# Fault Detection in Power Transformers Using Frequency Response Analysis and Machine Learning Models
## 4 Results and Discussion
This curve provides valuable insights into performance variations and potential anomalies in the signal. In addition to the C curve, the presence of V curves is clearly noticeable at 400 Hz, 100 Hz, and 1000 Hz, as depicted in the graph. These V curves indicate different response patterns across these specific frequencies, reflecting the system's behavior under varying frequency conditions. The distinct patterns observed in these curves can help in diagnosing performance characteristics and identifying potential issues such as resonance or structural changes within the transformer or system under analysis. Furthermore, Figure 4 illustrates an important trend: as the frequency increases, the amplitude of the magnitude also rises. This indicates a frequency-dependent response, where higher frequencies correspond to greater signal magnitudes. Insulation Deterioration in Power Transformer Detection Faults Using Ensemble, Trained Subspace KNN ML Model (10-15 MHz)  
Class A, faults for Insulation Breakdown were correctly classified with an average of 100 % see Figure 5a, all 13 samples were correctly classified, see Figure 5b. Class B, representing Corona Discharge, was successfully classified with perfect accuracy, achieving 100% across all 9 samples. As shown in Figure 5a,b, the model demonstrated flawless performance in predicting these faults. Similarly, Class C, which corresponds to thermal overstress, also achieved 100% accuracy, with all five samples correctly identified and classified, reflecting the model's high efficiency in detecting this type of fault. The perfect prediction rates across these classes indicate that the machine learning model is well-suited for identifying such faults, offering strong reliability in diagnostic assessments. However, Class D, corresponding to contamination-related faults, exhibited a significant issue in classification. Despite the otherwise accurate performance of the model, this particular class experienced 100% False Negative Rate (FNR), where the single sample for contamination was misclassified. This suggests that the model may struggle to differen  
Figure 4: Detection of Insulation Deterioration Faults in Power Transformers Using a Decision Tree Model Trained with Fine Tree ML Models (0–2000 Hz). tiate contamination faults from other classes, possibly due to the specific characteristics of the contamination-induced defects not being adequately captured in the training data. The misclassification of Class D emphasizes the need for further refinement in the model, potentially by incorporating additional data or adjusting the feature extraction process to better address the unique properties of contamination faults. While the model displayed exceptional accuracy in identifying the majority of fault classes, the misclassification of contamination faults highlights an area for improvement. Future work could focus on enhancing the model's ability to recognize and distinguish contamination faults, which would help further optimize fault detection capabilities for power transformer diagnostics. All the four faults classified are graphed in Figure 6. The trends of curves with V shapes have been observed in all four classes. 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.