# Six Sigma-Based Frequency Response Analysis for Power Transformer Winding Deformation
### Literature Survey
\begin{table}
\begin{tabular}{c c c c c} \hline
**Ref.** & **Fault Type** & **Category** & **Cause** & **Effect on Transformer** \\ \hline
[23; 24] & Inter-Turn & & Insulation breakdown & Increased winding currents, \\  & Short Circuit & Electrical Fault & between adjacent & localized overheating, \\  & & & winding turns. & and accelerated \\  & & & & insulation degradation. \\  & & & & High-circulating currents, \\  & & & & between phases. & increased loss, and potential \\  & & & & & failure of windings. \\  & & & & Breakdown of winding & Large fault currents, \\  & & & & insulation to transformer & overheating, risk of \\  & & & core or tank. & catastrophic failure. \\  & & & & & Reduced mechanical strength, \\  & & & & & increased stress on \\  & & & & & insulation, and possible \\  & & & & & turn-to-turn faults. \\  & & & & Short circuit forces push & Potential loosening of \\  & & & & windings up/down along & clamping structure, increased \\  & & & the core. & mechanical stress. \\  & & & & Mechanical vibrations, & Higher noise, excessive \\  & & & & & vibration, and risk of \\  & & & or thermal expansion. & progressive deformation. \\ \hline \end{tabular}
\end{table} 
Table 1: Comparison of electrical and mechanical faults in transformer windings. signals and statistical time features (STFs) to diagnose short-circuited turn (SCT) faults in transformers. The approach achieved 96.82% accuracy, enabling efficient and automated transformer fault detection. In [39], the authors proposed an SVM-based approach for detecting mechanical faults in transformer windings using online impulse FRA. The study reports that by analyzing real transformer fault data, the proposed method achieves high classification accuracy and improves fault diagnosis during transformer operation. In [40], a fault diagnosis method for transformer windings using decision tree (DT) and fully connected neural networks (FCNN) to analyze response signatures is proposed. With the classification of six fault types and a lumped parameter-based transformer model, the proposed approach demonstrates strong performance in training and validation with good generalization ability for real-world applications. The study by [PERSON] et al. [41] investigates the impact of temperature on FRA measurements using a machine-learning approach to improve fault classification in power transformers. The results show that incorporating temperature as an input feature prevents misclassification and enhances the accuracy of condition monitoring and fault detection using support vector machines (SVM). In addition to FRA, recent developments in long-term power transformer monitoring have introduced novel methods leveraging acoustic sensing, optical fiber sensors, and real-time remote data acquisition. For instance, remote monitoring of on-load tap changer (OLTC) switching cycles using acoustic emission techniques has been proposed to detect contact wear and mechanical anomalies without interrupting operation [42]. Similarly, advanced diagnostic systems for special power transformers incorporate combined thermal, electrical, and vibration monitoring, enabling condition-based maintenance and dynamic risk assessment [42]. These modern techniques are particularly valuable in detecting operational drift and insulation degradation under fluctuating grid conditions. While these methods offer valuable insights, they often require complex hardware integration or operate on secondary transformer parameters. In contrast, the proposed FRA6\(\sigma\) approach focuses on primary winding response behavior and introduces a structured, statistically controlled method that can complement such advanced systems. Its integration with conventional FRA enables objective, high-resolution fault detection without the need for continuous sensing infrastructure.