Application of an Artificial Neural Network for Measurements of Synchrophasor Indicators in the Power System
Abstract
:1. Introduction
2. Methodology of the Studies
2.1. The Requirements Imposed on the Estimation Methods of Phasor Parameters
- The sinusoidal function with a constant magnitude of 1 and a constant frequency of 50 Hz (denoted as function 1);
- Functions with a constant frequency of 50 ± 2 Hz for the P class and of 50 ± 5 Hz for the M class (denoted as functions 2 and 3);
- Functions with a magnitude change between 0.1 and 2. The authors assumed the values of 0.1, 0.8, 1.2 and 2 (denoted as functions 4, 5, 6 and 7, respectively);
- Functions including the harmonics from the 2nd to the 50th with a magnitude of 0.01 for the P class and 0.1 for the M class (denoted as functions from 8 to 56);
- Functions including out-of-band interference. These exist only in the M class and have a magnitude of 0.1. The input test signal frequencies are as follows:
- f = f0 − (FS/2) − (0.1 Hz × 2n) for n = 0, 1, 2, … to f ≤ 10 Hz for n = 0, 1, 2, … to f ≤ 10 Hz; i.e., they include the following frequency values: 12.2, 18.6, 21.8, 23.4, 24.2, 24.6, 24.8 and 24.9 Hz (denoted as functions from 57 to 64);
- f = f0 + (FS/2) + (0.1 Hz × 2n) for n = 0, 1, 2, … to f ≥ 2 × f0 Hz; i.e., they include the following frequency values: 75.1, 75.2, 75.4, 75.8, 76.6, 78.2, 81.4 and 87.8 Hz (denoted as functions from 65 to 72);
- Where FS—the reporting frequency—is assumed to be 50 samples/s. Assuming the reporting frequency to be 50 samples/s means that the estimated synchrophasor parameters should be obtained from the signal of the maximum length of 0.02 s, irrespective of the network frequency;
- 6
- Functions with a magnitude modulation, where the signal is a sum of the base signal and the sinusoidal signal of a magnitude of 0.1 and the frequency changes between 0.1 and 2 Hz for the P class and between 0.1 and 5 Hz for the M class, with a change occurring every 0.1 Hz (denoted as functions 57 to 76 for the P class and functions 73 to 122 for the M class);
- 7
- Functions with a phase modulation, where the base signal phase additionally contains the sinusoidal signal with a magnitude of 0.1 rad and the frequency changing between 0.1 and 2 Hz for the P class and between 0.1 and 5 Hz for the M class, with a change occurring every 0.1 Hz (denoted as functions 77 to 96 for the P class and functions 123 to 172 for the M class);
- 8
- Functions with linear ramp of system frequency, where the ramp range is ±2 Hz for the P class and ±5 Hz for the M class, with a ramp rate of 1 Hz/s (denoted as functions 97 and 98 for the P class and functions 173 and 174 for the M class);
- 9
- Functions with a step magnitude change of ±0.1 and with a step occurring at the beginning and in the middle of the measurement window (denoted as functions 99 to 102 for the P class and functions 175 to 178 for the M class); the functions having a step occurring in the middle of the measurement window are additional testing functions implemented by authors for research measurements;
- 10
- Functions with a step phase change of ±π/10 and with a step occurring at the beginning and in the middle of the measurement window (denoted as functions 103 to 106 for the P class and functions 179 to 182 for the M class).
- Response time of TVE (RT-TVE), which means a time difference between the point at which the TVE value decreases below 1% and the point at which the TVE increases above 1%;
- Response time of FE (RT-FE) which means a time difference as defined in point 4 but for the FE value of 0.005 Hz;
- Response time of RFE (RT-RFE), which means a time difference as defined in point 4 but for the RFE value of 0.4 Hz/s for the P class and 0.1 Hz/s for the M class;
- Delay time (DT), which is a time difference between the point at which the magnitude or phase reach 50% of the step value and the initial step value;
- Overshoot/undershoot value (OV), which is a difference between the maximum magnitude or phase value following a step and the step value, which is further divided by the step value.
