# Amplitude Distribution of Partial Discharge Signals on Tunnel-Installed High-Voltage Cables
## 5 On-Site Measurements  
A detection scheme combining the high-frequency current method and the ultra-high frequency (UHF) method was used for PD on-site detection of a 110 kV cable line. PD was confirmed and located in the cable termination of phase B by the time difference method [24]. The laying configuration of the cable line is sketched in Figure 9. The square tunnel can be regarded as a round tunnel with a radius of 2.3 m. The cable spacing is 0.26 m and the distance from the cable to the inner wall of the tunnel is 0.2 m. The earth resistivity is approximately 100 \(\Omega\cdot\)m. The calculated \(I_{\text{major}}\)/\(I_{\text{minor}}\) ratio is 1.52.  
Figure 9: Laying configuration of the 110 kV cable line.  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{\
\begin{tabular}{c} **Laying** \\ **Configuration** \\ \end{tabular} } & \multicolumn{3}{c}{**Peak-to-Peak Value**} & \multicolumn{3}{c}{**Average Amplitude Spectrum**} & \multicolumn{3}{c}{\(I_{\text{major}}\)/\(I_{\text{minor}}\)} \\ \cline{2-10}  & \multirow{2}{*}{**Phase A**} & \multirow{2}{*}{**Phase B**} & \multirow{2}{*}{**Phase C**} & \multirow{2}{*}{**Phase A**} & \multirow{2}{*}{**Phase B**} & \multirow{2}{*}{**Phase C**} & \multicolumn{2}{c}{**Peak-to-Peak Value**} & \multicolumn{2}{c}{**Average Amplitude**} & \multirow{2}{*}{
\begin{tabular}{c} **Theoretical** \\ **Value** \\ \end{tabular} } \\ \cline{2-10}  & & & & & & & & & & \\ \hline Mode a & 0.239 & 0.259 & 0.094 & 0.137 & 0.138 & 0.034 & 2.65 & 4.04 & 4.42 \\ Mode b & 0.269 & 0.236 & 0.138 & 0.119 & 0.124 & 0.051 & 0.183 & 2.38 & 2.64 \\ Mode c & 0.227 & 0.263 & 0.109 & 0.123 & 0.124 & 0.049 & 2.25 & 2.52 & 2.59 \\ Mode d & 0.233 & 0.216 & 0.187 & 0.119 & 0.119 & 0.083 & 1.20 & 1.43 & 1.41 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Measured Signal Amplitudes and the Ratio of \(I_{\text{major}}\)/\(I_{\text{minor}}\).  
Figure 10 shows the high-frequency current signal of the # 1 cross-bonding wires adjacent to the termination. The signal was recorded at a sampling rate of 2 GSa/s by the Keysight DSO6104 oscilloscope after passing a 40 dB, 2 MHz high-pass amplifier.  
Figure 10a shows that PD pulses existed on all the three-phase cross-bonding wires, and have a one-to-one correspondence in the time domain. The signals occurred in a 20-ms (50 Hz) cycle, and are distributed in both the positive and negative half cycle. The overall peak-to-peak values of the three-phase signals are 288 mV, 281 mV, and 184 mV, respectively. The \(I_{\text{major}}\)/\(I_{\text{minor}}\) ratio is therefore approximately 1.55. A rectangular window was used to extract the pulses contained in the sampling period and 26 groups of PD pulse signals were obtained. After suppressing the background noise using wavelet denoising, the average amplitude spectrum was calculated and normalized with the sum of the three phases. The result is shown in Figure 10b. The data of each group are similar to each other, where the amplitudes of phase A and B are roughly equal and are all larger than the amplitude of phase C. The mean value of the \(I_{\text{major}}\)/\(I_{\text{minor}}\) ratios is 1.47 and the standard deviation is 0.069, which is similar to that obtained from the peak-to-peak peak values.  
Since the amplitudes of the signals on the cross-bonding wires of phase A and phase B are equal, the wires should be directly connected with the defective phase according to the analysis of Section 2.2. In combination with the structure of the cross-bonded cable system in Figure 1, the A-B phase and the B-C phase are connected by the cross-bonding wires of phase A and phase B respectively. The two cross-bonding wires are directly connected to phase B, so the PD source should be located in phase B, which is consistent with the actual situation.