## 3 FRA Open Circuit Measurement  
End to end open circuit FRA measurement was performed using a commercial frequency response analyzer by injecting 20 V input voltage signal (V\({}_{\text{i}}\)) of low amplitude and variable frequency to one terminal of the HV winding and measuring the output voltage (V\({}_{\text{o}}\)) at the other end of the same winding while all LV windings are left open [7]. The FRA signature was plotted at all tap positions as the winding transfer function (V\({}_{\text{o}}\)/V\({}_{\text{i}}\)) in dB, as shown in Figure 4.  
According to [20], the FRA technique can be developed based on the fact that transformer components can be presented by a complex network of a distributed resistance R, inductance L, capacitance C, and conductance G parameters. In [21; 22], the equivalent circuit of the transformer considered the series and paralleled resistance, inductance, and capacitance RLC elements are presented, as shown in Figure 5. Where n is the number of disc. In this study, a new simplified circuit model was proposed to simulate the measured transformer FRA. Hence, the proposed lumped RLC circuit model in Figure 6 represented the transformer in a normal tap changer at the end-to-end open circuit measurement. The R\({}_{\text{s}}\) and L\({}_{\text{s}}\), refers to series resistance and inductance, and C\({}_{\text{p}}\) is the primary capacitance. Each wire resistance R and reference resistance R\({}_{\text{ref}}\) were 50 \(\Omega\).  
Figure 4: Measured frequency response analysis (FRA) at all tap changer positions.  
Figure 3: Tap surface pitting (**a**) 50% and (**b**) 100%.  
The parameters of the transformer equivalent circuit shown in Figure 6 obtained through finite element analysis simulation to the investigated transformer using its physical dimensions, insulation properties, and winding topology as detailed in [23; 24; 25]. These parameters are given in Table 2.  
Figure 4 shows that FRA signatures for all tap settings in normal tap conditions had a similar trend with the same resonance frequencies but slight changes in the transfer function's magnitude. The leakage and magnetizing inductances of the core affected the FRA at low frequency (below 2 kHz), which begins with the decreasing magnitude of \(-20\) dB/decade under normal tap changer contacts. At the mid-frequency range, resonances appeared intermittently due to parasitic capacitances and inductances of the transformer. At higher frequencies above 1 MHz, the transformer structure affected the signature. The connection leads and measurement setups were taken into this high-frequency range.  
\begin{table}
\begin{tabular}{c c c c c} \hline
**Tap Position** & **L (\(\mu\)H)** & **R\({}_{s}\)\(\Omega\)** & **L\({}_{s}\) (\(\mu\)H)** & **C\({}_{p}\) (pF)** \\ \hline Tap 4-5 & 5.00 & 1 & 100 & 100 \\ Tap 5–3 & 4.75 & 1.5 & 110 & 95 \\ Tap 3–6 & 4.50 & 1.10 & 120 & 90 \\ Tap 6–2 & 4.25 & 1.15 & 130 & 85 \\ Tap 2–7 & 4.00 & 1.20 & 140 & 80 \\ \hline \end{tabular}
\end{table}
Table 2: RLC circuit parameters for the tap changer at different positions for the FRA open circuit test.  
Figure 5: Equivalent schematic resistance, inductance, and capacitance RLC network of transformer winding.  
Figure 6: Simulated tap changer RLC circuit using MATLAB/Simulink.  
The FRA of the proposed lumped RLC model was plotted at the same tap positions by changing the RLC values shown in Figure 7, which shows a similar profile to the measured signatures shown in Figure 5. The slight change in the transfer function magnitude from a tap position to another was attributed to the change in the equivalent electrical parameters. However, the location of resonance frequencies was not changing.