**1. Introduction**

The optimal design and managemen<sup>t</sup> of these supergrids is a difficult task, since it is necessary to manage large systems that include heterogeneous power grids from different countries. Most investigations in power systems often analyse optimisation problems such as optimal power flow, unit commitment, and economic dispatch, among others [1,2]. The solutions to these problems are often determined by the symmetry of the admittance and Jacobian matrices [3,4], and the topology of high-voltage transmission lines that connect the power produced at generating stations to substations, at which point the power flow is derived to other transmission lines or stepped down in voltage, and then submitted across power distribution lines into the end users. Many publications have addressed the factors that constrain the development of electricity infrastructure [5,6]. In particular, experts have highlighted that existing electric grids are inadequate to cope with increasing volumes of renewable electricity [7]. For example, the transmission systems in European countries are old, and a many miles of lines need to be replaced, upgraded, and even expanded to secure market integration, ensure supply security, and cope with the expansion in renewable energy planned for the next few years [8]. A similar challenge is faced in the United States, where renewable energy generation also accounts for an increasingly high percentage of annual demand [9].

Taking into account the fact that worldwide demand for electricity has been increasing and will continue to, it is necessary to ensure the reliable and secure operation of electricity transmission networks to efficiently transport energy from generation sources to electricity consumers. To achieve this goal, decisions need to be supported by expert systems able to process a large number of variables. Graph-based network analysis is a powerful tool for describing many real systems in a variety of fields [10]. Topological analysis provides the infrastructural information of power systems that is essential to assess network robustness or to generate synthetic power grids [11]. For example, some studies have detected complex symmetric subgraphs in large-scale power grids [12], and have provided a list of symmetric subgraphs with respect to reference nodes observed in the US grid.

Most real networks (graphs) representing real systems have clusters, such that many edges connect nodes within the same cluster, and comparatively few edges connect nodes in different clusters. This is why community detection [13–15] has gained popularity in recent years, especially among researchers working with complex networks [16–18]. In particular, community detection has been applied in field of electrical engineering, including the managemen<sup>t</sup> of power grids [19–22]. However, keeping the complexity of the problem in mind, more work is needed to develop efficient algorithms to enable rapid community detection. With that aim, this paper evaluates the performance of evolutionary approaches for community detection in supergrids. These algorithms, which are guided by the modularity index [23] and consider different *degrees of abstraction* (i.e., detect any number of communities), enable a flexible and adaptive analysis of the power grid.

The remainder of the paper is organized as follows: Section 2 briefly describes the problem of community detection using graphs, and revises some previous studies that have been applied to electrical grids. Section 3 presents the main characteristics of two evolutionary algorithms used to solve the community detection problem using graphs [24]. Section 4 presents an empirical study that compares these methods for community detection in two supergrids. The conclusions of this work are provided in Section 5.
