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

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).

Community Detection in Electrical Grids Using Quantum Annealing

“…Each variable x i representing a bus can take a range of values K. D-Wave's internal algorithms enforce that this condition holds, meaning that no node i can be assign to more than one clusters. This conditions is exactly what Equation (7) describes. Consequently, one constraint and its λ parameter tuning are avoided.…”

“…As a preprocessing step, the Q e matrix must be calculated according to the procedure commented on Section III. Afterwards, we adapted the formulation of problem described by Equations ( 6) and (7) for the applied methods.…”

“…This approach has been applied from use cases in the transmission grid [6], [7] and the distribution grid [8]- [10]. [9] and [10] have used graph theory approaches as a framework to adapt conventional distribution networks into virtual microgrids that could increase the flexibility of electrical systems.…”

Photogrammetry as a New Scientific Tool in Archaeology: Worldwide Research Trends

“…For this purpose, a multitude of algorithms and objective functions have been proposed to solve the problem. Among them, the evolutionary algorithms and the modularity index have stood out as the main solutions accepted by the scientific community [47]. The software tool Vosviewer uses an algorithm for modularity-based community detection in large networks.…”

Study on Discovery Method of Cooperative Research Team Based on Improved Louvain Algorithm

“…e members of the community cooperate closely, while the connections between members of different communities are sparse. In a complex network, nodes belonging to the same community may have the same or similar properties in some respects, and the number of internal connections is more than the number of external node connections [13,14]. After dividing the entire network into communities, the entire network structure presents a high degree of modularity, and the nodes within each module present a high degree of aggregation.…”