## 2 Methodology
### Details of Inter-Turn Shorts and PD Models  
Table 1 shows the details of various cases investigated and the notations that were used for referring the same. Two cases of Inter-turn shorts within the (1U-1V) winding were experimented by connecting a 2400 \(\Omega\) resistor between the tappings; first, between the tappings t1 and t2 and, next, between the tappings t2 and t3. They are referred to as Sh-1 and Sh-2, respectively.  
Partial Discharges (PDs) are possible in both the solid and oil insulation portions of the insulation. Modelling of such PDs was done by several researchers in the form of the air gap and oil gap contained between point/plane/hemispherical/spherical electrodes [26; 27; 28]. In the present work, a potential source of PD was artificially emulated while using a series combination of oil gap of 2 mm across hemispherical electrodes and a 2400 \(\Omega\) resistor (hereafter referred as PD model). The oil gap was fixed at 2 mm, so that the discharge across the same can be incepted with switching impulses of moderate magnitude (around 30 kV). The 2400 \(\Omega\) resistor is purposefully included in the test circuitry in order to limit the impulse current and avoid any permanent damage to the transformer windings. Thus the PD model represents a practical and developing stage PD in the major insulation.  
Four PD cases were emulated during the work in order to check the usefulness of the switching impulse voltage based IFRA in diagnosing the PD. Their locations were also varied to check whether the IFRA approach could discriminate the PD location.  
The presence of the potential source of PD was emulated, first, by inserting the PD model between the tappings within the winding and, then, between the tappings and the grounded tank. In total, four PD cases were investigated. Two PD cases were emulated across the minor insulation of the transformer; first, by connecting the PD model across the tappings t1 and t2 and, next, by connecting the PD model across the tappings t2 and t3. They are referred as PD-1-minor and PD-2-minor, respectively. Similarly, two PD cases were emulated across the major insulation of the transformer; first, by connecting the PD model across the tappings t2 and the grounded tank and next, by connecting the PD model across the tappings t3 and the grounded tank. They are referred to as PD-3-major and PD-4-major, respectively.  
Figure 1a shows the circuit that represents the terminals and special tappings of the transformer. Figure 1b shows the photograph of the same. Figure 1c shows the circuit representation of the PD model. Figure 1d shows its photographic view. The oil-gap of the PD model was transparent. Hence, the occurrence of any PD during experimentation could be cross verified through visual observation of a spark across the electrodes.  
\begin{table}
\begin{tabular}{c l l} \hline \hline
**S.No** & **Description of Investigations** & **Notations** \\ \hline \multirow{2}{*}{1} & Developing the signature FRA pattern-for Transformer under the normal condition & \\  & (No inter-turn short and discharge free condition across a Potential source of PD) & Normal case \\ \hline \multirow{2}{*}{2} & Diagnosis of Inter-turn short between tappings t1 and t2 & Sh-1 \\ \hline \multirow{2}{*}{3} & Diagnosis of Inter-turn short between tappings t2 and t3 & Sh-2 \\ \hline \multirow{2}{*}{4} & Diagnosis of the presence of a potential source of PD between tappings t1 and t2 & PD-1-minor \\ \hline \multirow{2}{*}{5} & Diagnosis of the presence of a potential source of PD between tappings t2 and t3 & PD-2-minor \\ \hline \multirow{2}{*}{6} & Diagnosis of the presence of a potential source of PD between tappings t2 and the grounded tank & PD-3-major \\ \hline \multirow{2}{*}{7} & Diagnosis of the presence of a potential source of PD between tappings t3 and the grounded tank & PD-4-major \\ \hline \hline \end{tabular}
\end{table}
Table 1: Details of the investigations and their notations.