## 3 Results and Discussion
### Comparison of the Frequency Responses through the Statistical Parameters  
The difficulties in getting conclusions from the FRA results can be minimized using the statistical parameters. Accordingly, an additional comparison was made between the EEV TF data of the various cases [32; 33; 34; 35]. The statistical parameters 'CSD, DABS and MM ratio (absolute)' were estimated from the EEV TF magnitudes, by comparing two different cases at a time. Thus, the normal case frequency response (EEV TF data) was compared with the responses of various faulty cases by considering them one by one. Table 2 refers the statistical parameters used, their notations, formula, and the ideal values expected (when the two cases compared are similar). Table 3 shows the comparisons that were made through the statistical parameters. The total frequency spectrum was divided into three sub-bands and comparisons were made between the EEV TF data within the corresponding sub-bands. For any pair of cases compared, the highest magnitude of variations can happen at some specific and unique sub-band. With careful segmentation of the total frequency spectrum into sub-bands, the difference between any two cases can be easily distinguished. Table 3 shows the comparison that was made though the statistical parameters on sub-band basis with three different objectives. First, the EEV TF magnitudes of Normal case and the inter-turn short cases were compared. The parametric values were shown in the column 3 & 4. Subsequently, comparisons were made between Normal case and the PD cases across minor insulation and presented in column 5 & 6. Finally, comparisons were made between Normal case and the PD cases across major insulation and shown in column 7 & 8. The EEV TF data for the cases NC, Sh-1, and Sh-2 were collected through low voltage FRA with the switching impulse voltage at 5 kV (peak). The data for the voltage-dependent faulty cases PD-1-minor, PD-2-minor, PD-3-major, and PD-4-major were collected through the FRA test at 37.5 kV levels, which was much above their corresponding discharge inception voltages. Figure 10: Comparison of EEV TF plots for the diagnosis of sources of PDs across major insulation: Normal case (vs) PD-3-major (vs) PD-4-major. The highest deviations of statistical parameters from ideal values are highlighted in Table 3 for easy reference (bold and coloured). The corresponding sub-band indicates the most sensitive sub-band frequency of the total frequency spectrum, which can show the maximum difference between the compared cases. The following conclusions were drawn from Table 3. The three statistical parameters CSD, DABS and MM ratio (absolute) deviated widely from their ideal values and, thus, capable of distinguishing the faulty case from the normal case. The numerical values highlighted in the Table 3 indicates that their sensitivity in discriminating a faulty case from the normal case is found to be high at some sub-bands. For different faulty cases (which were compared one by one with the Normal case), the numerical values varied to a different extent at same sub-bands, as shown in Table 3. All of these variations indicated that the frequency response of the faulty cases was different from the frequency response of a normal transformer and, thus, switching impulse voltage-based FRA conducted at appropriate test voltages is capable of diagnosing faults. Thus, the observations and analysis on results in the three forms (i.e., input and response waveforms in the time domain, EEV TF plots, and statistical parameters estimated in the frequency domain) indicated that, with careful selection of the test voltage, the switching impulse voltage based frequency response approach can become useful in diagnosing the potential sources of PD across the minor and major insulations of the transformer winding. It can be noted that the impulse with a 37.5 kV peak was used in order to diagnose the PD sources which were emulated near the impulse injected end and whose inception voltage was less than the test voltage.