## 4 Field Test in a Substation  
To verify the effectiveness of the proposed separation method for separating PD sources in a substation, a field test was performed in a 500 kV power substation. Four omnidirectional antennas arranged in a planar rectangular were applied for collecting PD UHF signals. A spatial coordinate system was set with antenna 1 as the coordinate origin. Then, the coordinates of four antennas were fixed as (0, 0) for #1, (1.58, 0) for #2, (1.58, 1.16) for #3, and (0, 1.16) for #4 in meters, respectively, as shown in Figure 5a,b. The frequency response of each UHF antenna was same as the bandwidth, 0.2-6 GHz. An oscilloscope was used as a signal acquisition device, the received signals were collected synchronously with a sampling rate of 5 GHz. A PD simulator was placed in the substation at planar coordinates (\(-\)4, 5.5). The simulator can simulate PDs of different capacity between needle tips or plates, including 500-16,500 V contacts or air discharges, with an error of less than 5%. The rise time of the discharge pulse is 0.8 ns with an error of 25% or less. The frequency spectrum of the discharge signal produced is in the range of 0-2 GHz. Two PD sources were found in the substation. One is an external PD source at the terminal of an incoming line, which can be measured by an ultraviolet imager, and the other is produced by the PD simulator. The coordinates of the external discharge source is (\(-\)4.4, \(-\)7). Two hundred groups of PD UHF signals in the substation were acquired and analyzed. The first 20 groups of signals were used to determine the number of signal types by Fisher-like class separation measures described in Equation (9). A flow chart for determining how many signal types are in the substation is shown in Figure 6. Meanwhile, the signals and bispectra included in each type are stored  
Figure 5: Arrangement of the antenna array in the substation. (**a**) Antenna array in the substation. (**b**) Planar schematic diagram of the antenna array. respectively. The signal data and its estimated bispectra are denoted as \(x_{i}^{(j)}(n)\) and \(\overline{B}_{i}^{(j)}(\mathbf{\upxi})\), where the superscript \(j\) means the \(j\)th type of all signals, and the superscript \(i\) means the \(i\)th group among the \(j\)th type. By the steps shown in Figure 6, two types of signals are deduced--the waveforms and frequency spectra--and are shown in Figure 7a-d. The result is identical to the detected PD sources in the substation. Figure 6: Flow chart for obtaining the number of signal types. Figure 7: UHF signals radiated by the PD sources observed in the substation. (**a**): Waveform of UHF signals radiated by the PD simulator. (**b**): Waveform of UHF signals radiated by the extra discharge (**c**,**d**): Frequency spectra of (**a**,**b**), respectively. From the distribution of the frequency spectrum, it can be determined that PD UHF signals acquired in the substation are blended with white noises, wireless communication signals of 900 MHz, and radio signals of 100 MHz, which is similar to the noises simulated in Section 3. The bispectra of the two kinds of UHF signals are demonstrated in Figure 8a,b. From the signals collected in the substation, 20 signals of each type were selected as samples, and the Fisher-like class separation measures were calculated. The separation measure calculated by the bispectra is shown in Figure 9. Then, the radial basis neural networks used for separating PD sources can be trained. The PD sources calculated based on time delays are (\(-4.55\), \(-6.78\)) and (\(-3.83\), \(5.23\)) in meters, respectively, which were identified as the external PD source and the PD simulator applied in the substation. The two kind of signals were separated with the proposed bispectra method. The signals' separation rates are shown in Table 3 with different numbers of bispectra selected as characteristic parameters. It can be seen from Table 3 that the separation rate is more than 70% with the proposed algorithm.