Modified Erdős–Rényi Random Graph Model for Generating Synthetic Power Grids

Synthetic power graphs have recently been widely used to assist researchers in analyzing power grids as complex networks. In general, power graphs are sparsely connected, scale-free with consecutive numbering, which cannot be directly synthesized by existing random graph models, such as the Edrős–Rényi model. This article proposes a modified Edrős–Rényi random graph model (itself and Gilbert) to generate synthetic power graphs. Using vertex and component rewiring, the proposed algorithm can obtain sparsely connected graphs with average degree between 2 and 3 for different graph sizes. The proposed algorithm also uses reordering to obtain consecutive vertex numbering, and therefore, it can generate synthetic power graphs with a structure similar to power graphs. In addition to the structure of synthetic power graphs, the proposed algorithm provides some auxiliary operational data for the generated synthetic power graphs, i.e., the location of zero injection buses. The simulation results of optimal PMU placement problem for three IEEE cases and three real cases show the similarities of the two versions of generated graphs to the power graphs in terms of network structure and operational data. Also, the flexibility of the two versions of the proposed model in generating graphs with different network structures as well as operational data are shown in two simulations related to the domination number problem.