**5. Conclusions**

The optimal design of high-voltage transmission networks is a critical issue to supply electrical energy to residential areas and industries. In fact, the growing integration of power grids across regions requires investment in more transmission power supply systems to ensure system stability and guarantee power supplies. To reach that aim, it is important to investigate the topological characteristics of these supergrids. This paper opens a new avenue of research by analysing the community structures in supergrids in a fast and effective way. In particular, it is shown that solving the community detection problem with evolutionary algorithms allows one to obtain some key ideas about the structure of these networks. In particular, two evolutionary methods that include powerful initialisation methods and evolutionary search operators under the guidance of modularity were used to detect communities in large-scale networks. The evolutionary algorithms adopted a flexible and adaptive analysis of the characteristics of the power grids with different levels of detail (number of communities). The empirical study considered two large networks representing supergrids: (i) Europe, including Russia, North Africa, and part of the Near East (7893 nodes and 10,346 branches); and (ii) North America (16,063 nodes and 20,169 edges). In particular, these methods were able to partition the networks into some loosely coupled sub-networks (communities) of similar scale, such that nodes within a community were densely linked, while connections between different communities were sparser. Numerical and graphical analysis using graph visualisation tools showed that GGA+ slightly outperformed MIGA, especially when the number of communities increased. Both evolutionary approaches outperformed the modularity values of the communities detected by the Louvain method implemented in Gephi. The results obtained show that evolutionary approaches are efficient methods for detecting communities in supergrids having thousand of nodes, and provide interesting topological information about the physical distribution and concentration of these elements of the grids. Future work will apply parallel and multi-objective optimisation methods and include the electrical properties of the power networks.

**Author Contributions:** Conceptualisation, M.G. and R.B.; methodology, C.G. and R.B.; software, M.G. and R.B.; validation, M.G., R.B., and A.A.; formal analysis, F.G.M. and C.G.; investigation, M.G., R.B., and C.G.; resources, F.G.M.; data curation, R.B. and A.A.; writing—original draft preparation, R.B., F.G.M., and A.A.; writing—review and editing, R.B., F.G.M., and C.G.; visualisation, A.A. and F.G.M.; supervision, C.G. and R.B.; project administration, C.G. and F.G.M.

**Funding:** This research received funding by Spanish Ministry of Science, Innovation, and Universities (project PGC2018-098813-B-C33).

**Acknowledgments:** This research was supported by the Spanish Ministry of Science, Innovation and Universities (project PGC2018-098813-B-C33), and by the Regional Government of Andalusia (ceiA3 project).

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