**6. Conclusions**

In this contribution, experimental investigations on the flashover of a non-uniform field polluted insulators under AC was carried out. Different electro-geometrical parameters (conductivity, radius, inter-electrode distance, and the plane length) were considered.

The established model makes it possible to predict the flashover voltage of a polluted insulator, which is very useful information for electrical engineering. In addition, it is possible to determinate the initial value of the insulator degradation represented by the inception voltage. Knowledge of this data allows designers, builders, and managers of electrical power transmission lines to combat the inconvenience of insulator pollution in a technical manner. Moreover, it was confirmed that the flashover phenomenon depends on the interaction between the electric field and the conductivity of pollution layers.

The established model is in essence based on the electric field and the randomness of the evolution of the electric discharge on the surface of the polluted insulator. The choice of the progression criterion, which considers the modified Peek's law, confirms that the discharge bypasses the dry bands and evolves in the air in contact with the pollution layer.

From these investigations, we report that the flashover voltage increased with increasing inter-electrode distance and high-voltage electrode radius. It decreased with increasing conductivity. The arc development was particularly dependent on the pollution layer's conductivity and electrical field stress, which plays a primordial role on the flashover process. These observations were confirmed by the model.

The prediction of the electric arc initiation and development on a polluted surface is of significant interest for designing an HV system suitable for heavily polluted areas. It is hoped that the results presented can be viewed as a benchmark and a challenge for further research. It is also expected to have an impact on further modelling/simulation of discharge inception and propagation on polluted surface. Work is now in progress to improve the propagation concept and extend the model to non-uniformly polluted surfaces and real-life insulators. This should be of grea<sup>t</sup> help in outdoor insulation design.

**Author Contributions:** This research was conducted by M.L.A. under the supervision of S.B., I.F. and F.M.; M.L.A., F.M. and M.J. conducted the experimental investigations. Writing—original draft preparation, M.L.A.; writing—review and editing, S.B., I.F., D.K. and A.B. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work was partially sponsored by the Natural Sciences and Engineering Research Council of Canada (NSERC) under gran<sup>t</sup> no. RGPIN-201504403.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Acknowledgments:** M.L.A. is especially thankful to the Directorate General for Scientific Research and Technological Development—Algerian Ministry of Higher Education and Scientific Research for supporting his research stay in Canada.

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