Research gaps and limitations

We have identified the following research gaps through the above literature analysis:

• In current literature, classical ANN-based approaches were built for the detection of electrical faults in transmission systems such as linear SVM and tree-based models.
• There is still a need for performance enhancement for critical electrical fault detection in transmission systems. Moderate performance accuracy of 98% in literature is achieved, however, the 2% error still exists, which can be further overcome by advanced machine learning models.
• Current and voltages signals data patterns were not identified to apply appropriate machine learning approaches,

Phase 1: Line currents and voltages faults data

This research utilized a benchmark dataset [11, 17], comprising a collection of line currents and voltages under various fault conditions in the power transmission system. The data were modelled in MATLAB to simulate fault analysis within a power system framework. The modelled power system incorporates four generators, each with a voltage of 11 × 10³ V, positioned in pairs at both ends of the line transmission. The dataset is based on 12,001 transmission line data points. Transformers are also included in the power system to facilitate the simulation and analysis of numerous faults occurring at the middle of the line transmission.

The dataset was collected and recorded, detailing the measured line currents and line voltages at the output side of the power system. This collection encompasses nearly 12,000 data points, subsequently labelled as either ‘fault’ or ‘no fault’. The simulation inputs are designated as Phase A line current (Ia), Phase B line current (Ib), Phase C line current (Ic), Phase A line voltage (Va), Phase B line voltage (Vb), and Phase C line voltage (Vc). The outputs are categorized as 0 (No fault) or 1 (Fault present) in the power transmission system, as shown in Table 2.

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Table 2. Different types of faults analysis in the three-phase transmission line in the dataset.

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Phase 2: Signal data time series analysis

We have analyzed the signal data for faults over the transmission line. The analysis of voltage and current over time, during a fault or no-fault in electrical power transmission systems, is shown in Fig 4. The voltage signals over time are depicted in Fig 4(a). This analysis indicates that when Va voltage values are in the range of -0.6 to 0.6, there is no fault. However, when the Va is near 0.0, it means there is a fault over the transmission line. Similarly, this applies to Vb and Vc. The current signals over time are depicted in Fig 4(b). The analysis also shows that when Ia current values are near 0.0, there is no fault. However, when the Ia is in the range of -750 to 750, it means there is a fault over the line transmission. A similar pattern is observed for Ib and Ic.

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Fig 4. The voltage and current analysis overtime during a fault or not fault in electrical power transmission systems.

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Phase 3: SMOTE based data oversampling

After analyzing the signal data, we have determined that the dataset is unbalanced, as illustrated in Figure Fig 5(a). Then, we employed a well-known dataset oversampling technique, the Synthetic Minority Over-sampling Technique (SMOTE) [18]. The SMOTE approach, which focuses on data oversampling of line currents and voltage faults, emerges as a pivotal method for enhancing fault detection accuracy in electrical power transmission systems. By addressing the imbalance in datasets, where instances of faults are significantly underrepresented compared to normal operation data, SMOTE facilitates the generation of synthetic samples. The balanced dataset, after applying the SMOTE approach, is illustrated in Fig 5(b).

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Fig 5. The fault class distribution analysis before and after balancing.

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Phase 4: Signal data splitting

The signal data is then split to conduct further research experiments. We used a splitting ratio of 80:20. The dataset is divided into train (80%) and test (20%) portions. This research process is fundamental in avoiding overfitting, ensuring that the model can generalize well to new, unseen data by training the model on one subset of the data while validating and testing its performance on other subsets.

Phase 5: Applied artificial intelligence methods

Machine learning methods play a pivotal role in enhancing fault detection capabilities within electrical power transmission systems. By leveraging advanced algorithms [19–21], these systems can analyze vast datasets in real time, identifying subtle deviations from normal operating conditions. This proactive approach enables swift and accurate detection of potential faults, minimizing downtime and ensuring the reliability of power transmission networks.

