# Amplitude Distribution of Partial Discharge Signals on Tunnel-Installed High-Voltage Cables
## 4 Experimental Verification  
In order to verify the reliability of the characteristic admittance model and the accuracy of the PD signal amplitude distribution, RG223 coaxial cables were selected to simulate the three-phase cross-bonding cable system. In view of the fact that the tunnel radius \(R\) and the earth resistivity \(\rho\) have little effect on the signal amplitude distribution, the cable system was arranged in a shielded room for simulating the underground tunnel and reducing external interference. The equivalent radius of this tunnel was 4 m and the earth resistivity \(\rho\) is \(1\times 10^{-7}\)\(\Omega\)-m. The parameters of the RG223 coaxial cable are shown in Table 2.  
The total length of the cable system was 40 m. The cross-bonding connection was located in the middle of the cable system, 20 m on both sides. The PD pulse signal was a pulse generated by Tektronix AFG3101 (Beaverton, OR, USA) with an amplitude of 10 V and a rise time of 10 ns. The pulse signal was input through the end of the phase B cable. The remaining cable terminations were connected to 50 \(\Omega\) resistive loads. The detected signal was recorded by the Keysight DSO6104 (Santa Rosa, CA, USA) oscilloscope. The bandwidth of the high-frequency current transformers was 1-50 MHz and the sampling rate of the oscilloscope was 2 GSa/s. The schematic diagram of the experimental setup and the experimental site are shown in Figure 5(a,b, respectively. Four different laying methods were adopted in the experiment, as shown in Figure 7. In modes a and b, the cables were closely arranged and the distance between adjacent cables was 5.35 mm. In modes c and d, the cables were arranged horizontally and the distance between adjacent cables was 0.1 m, with an equivalent geometric spacing of 0.126 m. In modes a and c, the cables were in direct contact with the tunnel wall and the distance to the wall was 2.675 mm, while the distance in modes b \begin{table}
\begin{tabular}{c c c c} \hline Inner Conductor Radius \(r_{1}\)/mm & 0.45 & Insulating Layer Relative Dielectric Constant \(\varepsilon_{1}\) & 2.3 \\ Insulation radius \(r_{2}\)/mm & 1.475 & Sheath relative dielectric constant \(\varepsilon_{2}\) & 3 \\ Metal shielding radius \(r_{3}\)/mm & 2.1 & Inner conductor resistivity \(\rho_{1}\)/(\(\Omega\)-m) & \(1.75\times 10^{-8}\) \\ Cable radius \(r\)/mm & 2.675 & Metal shielding resistivity \(\rho_{2}\)/(\(\Omega\)-m) & \(1.75\times 10^{-8}\) \\ \hline \end{tabular}
\end{table} 
Table 2: Parameters of RG223 coaxial cables. Figure 6: Experimental setup. and d was 0.5 m. Each of the laying configuration was measured 5 times, and the results were highly consistent. Figure 8 shows one group of the measured results. The signals on the cross-bonding wires of phase A and B are similar while the signals in phase C are smaller. Besides, the polarities of the measured pulses are the same. To further confirm the influence of the laying parameters, two kinds of methods were used to characterize the measured signal amplitude. One is to directly use the peak-to-peak value in the time domain, i.e., the difference between the positive peak and the negative peak of the time domain signal. The other method uses the average amplitude spectrum in the frequency domain, namely, calculates the average value of the Fourier transform of the time domain signal in the range of 3-30 MHz. Since the amplitudes of the phase A and phase B are not exactly equal in practice, the measured \(I_{\text{major}}\)/\(I_{\text{minor}}\) ratio was calculated by dividing the average amplitude of the phase A and B by the amplitude of phase C. Table 3 shows that the \(I_{\text{major}}\)/\(I_{\text{minor}}\) ratio of the average amplitude spectrum is closer to the theoretical value than the peak-to-peak value and the error is less than 10%. This is because the average amplitude spectrum excludes the influence of propagation delay and low-frequency amplitude spectrum, which is more in line with the premise of the theoretical definition.