## 2 Methodology
### Methodology Algorithm
\begin{array}{ll}HHT&\text{Hilbert--Huang transform}\\ EMD&\text{Empirical mode decomposition}\\ IMF&\text{Intrinsic mode function}\\ ANN&\text{Artificial neural network}\\ A(t)&\text{Instantaneous amplitude of the signal}\\ \phi(t)&\text{Instantaneous phase of the signal}\\ f(t)&\text{Instantaneous frequency of the signal}\\ x(t)&\text{Original voltage signal in time domain}\\ \hat{x}(t)&\text{Analytic signal derived from }x(t)\\ \hat{x}(t)&\text{Hilbert transform of }x(t)\\ c_{k}(t)&\text{$k$-th intrinsic mode function}\\ r_{k}(t)&\text{Residual signal after extracting $k$ IMFs}\\ m_{k}(t)&\text{Mean envelope used in EMD}\\ A_{k}(t)&\text{Instantaneous amplitude of IMF $k$}\\ f_{k}(t)&\text{Instantaneous frequency of IMF $k$}\\ \phi_{k}(t)&\text{Instantaneous phase of IMF $k$}\\ t&\text{Time (in seconds)}\\ System&\text{IEEE 33-bus test system}\\ T_{d}&\text{Disturbance duration in seconds}\\ x_{i,d}(t)&\text{Signal at node $i$ under disturbance $d$}\\ \mathbf{F}_{i}&\text{Feature vector for signal $i$}\\ Y_{i}&\text{Class label for signal $i$}\\ \hat{Y}&\text{Predicted output of the ANN}\\ \theta^{*}&\text{Weights of the trained neural network}\\ \mathcal{L}(Y,\hat{Y})&\text{Loss function comparing ground truth and prediction}\\ TP&\text{True positive}\\ FP&\text{False positive}\\ FN&\text{False negative}\\ \text{Label 1}&\text{Interruption}\\ \text{Label 2}&\text{Normal}\\ \text{Label 3}&\text{Voltage sag}\\ \text{Label 4}&\text{Voltage swell}\\ \end{array} \]

## References

* _[PERSON] et al. (2024)_ [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON] Power Flow Analysis Using Deep Neural Networks in Three-Phase Unbalanced Smart Distribution Grids. In Proceedings of the 2024 IEEE Power & Energy Society General Meeting (PESGM), Seattle, WA, USA, 21-25 July 2024; pp. 1-5. [CrossRef]
* [PERSON] (2024) [PERSON] Coordination of Transmission and Distribution Systems in Load Restoration. In Proceedings of the 2024 IEEE Power & Energy Society Innovative Smart Grid Technologies Conference (ISGT), Bengaluru, India, 10-13 November 2024; pp. 300-305. [CrossRef]
* _Technical Report Std 1159-2019_; IEEE Recommended Practice for Monitoring Electric Power Quality. IEEE Power and Energy Society: New York, NY, USA, 2019. [CrossRef]
* _[PERSON] et al. (2023)_ [PERSON]; [PERSON]; [PERSON] Harmonic Emissions Assessment of Distributed Photovoltaic Systems in Low Voltage Network. In Proceedings of the 2023 Middle East and North Africa Solar Conference (MENA-SC), Dubai, United Arab Emirates, 15-18 November 2023; pp. 1443-1452. [CrossRef]
* _[PERSON] et al. (2023)_ [PERSON]; [PERSON]; [PERSON] Application of Artificial Intelligence Technology in Power Equipment Condition Prediction and Maintenance. In Proceedings of the 2023 International Conference on Artificial Intelligence, Kobe, Japan, 20-22 March 2023. [CrossRef]
* _[PERSON] and [PERSON] (2023)_ [PERSON]; [PERSON] Accurate Weather Forecasting for Rainfall Prediction Using Artificial Neural Network Compared with Deep Learning Neural Network. In Proceedings of the 2023 International Conference on Artificial Intelligence and Knowledge Discovery in Concurrent Engineering (ICECONF), Chennai, India, 5-7 January 2023; pp. 1-6. [CrossRef]
* _[PERSON] (2019)_ [PERSON]; [PERSON] Mode Decomposition and the Hilbert-Huang Transform. In Proceedings of the 2019 Russian Open Conference on Radio Wave Propagation (RWP), Kazan, Russia, 1-6 July 2019. [CrossRef]
* _[PERSON] et al. (2022)_ [PERSON]; [PERSON] Distribution Grid Fault Diagnostic Employing Hilbert-Huang Transform and Neural Networks. In Proceedings of the 2022 International Conference on Power Energy Systems and Applications (ICoPESA), Singapore, 25-27 February 2022; pp. 263-268. [CrossRef]
* _[PERSON] et al. (2025)_ [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON] Emerging Trends in Active Distribution Network Fault Detection. _Renew. Energy Focus_**2025**, _53_, 100684. [CrossRef]
* _[PERSON] et al.