3.2.2. A PD sequence

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

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

).

120 Plasma Science and Technology - Basic Fundamentals and Modern Applications

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

identical, which show that the simulation results are reasonable. However, there are some

) are

),

shorter than that of positive ions.

(b) on the lower surface of cavity (unit: cm<sup>2</sup>

slight differences due to the simplification of model.

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, 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.

voltage application due to the existence of a discharge time lag. After the discharge is terminated, the electric field within the cavity is dramatically reduced (as in Figure 8c), which is attributed to the effect of surface charge accumulation. Then, the surface charges begin to decay, and the electric field within the cavity gradually recovers. After it exceeds the critical

Numerical Modeling of Partial Discharge Development Process

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123

During the process of surface charge decaying (as in Figure 8b), the initial concentration of electrons and positive ions is approximately identical, but residual charges are completely distinct at the moment when a next discharge occurs. Due to the decay rate of positive charges faster than that of electrons, the concentration of residual negative surface charges is much higher. Therefore, compared with positive ions, residual electrons resulting from previous dis-

PD, a type of low-temperature plasma, has some distinctive features, which determines its simulation method different from that of other types. In detail, as for the most representative PD type, cavity PD, it is necessary to take the streamer propagation, surface charge accumulation and decay, free electron supply into account so that the PD mechanism could be clarified. Besides, due to the stochastic character of PD, a large number of PD data must be obtained

Traditional simulation models about PD could be mainly divided into two categories: based on the point of view of circuit and based on the point of view of field. The former indicates a-b-c model, in which the discharge process is replaced by capacitor charging and discharging. The latter consists of Pedersen's model, conductance model, and Niemeyer's model, in which the discharge process is modeled by the variation of gas volume conductivity or significant simplification of discharge

Based on the simulation method for a single PD, we develop it by using fluid equations combined with Poisson's equation. In terms of the model, microscopic physical processes, that is, streamer development and surface charge accumulation, could be obtained, as well as macroscopic parameters, that is, discharge current and discharge time, and the interaction between adjacent discharges. It is found that electrons and positive ions, respectively, land on the two surfaces of the cavity, and the accumulation time of positive ions is much longer than that of electrons. During a PD sequence, the decay of surface charges resulting from previous discharge could be considered to be the key factor, contributing to the occurrence of the subsequent one.

We would like to thank Prof. George Chen from the University of Southampton for the inspiring discussion and appreciate the financial support from the National Natural Science

process. Anyway, these models could not reflect the PD development process physically.

value, and the condition for discharge time lag is satisfied, the next PD takes place.

charge have a larger influence on the subsequent one during a PD sequence.

4. Conclusions

with the help of simulation.

Acknowledgements

Foundation of China (51607128).

Figure 8. The first eight discharges during the PD sequence: (a) discharge time and magnitude, (b) surface charge decaying process, and (c) evolution of electric field within the cavity.

Besides, by analyzing the PD sequence, the interaction between adjacent discharges is obtained. Figure 8 shows the temporal evolution of surface charges and electric field within the cavity of first eight discharges. The first PD does not take place immediately after the voltage application due to the existence of a discharge time lag. After the discharge is terminated, the electric field within the cavity is dramatically reduced (as in Figure 8c), which is attributed to the effect of surface charge accumulation. Then, the surface charges begin to decay, and the electric field within the cavity gradually recovers. After it exceeds the critical value, and the condition for discharge time lag is satisfied, the next PD takes place.

During the process of surface charge decaying (as in Figure 8b), the initial concentration of electrons and positive ions is approximately identical, but residual charges are completely distinct at the moment when a next discharge occurs. Due to the decay rate of positive charges faster than that of electrons, the concentration of residual negative surface charges is much higher. Therefore, compared with positive ions, residual electrons resulting from previous discharge have a larger influence on the subsequent one during a PD sequence.
