2. Review of PD simulation models

erode and change the composite of the remaining component, leading to the deterioration of insulation performance and even the insulation failure. For example, as for high voltage power cable, PD resulting from the insulation defects could induce degradation of the solid dielectric due to chemical effect and physical attack by charge bombardment, and electric trees will be present after long-term service [1]. When the solid dielectric is across by the trees, an insulation fault takes place. On the other hand, PD parameters, such as discharge magnitude, discharge time, and so on, are determined by the characters of the gas and the remaining insulation. In terms of this, the PD measurement is often employed to diagnose the insulation status of power equipment. Whether understanding the negative effect of PD on insulation or equipment condition maintenance in the usage of PD measurement, it is based on the clear PD

110 Plasma Science and Technology - Basic Fundamentals and Modern Applications

In essence, PD is a gas breakdown phenomenon. Similar to the other types of low-temperature plasmas, the temperature of electrons during a PD is much higher than that of ions, which is equivalent to the neutral gas molecules. However, PD also shows some distinctive features. For example, because PD always results from the local defect with a high electric field, the discharge channel is very narrow (the radius may be 100 μm) and the duration time is very short (several to tens of nanoseconds). During a PD sequence, once previous PD is terminated, and the subsequent one may take place after several milliseconds or even several days [2]. This phenomenon indicates that PD has a stochastic behavior, due to not only the effect of gas itself but also the interaction between gas breakdown and the remaining insulation. Therefore, as for the PD, the mere investigation of gas breakdown is meaningless. On the contrary, the interaction between PD and the remaining insulation should be considered. More importantly, a large number of PD data should be obtained to seek for its statistical characters because of its

According to the type of the remaining insulation and electrode configuration, PD could be divided into three categories [3]: internal discharge, surface discharge, and corona, as in Figure 1. Internal discharge indicates a gas breakdown taking place in a cavity embedded in solid or liquid dielectric. Generally, the former is more common. It consists of the streamer development and the interaction between streamer and cavity walls. A surface charge usually occurs along the solid dielectric surface due to a large tangential component of electric field,

Figure 1. Three categories of PD: (a) internal discharge, (b) surface discharge, and (c) corona.

mechanism.

stochastic behavior.

Since a-b-c model was proposed, numerical modeling of PD has been developed for decades of years. During this period, many kinds of simulation models have been constructed, which could be roughly 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 and the latter consists of Pedersen's model, conductance model, and Niemeyer's model.

2.2. Pedersen's model

2.3. Conductance model

process.

can be described by the following equations:

There are two important parameters of PD, that is, physical charges and apparent charges. The former indicate the charges generated during a discharge process, while the latter are measured charges through external circuit. In order to establish the link between physical charges and apparent charges, Pedersen proposed a model to describe the transient process [23]. Without considering the charge exchange between solid dielectric and the adjacent electrode, the amount of apparent charges equals the induced charges at an electrode surface due to charge generation, recombination, and movement during a discharge process. Therefore, if the

physical charge distribution is known, the apparent charges could be calculated [24]

<sup>Q</sup>app ¼ �ðððλrd<sup>V</sup> �

where ε<sup>0</sup> is the vacuum permittivity, and ε<sup>r</sup> the relative permittivity.

from the discharge process and keeps unknown in this model.

where r and σ indicate volume and surface charge density within the cavity, respectively. λ, a dimensionless function, depends on the charge location, which satisfies Laplace equation

Pedersen's model is helpful to understand the measured results by using the pulse current method. However, the apparent charges depend on physical charge distribution which results

When PD takes place, a plasma region with a high charge concentration in the cavity is formed, so the gas conductivity largely increases in comparison with the initial state. Based on this fact, the discharge process is simplified by the variation of gas conductivity [13], which

∂r

where D is the electric displacement field, J the free current density. At the initial state, the gas conductivity is set to be zero. When a discharge takes place, it is set to be γgd and hence the electric field distribution within the cavity changes. In terms of the electric field evolution, some PD parameters are obtained, for example, apparent charges and physical charges.

Forssen compared the simulation results with the experimental data, and they were in general agreement but with a slight difference. Furthermore, Illias developed the simulation model by taking the surface emission and temperature variation during the discharge into account [14]. However, in any case, the increment of gas conductivity could not represent the PD

∇ � J þ

ðð λσd<sup>s</sup> (1)

Numerical Modeling of Partial Discharge Development Process

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

113

∇ � ð Þ¼ ε0εr∇λ 0 (2)

∇ � D ¼ r (3)

<sup>∂</sup><sup>t</sup> <sup>¼</sup> <sup>0</sup> (4)
