TITLE:
Adaptive Artificial Neural Network (ADALINE) Dynamic Phase Error Estimation Based on the Average Correlation Coefficient
AUTHORS:
Gabriel Musonda, Charles Lubobya, Ackim Zulu
KEYWORDS:
DFT, Adaptive Neural Network (ADALINE), Correlation Coefficient, Time Skew Error, Frequency Drift, Phase Angle Error, Phasor Measurement Unit (PMU)
JOURNAL NAME:
World Journal of Engineering and Technology,
Vol.13 No.3,
July
3,
2025
ABSTRACT: This paper presents a new anomaly detection scheme based on modified DFT Adaptive Neural Network (ADALINE) for the determination of time skew error and frequency drift in the Phasor Measurement Unit (PMU). The modified DFT/ADALINE algorithm is used to determine time stamp errors and frequency drift errors through the determination of the change in the phase angle in terms of the correlation coefficient. The correlation coefficient, δ(φ0, t) is used to determine the relationship in the change of the phase angle, ∆φ0 with respect to the change in the reporting time, ∆t. Further, the correlation coefficient, δ(φ0, f) is used to determine the relationship between the change of the phase angle, ∆φ0 with respect to drift in the grid frequency, ∆f. The parallel ADALINE algorithms compute the correlation coefficient in the range −1 to 1 from which values of δ ≥ 0.8 represent normal correlation and δ ≤ 0.799 represents data anomaly in the grid frequency or the reporting time. ADALINE flags the values for δ ≤ 0799 only thereby reducing the memory requirements of the PMU. The results of PMU/ADALINE simulation in MATLAB/Simulink, show a smooth system response around the optimal operating point of 49.85 Hz at the maximum correlation coefficient value of 0.9974. It further shows that the correlation coefficient is above 0.8 for grid frequencies in the 49.55 Hz to 50.45 Hz range, signifying normal control area operating frequencies in accordance with South African Grid System Operation Code. It can also be seen that a drift in frequency produces a corresponding time error signifying the relationship between the time skew error and frequency drift with the phase angle error in the PMU. Correlation coefficient values below 0.8 signify data Anomalies for the grid frequency outliers i.e. corresponding to grid frequencies below 49.5 Hz and above 50.5 Hz. In conclusion, our proposed PMU/ADALINE model guarantees enhanced accuracy and precision of measurement devoid of doing a massive process of iteration as it employees deep learning AI to compute the correlation coefficient signifying the presence of time skew and grid frequency error.