## 5 Conclusions  
The research presented in this paper underscores the critical importance of accurate and reliable fault detection in power transformers, essential for maintaining network stability and minimizing operational costs. The novel approach introduced here leverages the RBSWT combined with enhanced long short-term memory (LSTM) networks to address the limitations of existing differential protection schemes, particularly under conditions of CT saturation and measurement uncertainties. Through rigorous testing and validation, the proposed method has demonstrated exceptional performance across various scenarios, including internal faults, external faults, inrush currents, and internal faults coinciding with CT saturation. The empirical results highlight the method's superiority, achieving higher detection accuracy and significantly reduced detection times compared to recent state-of-the-art techniques. Specifically, the proposed framework achieves approximately 99% accuracy in detecting internal faults, external faults, and inrush currents, with detection times substantially shorter than those of existing methods. These findings confirm the proposed framework's potential for real-time applications in power transformer fault detection. By effectively integrating RBSWT and LSTM networks, this approach not only enhances fault detection accuracy but also ensures faster response times, which are crucial for the protection and efficient operation of power systems. The advancements presented in this study pave the way for more reliable and cost-effective transformer protection solutions, reinforcing the critical role of innovative technologies in the power sector. Conceptualization, Q.A., M.S., S.G.S. and E.M.; Methodology, Q.A., M.S., S.G.S. and E.M.; Software, Q.A. ; Validation, Q.A., M.S., S.G.S. and E.M.; Investigation, Q.A., M.S., S.G.S. and E.M.; Data curation, Q.A. ; Writing--original draft, Q.A., M.S., S.G.S. and E.M.; Writing--review and editing, Q.A., M.S., S.G.S. and E.M.; Supervision, M.S., S.G.S. and E.M.; Administration, M.S., S.G.S. and E.M. All authors have read and agreed to the published version of the manuscript. This research received no external funding. **Data Availability Statement:** The data presented in this study can be obtained by sending an email to [EMAIL_ADDRESS]. accessed on 1 September 2024 These data are accessible upon request from the author and will be used in future studies. **Conflicts of Interest:** The authors declare no conflicts of interest. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Fault Type**} & \multicolumn{6}{c}{**Analysis of Correct Diagnosis by Different Methods**} \\ \cline{2-10}  & \multirow{2}{*}{**[5, 24, 27]**} & \multicolumn{2}{c}{[10, 25]} & \multicolumn{2}{c}{[9, 14]} & \multicolumn{2}{c}{**Present Method**} \\ \hline \multirow{3}{*}{Internal fault} & Number of cases & Number & \% & Number & \% & Number & \% & Number & \% \\ \cline{2-10}  & 500 & 489 & 97 & 476 & 95 & 482 & 96 & 498 & 99 \\ \cline{2-10}  & Average detection time (ms) & 340 & 380 & 410 & 130 & \\ \hline \multirow{3}{*}{External fault} & Number of cases & Number & \% & Number & \% & Number & \% & Number & \% \\ \cline{2-10}  & 500 & 469 & 93 & 471 & 94 & 463 & 92 & 499 & 99 \\ \cline{2-10}  & Average detection time (ms) & 362 & 310 & 510 & 110 & \\ \hline \multirow{3}{*}{Inrush currents} & Number of cases & Number & \% & Number & \% & Number & \% & Number & \% \\ \cline{2-10}  & 500 & 486 & 97 & 477 & 95 & 471 & 94 & 497 & 99 \\ \cline{2-10}  & Average detection time (ms) & 360 & 379 & 525 & & 120 & \\ \hline \multirow{3}{*}{Internal faults with CT saturation} & Number of cases & Number & \% & Number & \% & Number & \% & Number & \% \\ \cline{2-10}  & 500 & 462 & 92 & 420 & 84 & 431 & 86 & 496 & 99 \\ \cline{1-1} \cline{2-10}  & Average detection time (ms) & 390 & 428 & & 610 & & 170 & \\ \hline \hline \end{tabular}
\end{table}