1. Introduction

Partial discharge (PD) is usually observed in power equipment, such as transformers, cables, gas insulated switchgears, and so on, which indicates a gas breakdown in essence induced by a local electric field distortion. It should be noted that it does not bridge the electrodes, differing from the gas breakdown across conductors. The remaining component of the whole insulation which does not suffer from PD could be oil, solid, or gas. On one hand, during the PD process, the heat energy, the charges with high velocity and chemical-active substances are released to

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited. © 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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 mechanism.

during which the interaction between streamer development and dielectric dominates. Corona often takes places in the local region around a conductor, which mainly involves the streamer development. Therefore, internal discharge could best represent PD, because it includes the two processes. In fact, the majority of PD simulations are concentrated on the internal dis-

Numerical Modeling of Partial Discharge Development Process

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There are many factors that could affect PD characters, such as the applied voltage (voltage waveform, amplitude, and frequency), electrode configuration, cavity (transportation parameters of gas, location, and size), remaining dielectric (permittivity, conductivity, and surficial parameters, e.g., morphology, surface trap distribution), and so on. To sum it up, two intrinsic factors behind them determine the evolution of PD behavior, that is, electric field and seed electrons. Generally speaking, two conditions must be simultaneously satisfied in order that a gas breakdown can take place: there must be at least one free electron in the gas, and the electric field must be of sufficient strength and duration time to ensure that this electron generates a sequence of avalanches [8]. Based on the conditions, it is inferred that the supply of free electrons and electric field affect not only the occurrence of PD but also its characters. Actually, the electric field is related to the applied voltage, electrode configuration, residual charges within the cavity, the cavity size, and the permittivity of remaining dielectric, while the supply of free electron depends on the gas status and surficial conditions of dielectric,

charge (also called cavity discharge) [4–7]. And in this chapter, we also focus on it.

corresponding to the volume generation and surface emission, respectively [9].

Looking back at the evolution of PD simulation methods, the a-b-c model was initially proposed [10–12], in which the discharge process was considered as charging-discharging of capacitors. Subsequently, some researchers held that the discharge could be represented by the increase of gas conductivity, and the current continuity equation was used to calculate discharge parameters [13–15]. On the contrary, others thought that a discharge was actually the deployment of charges in the cavity, and Poisson's equation was enough [16–18]. Obviously, these models could represent the transient phenomenon of a discharge, but not reflect its physical processes. In recent years, a plasma model was employed to simulate single PD [19–21], in which the impact ionization, drift, diffusion, recombination, and other processes were quantitatively described by fluid equations. This model successfully obtained microscopic physical processes of a PD, but did not take the stochastic characters into account.

In this chapter, we firstly reviewed PD simulation models in brief, which consisted of the a-b-c model, Pedersen's model, conductance model, Niemeyer's model and plasma model, and analyzed their merits and drawbacks. Then, an advanced model was constructed to obtain physical processes, including the streamer propagation and surface charge dynamics, and macroscopic parameters, for example, discharge magnitude and moment of continuous PDs,

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

so that a comprehensive analysis was available.

2. Review of PD simulation models

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 stochastic behavior.

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.

during which the interaction between streamer development and dielectric dominates. Corona often takes places in the local region around a conductor, which mainly involves the streamer development. Therefore, internal discharge could best represent PD, because it includes the two processes. In fact, the majority of PD simulations are concentrated on the internal discharge (also called cavity discharge) [4–7]. And in this chapter, we also focus on it.

There are many factors that could affect PD characters, such as the applied voltage (voltage waveform, amplitude, and frequency), electrode configuration, cavity (transportation parameters of gas, location, and size), remaining dielectric (permittivity, conductivity, and surficial parameters, e.g., morphology, surface trap distribution), and so on. To sum it up, two intrinsic factors behind them determine the evolution of PD behavior, that is, electric field and seed electrons. Generally speaking, two conditions must be simultaneously satisfied in order that a gas breakdown can take place: there must be at least one free electron in the gas, and the electric field must be of sufficient strength and duration time to ensure that this electron generates a sequence of avalanches [8]. Based on the conditions, it is inferred that the supply of free electrons and electric field affect not only the occurrence of PD but also its characters. Actually, the electric field is related to the applied voltage, electrode configuration, residual charges within the cavity, the cavity size, and the permittivity of remaining dielectric, while the supply of free electron depends on the gas status and surficial conditions of dielectric, corresponding to the volume generation and surface emission, respectively [9].

Looking back at the evolution of PD simulation methods, the a-b-c model was initially proposed [10–12], in which the discharge process was considered as charging-discharging of capacitors. Subsequently, some researchers held that the discharge could be represented by the increase of gas conductivity, and the current continuity equation was used to calculate discharge parameters [13–15]. On the contrary, others thought that a discharge was actually the deployment of charges in the cavity, and Poisson's equation was enough [16–18]. Obviously, these models could represent the transient phenomenon of a discharge, but not reflect its physical processes. In recent years, a plasma model was employed to simulate single PD [19–21], in which the impact ionization, drift, diffusion, recombination, and other processes were quantitatively described by fluid equations. This model successfully obtained microscopic physical processes of a PD, but did not take the stochastic characters into account.

In this chapter, we firstly reviewed PD simulation models in brief, which consisted of the a-b-c model, Pedersen's model, conductance model, Niemeyer's model and plasma model, and analyzed their merits and drawbacks. Then, an advanced model was constructed to obtain physical processes, including the streamer propagation and surface charge dynamics, and macroscopic parameters, for example, discharge magnitude and moment of continuous PDs, so that a comprehensive analysis was available.
