## 2 Methodology
### Methodology Algorithm
Step 3:Perform Empirical Mode Decomposition (EMD) Decompose signal into Intrinsic Mode Functions (IMFs): \[x(t)=\sum_{k=1}^{n}c_{k}(t)+r_{n}(t)\quad\text{[Equation (\ref{



Results Validation

As defined in Table 1, each disturbance is assigned a numerical label to facilitate classification. Voltage sags are represented by label 3. The detection system was evaluated across multiple scenarios by introducing voltage drops at different time points. Figure 4 illustrates the network's response to a disturbance with a \(t=0.2\) s duration. The model successfully identifies the event onset and assigns the correct label with high temporal precision.

Figure 5 shows the response to a sag with a 0.4 s duration. The classification remains consistent, with the model correctly identifying the transition between normal (label 2) and disturbed (label 3) states, and returning to label 2 once the sag ends.

Figure 4: Detection of a voltage sag with 0.2 s duration. (**a**) Original voltage signal showing a sudden drop in amplitude between 0.3 s and 0.5 s. (**b**) Corresponding classification output, where class labels are interruption, normal, sag, and swell.

Figure 3: Voltage signal with an artificially injected sag event starting at approximately 0.3 s and lasting 0.2 s. The signal drop reflects a simulated voltage sag used for training and evaluation of the classification model.

The final test, presented in Figure 6, evaluates the detection of a longer-duration sag with 0.8 s duration. The classifier maintains its performance, demonstrating robustness in identifying the anomaly across varying time windows.

These results confirm the classifier's ability to accurately detect the onset, duration, and clearance of voltage sag events. The ANN demonstrates strong generalization to different temporal scales, a critical real-time power quality monitoring capability. Unlike traditional detection methods that often rely on fixed thresholds or frequency-domain analysis, the data-driven approach employed here adapts to dynamic signal behavior, offering improved flexibility and precision.

Moreover, the model's accurate identification of the transition boundaries between normal and abnormal states supports its application in intelligent fault detection systems, where rapid response and reliable classification are essential for maintaining grid reliability and service continuity.

Figure 5: Detection of a voltage sag with 0.4 s duration. (**a**) Original voltage signal showing a sudden drop in amplitude between 0.3 s and 0.6 s. (**b**) Corresponding classification output, where class labels are interruption, normal, sag, and swell.

Figure 6: Detection of a voltage sag with 0.8 s duration. (**a**) Original voltage signal showing a prolonged drop in amplitude from approximately 0.2 s to 1.0 s. (**b**) Corresponding classification output, where class labels are interruption, normal, sag, and swell.

### Case Study: Voltage Level Interruption

The IEEE 33-bus distribution system assesses the proposed methodology's ability to detect voltage interruption events. These are modeled in MATLAB/Simulink by inserting block-level modifications that simulate a complete voltage loss at selected nodes. Three distinct durations are defined for the analysis: 0.2 s, 0.4 s, and 0.8 s. Figure 7 presents the signal behavior during one such simulated interruption. The primary objective is to validate the neural network's capacity to identify and classify these events under varying temporal conditions.

Results Validation

As Table 1 indicates, voltage interruptions are represented by label 1. The neural network is evaluated across three scenarios in which the interruption begins at \(t=0.2\) s, 0.4 s, and 0.8 s, respectively. These events simulate the sudden loss of voltage due to faults, protection device operation, or equipment malfunction, all of which may lead to severe system consequences if undetected.

Figure 8 illustrates the detection output for the first case. The ANN correctly identifies the interruption onset, maintains label 1 during the disturbance window, and returns to label 2 upon signal recovery.

Figure 8: Detection of a voltage interruption with 0.2 s duration. (**a**) Original voltage signal showing a temporary loss of amplitude between 0.9 s and 1.2 s. (**b**) Corresponding classification output, where class labels are interruption, normal, sag, and swell.

Figure 7: Voltage signal with a simulated interruption event, showing a complete drop in amplitude from approximately 0.9 s to 1.2 s. This scenario is used to validate the model’s ability to identify sudden voltage losses under variable temporal conditions.

Figure 9 displays the detection behavior for a 0.4 s interruption. The network's consistent response, despite variation in timing, demonstrates its generalization capability.

In the final case, shown in Figure 10, the ANN again exhibits accurate temporal labeling of the event with no misclassifications, even for the longest duration scenario.

The model's consistent performance across these scenarios validates its robustness in detecting interruptions under varying durations and onset conditions. Such capabilities are essential for real-world deployment, where faults may occur unpredictably in time and magnitude.

Accurate classification of interruption events not only enables timely fault isolation but also supports the implementation of automated mitigation strategies. Therefore, the proposed supervised learning architecture strengthens early detection systems and enhances the intelligence and adaptability of modern distribution networks.

### Case Study: Voltage Swell

The IEEE 33-bus distribution system is employed as the simulation framework to evaluate the model's ability to detect swell events. In this case study, swell disturbances

Figure 10: Detection of a voltage interruption with 0.8 s duration. (**a**) Original voltage signal showing a complete amplitude drop from approximately 1.2 s to 2.0 s. (**b**) Corresponding classification output, where class labels are interruption, normal, sag, and swell.

