**6. Conclusions**

Breakdown experiments on multiple protrusions and on artificially roughed surfaces were done in uniform and weakly uniform background fields with SF6 and CO2 at 0.4 and 0.6 MPa, respectively. The voltage waveform was a stepped DC pulse with time to breakdown within 10 μs, which is comparable to that of standard lightning impulse (LI). With the multiple protrusion array, the number of protrusions and the lengths of the protrusions was varied in the ranges of 1–100 and 0.05–2 mm, respectively. For the roughened surfaces, a mean peak-to-valley roughness ( *Rz*) of 62 ... 65 μm was realized, and two di fferent surface areas were tested. From the breakdown experiments, Weibull breakdown probability distributions were deduced and 50% breakdown probability fields and the standard deviation σ of the distributions were determined. Enlargement law scaling predictions according to (1) were done to predict the e ffect of changing the number of protrusions or surface area. These predictions were compared to the experiments. Additionally, calculations by physical models, describing first electron, streamer inception and breakdown by leader propagation or streamer-to-spark transition at single protrusions were done for interpretation of the experimental results. The interpretations were supported by optical observation of the discharges.

The following main observations were obtained: In SF6, breakdown fields are well below the critical field, even for protrusions below 1 mm length, whereas for CO2 breakdown occurs closer to the critical field. The breakdown fields can be interpreted and roughly described by the physical models, taking into account the uncertainties of the experiments and of the models. In SF6 the leader propagation criterion is decisive for breakdown at both polarities for single protrusions. Increasing the number of the protrusions to 20 lowers the breakdown field for both gases in agreemen<sup>t</sup> with the predictions from the enlargement laws, compared to the single protrusion. No significant e ffect on the protrusions spacing was seen in CO2 with 20 protrusions. Discrepancies with the enlargement law scaling were observed for both gases in some cases when increasing the number of protrusions to 100. The results show that enlargement laws cannot be generally applied without considering the various physical processes which influence breakdown, i.e., the availability of a first electron, streamer and leader inception and propagation and spark transition. The decisive breakdown criteria depend on the gas, the protrusion lengths and polarity of the applied voltage, which leads to di fferent minimum limiting fields which cannot be exceeded by an enlargement law. Additionally, the various physical processes will not scale in the same way when using an enlargement law. All this limits the accuracy of an enlargement law scaling. This is confirmed by the results from the rough surfaces. At positive polarity the breakdown fields dropped for SF6 and CO2 approximately to the streamer inception field, when increasing the surface from 240 to 6450 mm2, i.e., there is a physical limit for breakdown which is reached for su fficiently large surfaces. This decrease was underpredicted by the enlargement law. At negative polarity and SF6, only a very small enlargement e ffect is seen in the experiments, in agreemen<sup>t</sup> with the predictions. In CO2 and negative polarity, there is a more pronounced e ffect of the surface area, which is still much smaller than for positive polarity, however. Again, this decrease is underpredicted by the enlargement law. The e ffect of the protrusion spacing was investigated only in CO2with 20 protrusions. No significant e ffect within the experimental scatter was seen.

**Author Contributions:** Conceptualization, M.S. and O.C.F.; methodology, M.S., D.O. and O.C.F.; software, D.O. and O.C.F.; validation, M.S., F.M. and K.N.; formal analysis, O.C.F.; investigation, O.C.F.; resources, M.S. and D.O.; data curation, O.C.F.; writing—original draft preparation, M.S. and O.C.F.; writing—review and editing, M.S., O.C.F., K.N. and F.M.; visualization, O.C.F. and M.S.; supervision, M.S., F.M. and K.N.; project administration, O.C.F. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Acknowledgments:** The authors would like to thank Filip Halak for assisting with experimental work and Anders Ulfsnes for performing field calculations in COMSOL during their internships at Hitachi ABB Power Grids Research, Switzerland.

**Conflicts of Interest:** The authors declare no conflict of interest.