2.2. The Flowchart of the Estimation Algorithm of the Phasor Parameters
- The filtering of the input signal was conducted by means of the FIR filter with a Kaiser window. The filter parameters were as follows: frequency of a passband edge of 50 Hz, frequency of a stopband edge of 100 Hz, passband ripple of 0.001 pu, stopband ripple of 0.1 pu, sampling frequency of fp = 12,800 Hz, order of 929 and Kaiser window beta of 5.6533.
- The zero-crossing method was used to estimate the frequency and phase;
- An RBF of the ANN was used to estimate the magnitude;
- A frequency-dependent algorithm to make corrections to the estimation results of the magnitude and phase was used.
2.3. The Phasor Magnitude Estimation Algorithm Using ANN
2.4. The Synchrophasor Frequency and Phase Estimation Algorithm Using the Zero-Crossing Method
2.5. Corrections of the Synchrophasor Magnitude and Phase Estimation
3. Results and Discussion
4. Conclusions
- The idea of using two algorithms operating simultaneously to estimate the synchrophasor magnitude, phase and frequency that applied identical calculation methods; the main difference between them was that the first one filtered the input signal using the FIR filter, while the second one operated without any filter;
- The method of the synchrophasor magnitude estimation by means of a suitably trained and applied RBF;
- The algorithm calculating corrections of the phase shift between the input and output signal;
- The algorithm calculating corrections of the magnitude estimation;
- The algorithm of phase estimation using the phase from the previous measurement window and the frequency value from a given window.
Author Contributions
Funding
Conflicts of Interest
References
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P Class | M Class | ||||||
---|---|---|---|---|---|---|---|
Function Number | TVE | FE | RFE | Function Number | TVE | FE | RFE |
% | Hz | Hz/s | % | Hz | Hz/s | ||
1 | 1 | 0.005 | 0.4 | 1 | 1 | 0.005 | 0.1 |
2, 3 | 1 | 0.005 | 0.4 | 2, 3 | 1 | 0.005 | 0.1 |
4 ÷ 7 | 1 | 0.005 | 0.4 | 4 ÷ 7 | 1 | 0.005 | 0.1 |
8 ÷ 56 | 1 | 0.005 | 0.4 | 8 ÷ 56 | 1 | 0.025 | - |
- | - | - | - | 57 ÷ 72 | 1.3 | 0.01 | - |
57 ÷ 76 | 3 | 0.06 | 2.3 | 73 ÷ 122 | 3 | 0.3 | 14 |
77 ÷ 96 | 3 | 0.06 | 2.3 | 123 ÷ 172 | 3 | 0.3 | 14 |
97, 98 | 1 | 0.01 | 0.4 | 173, 174 | 1 | 0.01 | 0.2 |
Step Functions—Response Times | |||||||
Function Number | RT-TVE | RT-FE | RT-RFE | Function Number | RT-TVE | RT-FE | RT-RFE |
S | S | s | s | s | s | ||
99÷102 | 0.04 | 0.09 | 0.12 | 175 ÷ 178 | 0.14 | 0.28 | 0.28 |
103÷106 | 0.04 | 0.09 | 0.12 | 179 ÷ 182 | 0.14 | 0.28 | 0.28 |
Step Functions—Delay Time and Overshoot/Undershoot Value | |||||||
Function Number | DT | OV | - | Function Number | DT | OV | - |
S | % | - | s | % | - | ||
99 ÷ 102 | 0.005 | 5 | - | 175 ÷ 178 | 0.005 | 10 | - |
103 ÷ 106 | 0.005 | 5 | - | 179 ÷ 182 | 0.005 | 10 | - |
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Binek, M.; Kanicki, A.; Rozga, P. Application of an Artificial Neural Network for Measurements of Synchrophasor Indicators in the Power System. Energies 2021, 14, 2570. https://doi.org/10.3390/en14092570
Binek M, Kanicki A, Rozga P. Application of an Artificial Neural Network for Measurements of Synchrophasor Indicators in the Power System. Energies. 2021; 14(9):2570. https://doi.org/10.3390/en14092570
Chicago/Turabian StyleBinek, Malgorzata, Andrzej Kanicki, and Pawel Rozga. 2021. "Application of an Artificial Neural Network for Measurements of Synchrophasor Indicators in the Power System" Energies 14, no. 9: 2570. https://doi.org/10.3390/en14092570