Figure 9: Detection of a voltage interruption with 0.4 s duration. (**a**) Original voltage signal showing a drop to near-zero amplitude from approximately 0.9 s to 1.3 s. (**b**) Corresponding classification output, where class labels are interruption, normal, sag, and swell.

are introduced at selected nodes in the MATLAB/Simulink environment. These surges represent temporary increases in RMS voltage levels. Three durations are considered: 0.2 s, 0.4 s, and 0.8 s. Figure 11 illustrates the signal profile during a simulated swell event.

Results Validation

According to the classification scheme in Table 1, swell events are labeled with identifier 4. The network was evaluated across three time-based scenarios, each representing a different moment of surge onset: 0.2 s, 0.4 s, and 0.8 s. These events are critical in power quality analysis, as they can severely damage sensitive electronic equipment or lead to misoperation of protection devices if not adequately addressed.

Figure 12 shows the neural network's output for the 0.2 s surge event. The system accurately detects the start and end of the disturbance and correctly assigns label 4 throughout the duration.

Figure 13 presents the network's classification for the 0.4 s case. The system demonstrates consistency by accurately labeling the anomaly and transitioning back to label 2 after the event concludes.

Figure 11: Voltage signal with a simulated swell disturbance, showing a temporary increase in amplitude around 1.8 s. This profile is used to test the model’s capability to detect and classify Swell events with short durations in distribution systems.

Figure 12: Detection of an overvoltage event with 0.2 s duration. (**a**) Original voltage signal showing an amplitude increase between approximately 1.5 s and 1.8 s. (**b**) Corresponding classification output, where class labels are interruption, normal, sag, and swell.

The last test, shown in Figure 14, evaluates the most extended event duration (0.8 s). Again, the model performs reliably, marking a clear boundary between normal and disturbed states with no false positives or missed detections.

The experimental results confirm the robustness of the proposed ANN-based classifier in recognizing Swell events of varying durations. The system's ability to maintain accuracy under multiple disturbance windows supports its deployment in predictive monitoring and adaptive protection schemes. Moreover, its strong generalization across different time scales reinforces its value as a dynamic fault detection tool within innovative grid environments.

### Results Summary

The Hilbert-Huang transform (HHT) was applied to extract relevant features from voltage disturbance signals in the IEEE 33-bus system. This adaptive time-frequency analysis combines empirical mode decomposition (EMD) with the Hilbert transform, enabling non-stationary signals to be decomposed into a set of intrinsic mode functions (IMFs), each capturing oscillatory behavior at different time scales. This decomposition facilitates the separation of fundamental signal components from transient irregularities, allowing for high-resolution and localized characterization of electrical disturbances.

Figure 14: Detection of an overvoltage event with 0.8 s duration. (**a**) Original voltage signal showing a significant amplitude increase from approximately 2.2 s to 3.0 s. (**b**) Corresponding classification output, where class labels are interruption, normal, sag, and swell.

Figure 13: Detection of an overvoltage event with 0.4 s duration. (**a**) Original voltage signal showing a temporary rise in amplitude between approximately 1.5 s and 1.9 s. (**b**) Corresponding classification output, where class labels are interruption, normal, sag, and swell.

Applying the Hilbert transform to each IMF yields instantaneous amplitude, phase, and frequency parameters. These descriptors form a detailed representation of the signal's dynamic evolution, particularly beneficial for identifying the timing, duration, and severity of non-stationary disturbances. Figure 15 illustrates this process for the first IMF, where high-resolution time-frequency data enables precise anomaly detection.

As shown in Figure 16, the visualization of each IMF's amplitude and frequency spectrum allows for identifying both abrupt and subtle alterations in the signal. This capability makes the HHT framework a powerful tool for advanced power quality assessment and transient event localization in modern distribution networks.

Figure 16: Hilbert–Huang analysis results for IMF 2. (**a**) Extracted IMF 2 component, representing lower-frequency oscillations. (**b**) Instantaneous amplitude of IMF 2, highlighting transient energy bursts. (**c**) Instantaneous frequency content captures subtle dynamic variations associated with event transitions.

Figure 15: Hilbert–Huang analysis results for IMF 1. (**a**) Extracted IMF 1 component from the original voltage signal. (**b**) Instantaneous amplitude profile of IMF 1, highlighting energy variations during disturbances. (**c**) Instantaneous frequency extracted via the Hilbert transform, capturing spectral shifts across time.

Once the HHT-transformed signals were used as training inputs, the neural network was optimized using a performance-based validation approach. As shown in Figure 17, the model achieved a classification error of 0.125 across 250,000 data samples. The rapid convergence observed demonstrates successful generalization and training stability.

To evaluate the generalization of the model under complex operating conditions, additional case studies were developed using a realistic simulation of the IEEE 33-bus system. In each scenario, simultaneous disturbances (sags, interruptions, and swells) were injected across all three phases at multiple time points (\(t=0.2\) s, 0.4 s, and 0.8 s). In Case 1 (Figure 18), the model successfully identified the type, timing, and duration of each event, demonstrating its ability to differentiate among label classes with no misclassification.

