*Article* **Evolutionary Algorithms for Community Detection in Continental-Scale High-Voltage Transmission Grids**

**Manuel Guerrero 1, Raul Baños 2,\*, Consolación Gil 1, Francisco G. Montoya 2 and Alfredo Alcayde 2**


Received: 22 October 2019; Accepted: 28 November 2019; Published: 3 December 2019

**Abstract:** Symmetry is a key concept in the study of power systems, not only because the admittance and Jacobian matrices used in power flow analysis are symmetrical, but because some previous studies have shown that in some real-world power grids there are complex symmetries. In order to investigate the topological characteristics of power grids, this paper proposes the use of evolutionary algorithms for community detection using modularity density measures on networks representing supergrids in order to discover densely connected structures. Two evolutionary approaches (generational genetic algorithm, GGA+, and modularity and improved genetic algorithm, MIGA) were applied. The results obtained in two large networks representing supergrids (European grid and North American grid) provide insights on both the structure of the supergrid and the topological differences between different regions. Numerical and graphical results show how these evolutionary approaches clearly outperform to the well-known Louvain modularity method. In particular, the average value of modularity obtained by GGA+ in the European grid was 0.815, while an average of 0.827 was reached in the North American grid. These results outperform those obtained by MIGA and Louvain methods (0.801 and 0.766 in the European grid and 0.813 and 0.798 in the North American grid, respectively).

**Keywords:** power grids; supergrids; high-voltage power transmission; complex networks; community detection; modularity; evolutionary algorithms; generational genetic algorithm; modularity and improved genetic algorithm; Louvain modularity algorithm