• Random Forest (RF): The RF method for Fault Detection in Electrical Power Transmission Systems operates by leveraging a combination of decision trees [22, 23]. Each tree is created using a random subset of features and a bootstrapped sample of the dataset, ensuring diversity in the individual models. During fault detection, the RF algorithm aggregates predictions from multiple trees, providing a robust and accurate assessment of the system’s health. This ensemble approach enhances the model’s resilience to noise and variability, making it particularly effective for detecting faults in complex and dynamic electrical transmission environments. Mathematically, the prediction y for a given input vector X can be represented as: (1) Where:
  • N is the number point of trees in the forest.
  • T_i(X;Θ_i) is the prediction of the i^th tree, trained with a randomly sampled dataset (with replacement) from the training set and feature subset, based on parameters Θ_i.
  • X represents the input features vector derived from the power system’s parameters.
  
  For fault detection, the output class can be determined based on majority voting among the trees: (2) Where Class(X) represents the predicted state (e.g., ‘normal’ or ‘faulty’) of the electrical power transmission system.
• Logistic Regression (LR): The LR operates as a powerful approach for Fault Detection in Electrical Power Transmission Systems by employing a probabilistic approach [24, 25]. It assesses the likelihood of a fault occurrence based on input features, such as voltage levels and current values. The LR model employs a logistic function to map the input data into a probability distribution, enabling the identification of potential faults through a threshold classification. This method proves effective in discerning abnormal patterns within the system, facilitating timely intervention and maintenance in power transmission networks. The logistic function, σ(z), is defined as: (3) where z data point is the linear data combination value of the input features data (x₁, x₂, …, x_n) and their corresponding weights (w₁, w₂, …, w_n), plus a bias term b. This can be expressed as: (4)
  Substituting z in the logistic function: (5)
  This model outputs the probability that a given set of input features (x₁, x₂, …, x_n) belongs to the “fault” category. To classify an input as “fault” or “no fault”, a threshold, typically 0.5, is applied to the model’s output: (6)
• Support Vector Classifier (SVC): The SVC operates by constructing a hyperplane in a space that effectively separates different classes of data points [26, 27]. In the context of fault detection in electrical power transmission systems, the SVC method utilizes historical data on normal system behavior and fault instances to define this hyperplane. By identifying the optimal hyperplane that maximally separates normal and faulty conditions, SVC enables efficient detection of abnormalities, enabling swift response to potential faults in the power transmission system. This method’s robustness lies in its ability to handle non-linear relationships and its sensitivity to critical features, enhancing its efficacy in safeguarding the electrical grid against potential faults. The fault detection in electrical power transmission systems, let’s consider the feature space to be and the two categories to be fault and no fault.
  The basic form of the SVC decision function is: (7) where:
  • is the weight data vector perpendicular to the SVC hyperplane.
  • is the bias term, which offsets the hyperplane from the origin.
  • is the input feature vector.
  
  The goal of the SVC is to find the optimal data points w and b such that the margin between the two classes is maximized, subject to the constraints: (8) where y_i ∈ {−1, 1} is the label of x_i, indicating the class (fault or no fault).
  The optimization problem for finding w and b can be formulated as: (9) subject to: (10)
  This formulation ensures that the hyperplane has the maximum line margin separating the two classes, which is a key concept in SVC for fault detection and classification tasks.
• Gated Recurrent Unit (GRU): The GRU deep learning model emerges as a potent tool for fault detection in electrical transmission systems [28, 29]. Leveraging its ability to capture temporal dependencies in data, the GRU efficiently processes sequential information from power transmission measurements, enabling the detection of subtle deviations indicative of faults. This model’s adaptability and streamlined architecture make it a promising solution for enhancing the reliability and efficiency of fault detection in critical electrical infrastructure. The fundamental equations governing the GRU operation are as follows: (11) (12) (13) (14) Where:
  • r_t is the data value of the reset gate activation vector.
  • z_t is the data value of the update gate activation vector.
  • h_t is the data value of the hidden state vector at time t.
  • x_t is the input data vector at time t.
  • is the candidate activation vector.
  • σ denotes the sigmoid value function.
  • ⊙ denotes data element-wise multiplication.
  • W_r, W_z, W and b_r, b_z, b are the weights and biases that need to be learned during training.

