# Fault Detection in Power Transformers Using Frequency Response Analysis and Machine Learning Models
## 4 Results and Discussion
All classes in the study formed similar shapes in the frequency spectrum, with peaks occurring at the same frequencies but at varying magnitudes. The trend in the pattern was continuous across all fault types, indicating a consistent response of the system to different types of faults. These peak frequencies, which appeared in each class, were indicative of specific fault signatures, although the magnitudes differed depending on the fault class. This uniformity in the shape of the curves across the different classes suggests that the model was effectively capturing the key features of the faults, albeit with slight variations in intensity. Notably, there was an intersection between Classes D and C at a frequency of 14 MHz. This intersection point suggests a potential overlap or similarity in the frequency response of the faults represented by these classes. It may indicate that the model faces difficulty distinguishing between certain fault types at this frequency, leading to a potential for misclassification or ambiguous fault identification. Further investigation into this intersection could help refine the model, allowing for better differentiation between faults with similar spectral characteristics. Insulation Deterioration in Power Transformer Detection Faults Using Decision Tree, Trained with Fine Trees ML Model (20-100 MHz)  
As seen in Figure 9, in Class A, representing Insulation Breakdown, the model demonstrated flawless performance, achieving 100% accuracy in fault detection. All eight FRA samples were correctly classified and predicted, underscoring the model's exceptional ability to accurately identify insulation breakdown faults. This remarkable result can be visually confirmed in Figure 9a,b below, where the predictions align perfectly with the actual fault data. For Class B, representing Loss Connections, the model achieved a commendable accuracy rate of 85.7%, with only one misclassified FRA sample out of a total of seven. This yields a True Positive Rate (TPR) of 85.7% and a False Negative Rate (FNR) of 14.3%, showcasing the model's strong ability to detect loss connections, though with room for improvement. Figure 9: Lead connection issues in Power Transformer Detection Faults using Decision Tree with Fine Tree ML models: (**a**) Validation Confusion Matrix (TPR and FNR) and (**b**) Validation Confusion Matrix Samples. NB: Blue represents correct classifications (true positives), while light blue and orange indicate misclassifications, with orange highlighting higher false negative rates. In Class C, which represents Corrosion faults, the model exhibited flawless performance once again, achieving 100% accuracy. All 12 FRA samples were correctly classified and predicted, confirming the model's reliability in identifying corrosion-related faults. This outstanding performance is illustrated in Figure 9a,b, where the accuracy of the predictions is clearly depicted. For Class D, representing Improper Termination faults, the model correctly detected three out of four FRA samples, achieving a TPR of 75% and an FNR of 25%. While the model performed well, there was a single misclassification, indicating that further refinement could enhance the model's accuracy in this class. The diagonal elements formed by the confusion matrix across all classes provide strong evidence of the model's overall accuracy, with the majority of predictions falling on the diagonal. Notably, the two classes with less than 100% accuracy, Classes B and D, are positioned off-diagonal, highlighting areas for potential improvement. However, the overall pattern of correct classifications emphasizes the robustness of the model in accurately identifying different types of faults across all classes. All four faults predicted above have been plotted graphically in Figure 10, providing a clear visual representation of the model's performance. One of the key observations is the presence of valleys in the graphics for each class, which play a crucial role in the accuracy of the model.