# Interpretation of Frequency Response Analysis for Fault Detection in Power Transformers
## 2 Transformer Frequency Response Analysis  
The principal function of the FRA is to detect winding and core deformation. Nowadays, the FRA test is recommended to be performed before and after transportation or relocation, on suspected units, and during regular offline maintenance. The transformer frequency response is obtained by injecting a low (<20 V) AC input signal, 'Vin', of varying frequency at one terminal of a transformer winding [30]. The output voltage, 'Vout', is measured at the other terminal of the same winding, as shown in Figure 2. The frequency response, usually the transfer function, 'H(f)', of Vout to Vin, is plotted as phase, '@(f)', and magnitude, 'K(f)', in dB, in a frequency range of 2 MHz \begin{table}
\begin{tabular}{l c c c} \hline \hline
**Proposed Methods** & \multicolumn{2}{c}{**Advantages**} & \multicolumn{1}{c}{**Disadvantages**} \\ \hline \multirow{6}{*}{Mathematical models [16, 17, 18]} & - & They take into account the magnitude and phase of the FRA signature. & - & Transformers have different structures, so every transformer case needs a particular and complex mathematical model. \\  & - & The functions are not given in any particular order. It is a correct fit of the & - & Interpretation of the measured FRA still needs an expert. \\  & & measurement. & - & \\ \hline \multirow{3}{*}{ANNs [19, 20, 21]} & - & ANNs help estimate the transformer winding RLC values using the FRA trace. & - & Applicability is limited due to its complexity. \\ \hline \multirow{6}{*}{Proposed guidelines in this study} & - & Easy to use by inexperienced engineers & \multirow{6}{*}{-} & \multirow{6}{*}{-} \\  & - & Presents major transformer faults & & \\ \cline{1-1}  & - & The proposed table shows the directions of response & & is required. \\ \cline{1-1}  & & due to fault in three & & \\ \cline{1-1}  & & frequency regions. & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: _Cont._  
Figure 1: Steps and procedures of the proposed method. as given by (1) and (2). The most commonly used plot for analyzing the response is the magnitude plot. \[K(f)=20\log_{10}\frac{V_{out}}{V_{in}} \tag{1}\]  
\[\phi(f)=\tan^{-1}\frac{\angle V_{out}}{\angle V_{in}} \tag{2}\]  
FRA test configuration refers to the connection of the frequency response analyzer to the transformer. According to CIGRE WG A2/26 [2], IEEE Std. C57.149-2012 [1], and IEC 60076-18 [3], four different configurations can be used to perform FRA measurement. These are the end-to-end open circuit test, the end-to-end short circuit test, the capacitive inter-winding test, and the inductive inter-winding test. The end-to-end open circuit configuration is performed by injecting the signal into one end of the winding and measuring the transmitted signal at the other end of the same winding. This configuration is commonly used because it can provide more information regarding the winding and core. An example of a typical frequency response using end-to-end open circuit configuration is shown in Figure 3a. On the other hand, in the end-to-end short circuit configuration, the secondary winding of the same phase is shorted to eliminate the influence of the core on the measurement, since the low-frequency response results from the magnetizing inductance of the iron core [25]. The typical frequency response of end-to-end short circuit configuration is shown in Figure 3b. To interpret the FRA signature, it is necessary to analyze all frequency ranges. The frequency response can be divided into three regions as per IEC 60076-18 [3]: the low-frequency (LF) region, the mid-frequency (MF) region, and the high-frequency (HF) region, as shown in Figure 4. These responses are from measurements using end-to-end open and short circuit tests. However, there is no general frequency limit specified for each region as this mainly depends on the size and rating of the transformer. In the IEEE std. C57.104 [1], the frequency sub-bands are divided into four regions.