## 4 Result Analysis and Discussion  
In the study presented, the proposed framework was tested and validated through a simulation case, illustrated in Figure 6. A comprehensive approach was adopted, incorporating numerous case studies using a blend of simulation techniques, real-world data, and data augmentation methods. This multifaceted strategy allowed the methodology to be validated across various experimental scenarios. Specifically, a simulation model of a \begin{table}
\begin{tabular}{c c} \hline \hline
**Fault Type** & **Binary Code** \\ \hline Internal faults & (0,0) \\ External faults & (0,1) \\ Inrush current & (1,0) \\ Internal faults and inrush current (under CT saturation) & (1,1) \\ \hline \hline \end{tabular} \(x_{t}\): A vector of features, such as \(S_{x}\) and \(W_{x}\), extracted from the wavelet transform.  
\end{table} 
Table 1: Binary Code for Different types of the fault in power transformer. 132/33 kV power transformer with a 63 MVA capacity was created, meticulously calibrated to match a real-world counterpart under different fault conditions. Detailed specifications of the transformer under study are provided in Table 2. This calibration enabled the accurate replication of the real transformer's behavior under diverse operating conditions and fault scenarios. Throughout the process, the measured signals at each simulation step were rigorously compared to ensure consistency with those observed in the real transformer under identical conditions. Additionally, data from multiple sources--including simulated, real-world, and augmented datasets--were integrated to construct a comprehensive training dataset. This approach ensured that the synthesized data authentically reflected real-world transformer operations and fault conditions. The robustness and capability of the model to handle a wide range of experimental data in real-world scenarios were ensured through this thorough and integrative approach, providing a strong foundation for validating and ensuring the reliability of the methodology. The simulation was designed to emulate a real-world power transformer, considering source phase angles ranging from 0 to 360 degrees to cover all possible transformer switching conditions. Additionally, various load scenarios and multiple cases of internal faults with varying ground resistance were simulated. A total of 2000 cases were gathered through a comprehensive approach that combined simulations with real-world data and data augmentation techniques. These cases were used for training and validating the LSTM network. \begin{table}
\begin{tabular}{c c} \hline \hline
**Connection of Transformer** & **YnD11** \\ \hline Nominal apparent power (MVA) & 63 \\ Voltage ratio (kV) & 132/33 \\ Rated frequency (Hz) & 50 \\ Percentage impedance (\%) & 10 \\ CT ratio primary side & 300:5 \\ CT ratio secondary side & 1200:5 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Detailed data of understudied power transformer. Figure 6: Schematic diagram of the power system with the transformer under study. Data augmentation methods included introducing noise, applying transformations such as scaling and rotation, and generating synthetic samples using techniques like the synthetic minority over-sampling technique (SMOTE). Diverse data sources--simulated, real-world, and augmented data--were integrated to create an extensive training dataset. Throughout this process, it was ensured that the synthesized data accurately represented the underlying distribution of transformer operations and fault conditions. According to the Table 3, the data collection approach systematically explored different scenarios, as detailed in the following points:  
1. Running the power system with varying power supply phase angles (0-360\({}^{\circ}\)). 2. Modifying fault ground resistance within a range (0.001, 0.01, 0.1, 1, 2, 10, \(\ldots\), 75, 125, 150). 3. Adjusting transformer load from 5 MVA to 33 MVA. 4. Manipulating fault location timing on both the LV side (33 kV) and HV side (132 kV) as per the provided table.