The GRU’s ability to effectively blend past information with current inputs through its gating mechanisms makes it particularly suited for detecting anomalies over time in power transmission systems. The layered architecture is analyzed in Table 3.

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Table 3. The layers architecture stack of applied neural network based GRU method.

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Phase 6: Novel glassbox-based proposed EB approach

The proposed EB approach for fault detection in electrical power transmission systems employs an ensemble of decision trees to analyze the system’s data. The proposed EB method combines the strengths of boosting and interpretable models as glassbox, providing a transparent and accurate framework for fault detection. Through iterative training, the EB model assigns weights to individual decision trees, emphasizing the contribution of each tree to the overall predictive outcome, facilitating a clear understanding of the features and patterns crucial for detecting faults in the power transmission system. The basic form of a model under the EB approach, adapted for fault detection, can be represented as follows: (15) Where:

• is the predicted outcome (e.g., the presence or absence of fault data in the power transmission system).
• φ₀ is the model’s intercept.
• M is the number of features (e.g., voltage, current, temperature, etc.) used in the model.
• x_i represents an individual feature.
• φ_i(x_i) is the contribution values of the i-th feature to the prediction, modeled by a shape function, which is learned during training for maximum interpretability.
• φ_ij(x_i, x_j) represents the interaction term between features i and j, capturing the joint effect of these features on the prediction. This term allows the model to consider how combinations of different conditions affect the system’s health.
• ϵ is the error term.

Our proposed methodology enables the development of boosting models that are not only highly accurate in identifying and classifying electrical faults but also provide clear insights into their decision-making processes. By leveraging the glassbox model, we can pinpoint the specific characteristics and conditions under which faults occur, facilitating more effective prevention strategies. This approach significantly enhances the reliability and safety of electrical power transmission systems, offering a clear window into the inner workings of complex AI-driven fault detection mechanisms. The architecture of the proposed approach is illustrated in Fig 6 and Algorithm 1.

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Fig 6. The proposed glassbox-based optimized explainable boosting workflow analysis.

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Algorithm 1 Training proposed EB Classifier for Fault Detection in Power Transmission Systems

Input: Dataset D containing line currents and voltages under various fault conditions. Each instance x_i has a label y_i where y_i ∈ {0, 1} (0 for No fault, 1 for Fault present).

Output: A trained Explainable Boosting Classifier model

Initialize the Explainable Boosting Classifier M

Configure model parameters (if any specific configuration is needed)

Train the model M using the dataset D

Evaluate the model performance using suitable metrics (e.g., accuracy, F1-score)

return Trained Model M

Phase 7: Models perparameters settings

This section analyzes the hyperparameter tuning of applied machine-learning models for electrical fault detection. Hyperparameter tuning helps to improve the generalization of applied machine learning models and prevents overfitting issues. The best-fit hyperparameters in this study are determined through a recursive training and testing process using the k-fold cross-validation process. The final selected hyperparameter settings of the applied method are described in Table 4.

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Table 4. Analysis of parameter optimization in machine learning applications.

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Experimental setup

This section scrutinizes the experimental setup of our study. We utilized Python programming language 3.0 to implement the applied machine learning approaches. All experiments are conducted in the Google Colab platform, utilizing a GPU backend with 90 GB disk space and 13 GB RAM. Established statistical metrics like accuracy, F1, precision, and recall are employed to evaluate the models. The basic evaluation terms are based on False Positives (FP), True Positives (TP), True Negatives (TN), and False Negatives (FN) for each metric. The mathematical representation of these evaluation criteria, such as accuracy, is provided: (16) Where TP denotes correctly identified faults, TN denotes correctly identified non-faults, FP denotes incorrectly identified faults, and FN denotes incorrectly missed faults, respectively.

Similarly, precision is the ratio of TP to the sum of TP and FP, denoted as precision (P). It represents the ratio of accurately predicted erroneous data to the total data predicted to be erroneous: (17)

Recall measure is measured as the proportion of correct predictions generated by the model in comparison to the overall number of true occurrences: (18)

The F1 score measure can be computed by taking the harmonic mean of recall and precision: (19)

Additional factors, including the duration of training and testing, the layer and node count, and the epoch number, are assessed to facilitate a comparative evaluation between the suggested EB approach and conventional ANN techniques.

