**2. Test Setups**

### *2.1. Test Circuit and Protrusion Setup*

The experiments and the analysis were performed at Hitachi ABB Power Grids Research, Switzerland. The setup is shown schematically in Figure 1. It is a similar setup as used in previous investigations where the partial discharges and breakdown at a single protrusion was investigated [37,38]. In the present investigation, the plate electrode with the protrusion on the ground

side was replaced by a plate with a protrusion array. The protrusion array plate had 20 × 20 holes of 1.2 mm diameter and 2 mm center to center spacing—see Figure 2a. The protrusions were at ground potential. When we refer to polarity in the following always the polarity of the protrusions is meant.

**Figure 1.** Schematic setup with a single protrusion. The gap length was D = 10 or 15 mm. The load capacitance was charged via a Van de Graaf (VdG) DC source and switched via a resistor and closing switch onto the test gap. The discharges were observed by a high-resolution digital camera (Nikon D9000).

**Figure 2.** Protrusion array. (**a**) Protrusion array with 100 protrusions. (**b**) Protrusion tip details.

In the shown case in Figure 2a, 100 protrusions were inserted, but also fewer protrusions were tested. The protrusions were fixed to a matching grid by a magne<sup>t</sup> on a table below the perforated plate. The matching grid was moved by a stepper motor (Thorlabs GmbH, Bergkirchen, Germany, Model ZFS13B) with high positioning accuracy (<1 μm). The setup was placed, as in previous experiments, in a GIS test vessel filled with 0.4 MPa SF6 or 0.6 MPa CO2. With the stepper motor the protrusion lengths could be adjusted from outside, i.e., without opening the GIS. The overall reproducibility of the length adjustment was experimentally determined to be better than 20 μm for a single protrusion. In experiments with several protrusions, the total variation of lengths was less than 100 μm.

The protrusions were made out of steel with diameter 1 mm and had a conical tip of 1.6–1.7 mm length and tip radius of 66 μm at its end, marked by the yellow circle—see Figure 2b. The spacing between the protrusions was usually 4 mm. Only for CO2 when using 20 protrusions also a spacing of 2 mm was tested. The protrusions were replaced regularly, typically after a few hundred tests. The effect of erosion was checked by repeating experiments in new and worn conditions. The differences in the breakdown voltages due to this were within the uncertainties of protrusion lengths adjustments, i.e., repeating experiments with the same protrusion in new condition led to a similar breakdown voltage as in worn condition.

The applied voltage was a stepped DC pulse, as used in [37,38], with a rise time of 200 ns and voltage application time of 15 s, typically. In experiments with multiple protrusions, the voltage dropped due to partial discharges after a few 10 μs; thus, we focused on early breakdowns in the time range from the voltage peak to 10 μs after the peak was reached. From the time to breakdown, this can be associated with standard lightning impulse (LI) breakdown.

The applied voltage peak was varied over a wide range in order to obtain breakdown and withstand values. Typically, at least 100 tests were done per case. Between the tests, a small bias voltage of 20 kV was applied for 2 s to remove remaining ions from the gap, which could influence the start electron statistics. Thus, in the present investigation we determine breakdown fields at protrusions which can be related to LI standard wave shape. For small protrusion size in the order of 100 μm, breakdown also occurred at the plate electrode, e.g., at dust particles. With a single-shot digital camera (see Figure 1), it was checked that only breakdowns that occurred at a protrusion were taken into consideration.

### *2.2. Electrodes with Surface Roughness*

Two different electrode types were tested: a small plug-type contact of 19 mm diameter, as seen in Figure 3, and a larger Rogowski-shaped electrode of 120 mm diameter. The electrodes were placed against a plate electrode, as in setup 1 with a 10 mm gap. Both electrodes were made from stainless steel and were sandblasted with Corundum white grains, resulting in a surface roughness of *Ra* = 5–7 μm and *Rz* = 62–65 μm with the average roughness *Ra* = 1*L* - *L*0 *z*(*x*)·*dx* over the sampling length L of the contour *z*(*x*) and the mean peak-to-valley height *Rz* = 1*N* · *Ni*=<sup>1</sup> *Rt*,*<sup>i</sup>* over an assessment length consisting of various sampling sections with the maximum peak to valley height *Rt,i* within each section; see [43] for details. The surface roughness was determined by a non-contacting 3D profilometer Hyperion Compact from OPM. The effective area of the electrodes exposed to the electric field was about 240 and 6450 mm2, respectively. This effective field exposed area was determined from the location of the breakdown marks after test, as can be, e.g., judged from the photographs in Figure 3 for the plug-type contact. For the plug-type contact, the field enhancement factor was calculated to be 1.42.

**Figure 3.** Plug-type contact with diameter 19 and 10 mm length in new (**right**) and worn condition after test (**left**). The surface has a biradial shape with a radius of 5 mm at the side and 20 mm at the tip, respectively.
