3.2.1. A PD development process

The process of PD development in the cavity consists of two stages: the streamer propagation and surface charge accumulation. Figures 4 and 5 show the temporal and spatial distribution of electrons and positive ions during this process, respectively. After discharge conditions are satisfied, the streamer is initiated near the lower surface of dielectric. With the help of applied field, electrons propagate toward the anode. At 0.72 ns, the head of streamer arrives at the upper surface of dielectric. Based on this, the streamer development velocity could be

Figure 4. Evolution of electron concentration distribution during the first PD (a) within the cavity volume (unit: cm<sup>3</sup> ) and (b) on the upper surface of the cavity (unit: cm<sup>2</sup> ).

Charge transportation within the cavity will induce a current pulse, as in Figure 6, which could reflect the streamer development. The peak value of pulse appears at 0.72 ns; at this moment, the streamer head arrives at the upper surface of the cavity. The pulse width lasts for 1.4 ns; during this period, the accumulation of electrons is terminated. On the contrary, positive ions still move in the cavity volume. It is inferred that positive ions have a minor contribution to the current pulse because of their low drift velocity. A low-inductance resistor connected to the cathode is usually employed to detect a current, but this current slightly

Numerical Modeling of Partial Discharge Development Process

http://dx.doi.org/10.5772/intechopen.79215

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A PD sequence consisting of 100 continuous discharges is obtained by the simulation (Figures 4–6 show the first discharge development process). Figure 7 shows the discharge time and the peak value of current of each discharge. In terms of this information, some statistical parameters of PDs, for example, discharge frequency and average discharge magnitude, could be calculated,

differs from that in Figure 6 [40].

and discharge patterns could be depicted.

Figure 6. Current pulse waveform of the first PD obtained by simulation.

Figure 7. A PD sequence with 100 continuous discharges.

3.2.2. A PD sequence

Figure 5. Evolution of positive ion concentration distribution during the first PD (a) within the cavity volume (unit: cm<sup>3</sup> ), (b) on the lower surface of cavity (unit: cm<sup>2</sup> ).

calculated, which equals 3.5 107 cm/s and the order is in accordance with other researcher'<sup>s</sup> simulation result [39]. Then, electrons begin to accumulate on the upper surface of dielectric, and the density of surface charges reaches a saturation value after 1.4 ns. During this period, positive ions almost maintain stationary because the drift velocity is approximately 1/100 of the electron. However, positive ions seem to move according to Figure 5, and the distribution appearance looks like a ladle, which are attributed to the impact ionization of electrons. At 11.9 ns, a large number of positive ions land on the lower surface of dielectric, and the accumulation is terminated at 147.8 ns. Therefore, the accumulation time of electrons is much shorter than that of positive ions.

Based on the simulation results, it is found that the distribution of surface charges appears as a spot, and the maximum charge density locates at the middle of a spot. Compared with the experimental results [36], the distribution shape and surface density level (0.1 nC/mm2 ) are identical, which show that the simulation results are reasonable. However, there are some slight differences due to the simplification of model.

Charge transportation within the cavity will induce a current pulse, as in Figure 6, which could reflect the streamer development. The peak value of pulse appears at 0.72 ns; at this moment, the streamer head arrives at the upper surface of the cavity. The pulse width lasts for 1.4 ns; during this period, the accumulation of electrons is terminated. On the contrary, positive ions still move in the cavity volume. It is inferred that positive ions have a minor contribution to the current pulse because of their low drift velocity. A low-inductance resistor connected to the cathode is usually employed to detect a current, but this current slightly differs from that in Figure 6 [40].
