# Interpretation of Frequency Response Analysis for Fault Detection in Power Transformers  
[PERSON]  
1 Department of Power Electrical, Faculty of Electrical and Electronic Engineering, University Tun Hussein Onn Malaysia, Bata Pahat 86400, Johor, Malaysia, [EMAIL_ADDRESS] (S.M.A.-A. ); [EMAIL_ADDRESS] (A.A.S.) 2 Electrical and Computer Engineering Department, Curtin University, Bentley, WA 6152, Australia; [EMAIL_ADDRESS]  
3 Electrical and Electronics Engineering Technology Department, Yanbu Industrial College (YIC), Alnahdah, Yanbu Al Sinaiyah, Yanbu 46452, Saudi Arabia; [EMAIL_ADDRESS]  
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[PERSON]  
the CC is 1; otherwise, it is 0. The CC is sensitive to changes in response resonance and anti-resonance frequencies, and it is widely used for FRA. The SSE can show the deviation between normal and faulty responses. The ASLE is highly recommended in the latest studies and is reported to be more pertinent than the SSE. SD has also been used to detect variation between frequency responses for normal power transformers and winding deformation [9]. Typically, SD shows similar sensitivity to the ASLE. On the other hand, some methods have been proposed for a more objective interpretation of FRA measurements, as elaborated below. Past studies adopted a transformer-equivalent high-frequency circuit by representing the winding using resistance, inductance, and capacitance (RLC) ladder circuit [10; 11; 12], due to the difficulty of staging physical faults on real transformers. The equivalent circuit enables understanding of the changes in response due to specific faults that might otherwise be impossible to reproduce on actual winding. Several transformer faults can be simulated using the equivalent circuit, including short circuit turns, inter-disk deformation, axial displacement, buckling faults, bushing and insulation faults, and clamping pressure loss [13; 14; 15]. In the mathematical models presented in the literature, the frequency response is modeled as a rational function with actual coefficients. For comparison purposes, the parameters of the model can be indicated, but their sensitivity to various types of faults is not stated [16; 17]. The disadvantage of using this numerical method is the time-consuming nature of solving complex mathematical equations [18]. The use of artificial neural networks (ANNs) to identify transformer failure is also reported. Essentially, ANNs are used to estimate transformer parameters over a wide frequency range. ANNs are also used as a complementary technique to statistical indicators to improve the FRA interpretation process's reliability [19; 20]. Digital image processing has been used on 2D and 3D FRA plots to extract unique features for each fault type [21]. In [21], a three-dimensional-FRA trace in one plot that includes frequency, magnitude, and phase is presented. Compared to the current interpretation practice, which relies only on the magnitude plot, more features can be extracted from the proposed 2D and 3D FRA signature, hence increasing the accuracy of the FRA classification. Previous works in [22; 23; 24] investigate the impact of winding deformation, bushing, and inter-disk faults on the FRA signature. The effects of tap changer variation and the loss of clamping pressure on the FRA signature were also studied in [25; 26; 27; 28; 29]. These studies were based on statistical indicators and necessary visual inspection. A comparison between the latest proposed methods for FRA interpretation is given in Table 1.