Results with balanced data

During our initial experiments, we found that the dataset was slightly imbalanced. To address this issue, we used the SMOTE to balance the data, and the results are described in this section. The performance of the applied machine learning models with the balanced dataset is illustrated in Table 5. The analysis shows that the highest accuracy score achieved with the balanced dataset is 89% using the Random Forest (RF) method. However, these seemingly high scores may indicate low performance, possibly due to the introduction of noise from the newly generated synthetic dataset.

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Table 5. The testing results of applied neural network methods for fault detection with balanced dataset.

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Results with original data

The performance results of the applied learning models with the original dataset features are analyzed in this section. In previous analyses, we concluded that the synthetic generation of balanced datasets achieved moderate performance scores. The results with the original dataset features are demonstrated in Table 6. This analysis reveals that the applied learning models achieved good performance scores. The applied tree-based RF model achieved a notable performance score of above 90%. The applied linear models, LR and SVC, achieved lower performance scores. The neural network-based GRU achieved a high-performance score of 92% in this analysis. This analysis infers that the applied machine learning models achieve good performance scores using the original dataset features for electrical fault detection in transmission systems.

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Table 6. The testing results of applied neural network approaches for fault detection.

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The confusion matrix-based performance assessment of applied neural network models for electrical fault classification is illustrated in Fig 7. The analysis reveals that during the testing phase, the applied machine learning models, LR and SVC, recorded the highest rates of incorrect predictions. In contrast, the RF and GRU models achieved lower rates of incorrect predictions. Thus, this analysis concludes that tree-based and neural network models demonstrate superior performance scores for fault detection.

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Fig 7. The confusion matrix-based error rates analysis for fault detection.

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Performance analysis of proposed method

The performance results of the proposed EB approach are analyzed in this section. The results of the EB approach are presented in Table 7. The analysis expresses that our optimized EB approach achieved 99% accuracy performance scores compared to other applied methods. The class-wise performance results show the exceptional performance of the EB approach. This analysis infers that our novel proposed method outperformed other applied methods with high electrical fault detection rates.

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Table 7. The testing results of proposed EB method for fault detection.

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The comparison of histogram-based results of applied machine learning models was conducted to assess the overall performance relative to the proposed approach. Fig 8 illustrates the histogram comparison results, indicating that the machine-learning-based models LR, SVC, and RF achieved lower performance results. However, the deep learning-based neural network model, GRU, achieved respectable scores but not as high as our proposed method, EB. This analysis highlights the significant performance advantage of our proposed approach in electrical fault classification.

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Fig 8. The histogram-based results comparisons of applied machine learning models.

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Fig 9 demonstrates the assessment of the performance of applied neural network models through Receiver Operating Characteristic (ROC) analysis. The analysis reveals distinct variations in the Area Under Curve (AUC) scores, highlighting the effectiveness of the different models in accurately classifying electrical faults. The LR model exhibited a modest AUC of 0.58, indicating its relatively weak capability in effectively distinguishing between the classes. In contrast, the RF model marked a significant improvement, achieving an AUC of 0.97, which suggests a high degree of accuracy in fault classification. Most notably, our proposed model, referred to as EB, surpassed the conventional models by securing an AUC of 0.99. This superior performance of the EB model, as depicted in the ROC plot, illustrates its exceptional ability to correctly classify the positive class from the negative, establishing it as a highly reliable model for electrical fault classification. Thus, the ROC plot analysis provides compelling evidence of the advanced discriminative power of the EB model over traditional machine learning approaches.

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Fig 9. The ROC curve analysis of applied neural network methods.

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In addition, we have provided a radar chart-based performance area analysis, as shown in Fig 10. This analysis, based on performance metrics coverage across the radar, demonstrates that our proposed approach covers more performance scores on the radar compared to other applied methods. It also highlights the superior performance results scores of the proposed EB method for electrical fault classification.