Figure 17: Training performance of the neural network over 381 epochs using the cross-entropy loss function. The curves represent the evolution of training, validation, and testing errors, with the green circle marking the best validation performance. The convergence trend indicates stable learning and minimal overfitting.

Figure 18: Case 1: Neural network classification of a composite disturbance scenario with events occurring at \(t=0.2\) s (sag), \(t=1.0\) s (interruption), and \(t=1.6\) s (swell). (**a**) Original voltage signal showing distinct amplitude variations for each disturbance type. (**b**) Corresponding classification output, accurately identifying and labeling each event in time. Class labels: interruption, normal, sag, swell.

Figure 19 shows the system's response to the second event set. The classifier maintained high precision in distinguishing transitions between normal (label 2), interruptions (label 1), sags (label 3), and swells (label 4). This highlights the model's robustness against temporal variability in fault occurrence.

The third test, presented in Figure 20, validated the network's ability to detect extended and overlapping anomalies under multiphase symmetrical conditions. The classifier's consistent behavior across all tests confirms its high generalization capacity and resilience to complex dynamic operating states.

Overall, the combined use of the HHT and neural networks provides a comprehensive and adaptive strategy for real-time monitoring. The model not only detects and classifies transient disturbances with high precision but also retains performance under multiphase, time-variable conditions. This positions the approach as a scalable and intelligent solution for power quality assurance and advanced fault diagnostics in modern distribution grids.

The results obtained demonstrate the effectiveness of the proposed HHT-based ANN classification framework in fulfilling the primary objectives of this study. The model

Figure 19: Case 2: Neural network classification of a composite disturbance scenario with events occurring at \(t=0.4\) s (sag), \(t=1.0\) s (interruption), and \(t=1.6\) s (swell). (**a**) Original voltage signal illustrating distinct drops and surges in amplitude. (**b**) Predicted class labels accurately track each disturbance type and transition, confirming the classifier’s temporal sensitivity and robustness. Class labels: interruption, normal, sag, swell.

Figure 20: Case 3: Neural network classification for a multievent sequence beginning at \(t=0.8\) s. (**a**) Voltage signal exhibiting sequential voltage sag, interruption, and swell phenomena. (**b**) Predicted class labels show accurate transitions across all events, highlighting the model’s robustness in handling composite disturbances. Class labels: interruption, normal, sag, swell.

achieved an overall classification accuracy of 94.09%, with strong generalization across varying disturbance durations (0.2 s, 0.4 s, 0.8 s) and spatial locations within the IEEE 33-bus system. The confusion matrix shows that the classifier reliably distinguishes between voltage sag, swell, and interruption events, each associated with distinct voltage signatures defined by IEEE 1159.

The relatively shallow ANN architecture enabled fast convergence (as seen in the training curve) while maintaining low computational complexity, making the approach suitable for real-time deployment. These results confirm that the integration of HHT features (instantaneous amplitude and frequency) provides a rich, non-stationary feature space that enhances the classifier's ability to detect subtle transient patterns.

Furthermore, the method's robustness across buses and time windows suggests that it can be effectively deployed in smart distribution networks where operating conditions are dynamic and disturbance propagation is topology-dependent. Thus, the presented results validate the proposed approach not only in terms of raw performance metrics but also in terms of its alignment with real-world monitoring requirements.

### Expanded Experimental Validation

The training dataset was constructed using simulated voltage signals in the IEEE 33-bus test system under four event classes: normal operation and voltage sag, swell, and interruption. Each class contains 300 labeled signals per duration (0.2 s, 0.4 s, and 0.8 s), yielding a total of 3600 signals. Disturbance events were injected with randomized onset times, amplitudes, and durations within the IEEE 1159-2019 guidelines. Voltage sags varied between 60 and 90% of nominal voltage, swells between 110 and 130%, and interruptions dropped below 10% for specified intervals. No synthetic noise was added, but signal diversity was ensured through perturbation variability and randomized bus locations.

To assess generalization capability, we adopted five-fold cross-validation over a stratified 80/20 training/test split, ensuring that all event types and durations were proportionally represented across folds. This method provides robust performance estimation and reduces the risk of overfitting, comparable to using an independent test set, without requiring additional simulations. The average classification accuracy across folds was 94.09%, with standard deviation below 1%, confirming stable model behavior.

A confusion matrix summarizing classification outcomes is shown in Figure 21, with strong per-class separability. Table 4 provides precision, recall, and F1-score metrics for each class, highlighting the model's balanced accuracy across all types of disturbances.

To formally define these metrics:

* Precision: \[\text{Precision}=\frac{TP}{TP+FP}\] (11)
* Recall: \[\text{Recall}=\frac{TP}{TP+FN}\] (12)
* F1-score: \[\text{F1-score}=2\cdot\frac{\text{Precision}\cdot\text{Recall}}{\text{ Precision}+\text{Recall}}\] (13)

Although a comparison with other classifiers (e.g., SVM, decision tree) could offer additional insight, the focus of this work was to validate the neural network approach under multiscale event durations using a consistent, diverse dataset.