*4.1. Test Cases*

To analyse the performance of the genetic algorithms, graphical models of two supergrids were considered: the European grid, including part of Russia, North Africa, and part of the Near East; and the North American grid.

• The European electric network was obtained from the European Network of Transmission System Operators (ENTSO-E) [58]. The ENTSO-E group consists of 43 electricity transmission system operators from 36 countries across Europe who are responsible for the bulk transmission of electric power on the main high-voltage electric networks. This power network, which also includes data from North African and Near Eastern countries, is formed by transmission lines designed for 220 kV voltage and higher and generation stations with a net generation capacity of more than 100 MW.

• The North American electric network was obtained using the GridKit 1.0 toolkit, which was developed in the context of the SciGRID project at the NEXT ENERGY-EWE Research Centre for Energy Technology [59]. GridKit is a power grid extraction tool that converts geographical objects representing elements of power systems in OpenStreetMap to model the electric network. This network covers the United States, Canada, and Mexico and includes transmission lines that operate at relatively high-voltages varying from 69 kV up to 765 kV. The power grid of the United States is probably the best system studied in the literature, due to the particular characteristics of the network. The regions covered receive their bulk electricity from three separate electric grids: the huge Eastern Interconnection, the Western Interconnection, and the relatively small Texas grid [60], which is almost entirely managed by the Electric Reliability Council of Texas (ERCOT).

Table 1 describes some graphical characteristics of these networks. The number of nodes and edges is very large, which denotes the high complexity of community detection in these networks. Note that the dimensions of these networks are significantly larger than other power grids considered in recent studies (see, e.g., [22]). In fact, to our knowledge, no previous paper has applied graph-based analytical methods to power networks of these dimensions.


**Table 1.** Graph description of the European (EU) and North American (NA) power grids.

