**2. Physical Fundamentals**

Comprehensive knowledge about the physical fundamentals of the discharge formation is necessary, in order to understand the different discharge phenomena observed in this investigation.

A necessary requirement for the discharge inception is the presence of a starting electron. It can be emitted from the cathode [19] or by electron detachment of gas molecules. This detachment mainly occurs due to cosmic radiation [20,21]. The starting electron will be accelerated in the stationary electric field. As soon as the kinetic energy, absorbed from the electric field, is high enough, ionization due to the collision with other molecules or ions takes place. Newly generated electrons are again accelerated in the electric field. The number of ionization processes per electron and per unit of distance is described by the ionization coefficient *α*. At the same time, *η* electrons are attached to molecules or ions. If more electrons are generated than attached to ions or molecules (*α* > *η*), an electron avalanche develops. Hence, the main parameter characterizing insulating gases is the effective ionization coefficient *α*¯ = *α* − *η*. If the effective ionization coefficient becomes *α*¯ > 0, the number of free electrons in the gas increases like an avalanche. The ionization coefficient depends on the type of insulating gas [22], mainly determined by its electron affinity. For example, the electron affinity of oxygen is lower than that of SF6. Nitrogen has no ability to attach free electrons. Hence, the electrical strength of synthetic air is lower than that of SF6. The effective ionization coefficient *α*¯ can be calculated according to Equation (1) for SF6 and according to Equations (2) and (3) for atmospheric air depending on the electric field strength *E* and the gas pressure [21,23]. Since the dielectric strength of an insulating gas depends on its gas density, *α*¯ is related to *p*20°C, the gas pressure at 20 °C, in order to specify this density

dependence. It is assumed that the discharge behavior of pressurized synthetic air and pressurized atmospheric air is comparable.

$$\frac{n\_{\rm SF\_6}}{p\_{20\,\text{°C}}} = 28 \frac{1}{\text{kV}} \cdot \left(\frac{E}{p\_{20\,\text{°C}}} - 89 \frac{\text{kV}}{\text{mm} \cdot \text{MPa}}\right) \tag{1}$$

$$\frac{\frac{R\_{\text{air}}}{P\_{20} \cdot \text{°C}}}{\frac{P\_{20} \cdot \text{°C}}{P\_{20} \cdot \text{°C}}} = 0.22 \cdot \frac{\text{mm} \cdot \text{MPa}}{\text{kV}^2} \cdot \left(\frac{E}{p\_{20} \cdot \text{°C}} - 24.4 \frac{\text{kV}}{\text{mm} \cdot \text{MPa}}\right)^2 \tag{2}$$

 *E* kV

*E*

kV

$$\frac{\frac{R}{k}\text{air}}{\frac{p\_{\text{air}}}{p\_{\text{20}}\cdot\text{°C}}} = 0.5 \cdot \frac{\left(\text{mm} \cdot \text{MPa}\right)^{0.75}}{\text{kV}^{1.75}} \cdot \left(\frac{E}{p\_{20}\cdot\text{°C}} - 24.4 \frac{\text{kV}}{\text{mm} \cdot \text{MPa}}\right)^{1.75} \tag{3}$$

$$\left(\frac{E}{p\_{20}\cdot\text{°C}} \left[\text{no} \cdot \frac{\text{kV}}{\text{mm} \cdot \text{MPa}} \cdot \frac{\text{kV}}{\text{m} \cdot \text{m} \cdot \text{MPa}}\right]^{1.75}\right)^{-1.75}$$

According to the physics, the ionization coefficient of SF6 is considerably lower than that of synthetic air (Figure 1). This leads to the assumption that the inception and growth of the PD avalanches will show remarkable differences between the insulating gases. Due to the significantly higher slope of the effective ionization coefficient of SF6 compared to air in the zero crossing (*α*¯ ≥ 0), the discharge behavior of SF6 is expected to be much stronger, dependent on small changes of the electric field strength.

**Figure 1.** Effective ionization coefficient of air and SF6 in dependence of electrical field strength and gas pressure (according to Equations (1)–(3)).

The charge carriers, electrons and ions, generate drift in the electric field with a certain velocity, which is inversely proportional to the gas pressure [20]. Due to their higher mass, the mobility *μ*ion of positive and negative ions is significantly lower than the mobility *μ*e of electrons (Table 1).


**Table 1.** Mobility of ions and electrons in SF6 and air at approximately 0.1 MPa.

The differences in the drift velocities of electrons and ions lead to a concentration of electrons in the avalanches' head, whereas the generated ions can be considered as remaining at their position. If the number of electrons in the avalanches' head exceeds the critical number of 108, the electric field strength of the avalanche, in addition to the background field, is sufficiently high to initiate photoionization, and thus, additional electron avalanches in the vicinity of the first discharge channel are started. This discharge process is well known as streamer discharge [30,31]. If streamer inception takes place, the electrical field strength exceeds the gas density dependent dielectric strength of the insulating gas in a certain region, the so-called critical volume.

In SF6, the discharge inception is equivalent to the streamer inception [21]. In addition to this single streamer discharge, it is reported in the literature that one PD impulse with a high magnitude can be followed by several impulses with a lower magnitude [32,33]. These subsequent PD events are generated in the channel of the first streamer [32].

The charge carriers, generated by the streamers, can form a stable space charge, which significantly influences the electric field strength in this region. If the number of charges generated is equivalent to the number of charges drifting off from the space charge region, a constant pulseless direct current can be measured, known as glow discharge. It is evident that a streamer discharge might be superimposed on this glow discharge, if the space charge region becomes instable [21].

The described charge carrier movement in the electric field can be measured as a current (Figure 2). This current consists of a fast rising electron current *I*e, representing the growth of the electron avalanche, and a slow ion current *I*ion, representing the ion drift. According to the literature [33,34], the electron current is significantly higher than the ion current.

**Figure 2.** Partial discharge current consisting of electron current *I*e and ion current *I*ion [33].

To the authors' knowledge, there is no comprehensive study of the partial discharge behavior of a protrusion in gas-insulated systems under DC voltage stress with respect to PD current measurements. For this reason, in this contribution, the electron current *I*e and the ion current *I*ion are measured depending on the polarity, the applied voltage, and the gas pressure. It is expected that a classification of the occurring PD types can be derived from the measurements considering the current amplitudes and the time differences between subsequent discharge impulses. This classification would provide a basis for a meaningful interpretation of PD measurements in gas-insulated DC systems. A comparison of the results obtained in SF6 with measurements in pressurized synthetic air will give an outlook for future research focusing on alternative insulating gases under DC voltage stress.