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Fig 10. The radar chart-based performance area coverage analysis.

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In evaluating the performance results of the proposed EB model, the confusion matrix is illustrated in Fig 11. Remarkably, the plot reveals that the model has achieved an impressive level of precision, with only 13 instances of misclassification. This outcome underscores the model’s robustness and effectiveness in accurately distinguishing between categories, affirming its potential for widespread application in scenarios where precision is paramount. The low number of misclassifications is indicative of the model’s advanced learning capabilities and its suitability for handling complex classification challenges, such as electrical fault classification in transmission systems.

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Fig 11. The confusion matrix-based error rates analysis of proposed EB method for fault detection.

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K fold cross-validation analysis

We employed the K-fold validation technique to authenticate the performance scores of the applied method. In this method, the fault-related signal data are divided into k equal-sized folds, and the method is trained and validated k times, with each fold being used once as a validation set. This approach helps evaluate the model’s performance and addresses issues such as overfitting. The results of the K-fold approach for applied neural network methods are reported in Table 8. The analysis shows that the applied method achieved lower K-fold accuracy scores than our proposed EB approach. This analysis validates the high-performance scores of our proposed EB method, which achieved 99% K-fold accuracy with a minimum standard deviation score of 0.0009 for electrical fault detection.

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Table 8. The k-fold-based performance validations of applied machine learning methods for fault detection.

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Fault detection time computational complexity analysis

The computational complexity analysis of fault detection time for applied artificial neural networks is presented in Table 9. We measured the training time of each applied method and reported the results. The analysis shows that RF achieved the minimum electrical fault detection time; however, the performance accuracy of RF is low. The fault detection time of the proposed EB model is 23.5848 seconds, which is high compared to others; however, the accuracy score of the proposed approach is also 99%. We consider performance score a priority for this critical electrical fault detection. We will further reduce the architecture of the proposed EB to reduce its computational time.

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Table 9. The fault detection training time analysis of applied methods.

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eXplainable Artificial Intelligence (XAI)

The implementation of the XAI approach [30] in our study has yielded significant advancements in understanding and interpreting the decision-making processes of the proposed model used for fault detection in electrical transmission systems. Through the application of the XAI technique, as shown in Fig 12. We can demystify the operational logic of the proposed model, particularly shedding light on how these models discern and classify different types of faults. This transparency not only enhances trust in AI-driven systems but also facilitates a deeper insight into the strengths and limitations of the employed models. Most notably, the XAI analysis revealed that certain features, such as the phase line current and voltage variations, play a pivotal role in the models’ fault detection capabilities.

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Fig 12. The SHAPE chart-based XAI analysis of proposed EB method for fault detection.

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State of the art comparisons

To ensure a fair performance comparison of the proposed EB approach, we have collated the performance results with the state-of-the-art methods used for electrical fault detection. The results of the comparison studies using the same dataset are described in Table 10. The analysis shows that the previous highest accuracy achieved was 97%, which is considered low. This investigation demonstrates that our suggested EB methodology exceeds the performance of current leading techniques, achieving an impressive.

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Table 10. The state of art research studies analysis for fault detection in electrical power transmission systems.

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Discussions

We have proposed an innovative research approach for electrical fault classification and detection timely:

• ANNs prove to be a reliable and efficient approach for classifying and detecting faults in electrical power system transmission lines, particularly given the growing dynamic connectivity of contemporary power transmission systems.
• Before applying an artificial neural network in a practical scenario, it is essential to thoroughly evaluate its performance, considering the specific neural network structure and learning algorithm.
• The Explainable Boosting (EB) neural networks exhibit impressive performance when trained with extensive datasets, readily accessible in power systems. Hence, the proposed method opts for EB due to its efficacy.

Study limitations

The proposed research outperformed the state-of-the-art methods with the high performance of fault detection, however, there are still some limitations, as follows:

• The calculation time of the proposed method is higher compared to applied methods. In future, we will try to optimize the architecture of the proposed method to minimize the computational time.