wide Frequency Deviations
Abstract
:1. Introduction
2. Theoretical Background
2.1. IEEE Std. C37.118.1
2.2. M-Class Filter
2.3. Steady-State and Dynamic Tests
2.4. Applications Related to Wide Frequency Deviations
3. Proposed Methodology to Obtain the Compensation Model
4. Experimentation and Results
4.1. Model Results
4.2. Steady-State Test
4.3. Dynamic Test: Linear Frequency Ramp
4.4. Dynamic Test: Sinusoidal Frequency Variation
4.5. Signals in a Real Time Digital Simulator (RTD)
4.6. Comparison for M-Class Algorithms
5. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Steady-State Test | Dynamic Test | ||
---|---|---|---|
Description | Steady state signals with different ΔFreq | Linear frequency ramp | Sinusoidal frequency variations |
Range | ±2.0 Hz for Fs < 10; ±Fs/5 for 10 ≤ Fs ≤ 25; ±5 Hz for Fs ≥ 25 | Lesser of ±(Fs/5) or ±5 Hz | No defined |
Limit errors | TVE = 1% | TVE = 1% | No defined |
Coefficients | ||||
---|---|---|---|---|
C0,0 = 0 | C5,0 = 2.20676 × 10−7 | C0,6 = −1.4120 × 10−9 | C5,1 = 2.10556 × 10−10 | C1,3 = 2.15466 × 10−6 |
C1,0 = −6.0525 × 10−2 | C0,1 = 3.7635 × 10−4 | C1,1 = 6.66086 × 10−3 | C1,2 = −1.86745 × 10−4 | C2,3 = 1.50529 × 10−7 |
C2,0 = −3.28595 × 10−3 | C0,2 = −6.57461 × 10−5 | C2,1 = 1.83899 × 10−4 | C2,2 = −1.04144 × 10−5 | C3,3 = −5.62059 × 10−12 |
C30 = 3.4396 × 10−4 | C0,3 = 1.2709 × 10−6 | C3,1 = −9.29113 × 10−7 | C3,2 = 2.05616 × 10−8 | C1,4 = −8.33054 × 10−9 |
C4,0 = −1.5051 × 10−4 | C0,4 = −6.51693 × 10−9 | C4,1 = 2.07606 × 10−8 | C4,2 = −3.06276 × 10−10 | C2,4 = −6.75353 × 10−10 |
Reporting Rate (fps) | 10 | 12 | 15 | 20 | 30 | 60 | 120 |
---|---|---|---|---|---|---|---|
Range established by the IEEE Std. C37.118.1 (Hz) | ±2 | ±2.4 | ±3 | ±4 | ±5 | ±5 | ±5 |
Range with the proposal (Hz) | ±5 | ±6 | ±8 | ±10 | ±15 | ±30 | +60, −23 |
Reporting Rate (fps) | 10 | 12 | 15 | 20 | 30 | 60 | 120 |
---|---|---|---|---|---|---|---|
Range established by the IEEE Std. C37.118.1 (Hz) | ±2 | ±2.3 | ±3 | ±4 | ±5 | ±5 | ±5 |
Range with the proposal (Hz) | ±2 | ±2.5 | ±4 | ±8.5 | ±14 | ±26 | 35 to 100 |
Amplitude Step Test | Phase Step Test | Frequency Deviation Steady-State Test | Positive Ramp Test | Negative Ramp Test | IEEE Std. C37.118.1: Fs/RT limit/TVE limit | Frequency Range | |
---|---|---|---|---|---|---|---|
Algorithm M-Class | Response Time [ms] | Response Time [ms] | TVE [%] | TVE [%] | TVE [%] | ||
Complex filters [4] | 49 | 58 | 2.6 × 10−5 | 0.0953 | 0.0953 | 60 fps 79 ms 1% | 60 ±5 Hz |
Adaptive extended Kalman Filtering [8] | 65.1 | 17.85 | 0 | NR | NR | 60 fps 79 ms 1% | 60 ±15 Hz |
Second-order Taylor [23] | 32 | 37 | 0.123 | 0.021 | NR | 50 fps 199 ms 1% | 50 ±5 Hz |
Empirical wavelet transform [24] | 17.8 | 17.8 | 9.7 × 10−4 | 1.4 × 10−4 | NR | 50 fps 199 ms 1% | 50 ±5 Hz |
Interpolated DFT and Taylor Fourier Transform [25] | NR | NR | 0.01 | 0.02 | 0.02 | 50 fps 199 ms 1% | 50 ±5 Hz |
Improved Taylor weighted least square [26] | 52 | 32 | 1.1 × 10−5 | 0.003 | 0.003 | 100 fps 50 ms 1% | 50 ±5 Hz |
Real value Taylor weighted least square [26] | 84 | 39 | 1.158 | 1.156 | 1.156 | 100 fps 50 ms 1% | 50 ±5 Hz |
DFT-based demodulation [26] | 70 | 37 | 0.064 | 0.074 | 0.074 | 100 fps 50 ms 1% | 50 ±5 Hz |
Frequency-tracking and fixed-filter [27] | 29.97 | NR | 0.07 | 0.07 | 0.07 | 50 fps 199 ms 1% | 50 ±5 Hz |
Proposal | 15 | 15 | 1 | 1 | 1 | 120 fps 35 ms 1% | 60 +60, −23 Hz (steady-state test) and +40, −25 Hz (dynamic test) |
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Razo-Hernandez, J.R.; Urbina-Salas, I.; Tapia-Tinoco, G.; Amezquita-Sanchez, J.P.; Valtierra-Rodriguez, M.; Granados-Lieberman, D. Improved Performance of M-Class PMUs Based on a Magnitude Compensation Model for Wide Frequency Deviations. Mathematics 2020, 8, 1361. https://doi.org/10.3390/math8081361
Razo-Hernandez JR, Urbina-Salas I, Tapia-Tinoco G, Amezquita-Sanchez JP, Valtierra-Rodriguez M, Granados-Lieberman D. Improved Performance of M-Class PMUs Based on a Magnitude Compensation Model for Wide Frequency Deviations. Mathematics. 2020; 8(8):1361. https://doi.org/10.3390/math8081361
Chicago/Turabian StyleRazo-Hernandez, Jose Roberto, Ismael Urbina-Salas, Guillermo Tapia-Tinoco, Juan Pablo Amezquita-Sanchez, Martin Valtierra-Rodriguez, and David Granados-Lieberman. 2020. "Improved Performance of M-Class PMUs Based on a Magnitude Compensation Model for Wide Frequency Deviations" Mathematics 8, no. 8: 1361. https://doi.org/10.3390/math8081361