## 1 Introduction
### Reference PD Pulses and Pulsating Noise Trains
#### 2.1.2. PD Pulse Trains in GIS, Cable Systems, and AIS under HVDC Stress
\[\text{u(t)}=\text{Uo}\cdot(1-\text{e}^{-\text{t/$\tau$}}) \tag{1}\]  
A summary of the most relevant information about the PD pulse trains is shown in Table 2.  
For each defect and polarity, it is indicated the number of available PD trains and their main parameters: average number of pulses per train, \(m\), mean charge value, \(q\), and the accumulated charge value \(q_{a}\) in the testing time interval of 150 s. Furthermore, in the testing time interval of 150 s, the following complementary parameters were analysed in two periods, in the first 50 s and in the rest 100 s: average current, \(I\), expressed in pA, average number of pulses, \(m\), and PD repetition rate expressed in pulses/s. For cavity and floating potential defects, the PD activity is less significant in the second time interval. However, for corona and surface defects, the PD activity remains nearly constant in both periods. For each insulation defect, the following six graphs were considered: apparent charge of individual pulses vs. time in 150 s, accumulated charge vs. time in 150 s, PD histogram of the charge intervals, monotonous decreasing PD histogram, \(\Delta\text{q}_{\text{n}}-\Delta\text{q}_{\text{n}-1}\) pattern and \(\Delta\text{t}_{\text{n}}-\Delta\text{t}_{\text{n}-1}\) pattern, with the last two corresponding to at least 500 pulses collected from a set of 150 s testing time intervals. As an example, the graphs corresp  
Figure 1: Test cell of moving particle insulation defect in SF\({}_{6}\): (**a**) dimensional drawing, (**b**) electric field model, (**c**) internal view of the test cell being: (1) HV electrode, (2) grounding electrode, (3) moving particles, (4) support insulating bars, (5) insulating envelope and (**d**) external view of the test cell. measured in positive and negative polarity are displayed in Table 3. These same graphic representations are shown also for an impulse noise type of an HVDC installation. Different studies show that PD pulses appear in these elements [10; 11; 12] when the voltage blocking is stressed due to the local electric field between the silicone gel and the metallised ceramic, to the sharp edges of the copper metallisation, or to the internal defects in the substrate. The current standard IEC 61287 [13] states two testing cycles. The first one to prove the electrical insulation under ac voltages for 1 min and the second one related to a PD test after a pre-stress voltage at 1.5 times its maximum permissible blocking voltage, U\({}_{\text{m}}\), for 1 min, then the voltage is decreased to 1.1 times U\({}_{\text{m}}\) for 30 s to measure PD in the last 5 s. However, to obtain representative PRPD patterns related to aging conditions, a PD analysis has been performed in a semiconductor junction under a repetitive overvoltage of around 16% of its maximum repetitive peak reverse voltage (U\({}_{\text{RRM}}\) = 1.4 kV, 70 A). The rise time of the surge was chosen to be a few ms (\(\tau\approx\) 2 ms), for instance, the rise time of a 50 Hz sinusoidal waveform. The charge and PD repetition rate values were analysed during 400 overvoltage cycles when the semiconductor temperature changed from 125 \({}^{\circ}\)C to 88 \({}^{\circ}\)C. The PD representative graphs and patterns of this semiconductor defect are shown in Figure 2. The temperature influence versus the average number of PD pulses and the mean value of the apparent charge is shown in Figure 3. The higher the temperature, the greater the number of PD pulses, but the average charge value of the PD pulses, \(q\), remains nearly constant. The average number of PD pulses generated in these working conditions is 8.4 pulses per overvoltage cycle with an average charge of around 31 pC. The main PD pulse activity appears once the maximum repetitive peak reverse voltage is overpassed. However, when the temperature increases the probability of PD pulse occurrence close to the maximum repetitive peak reverse voltage increases (see Figure 3).