Analysis of structural vulnerabilities in power transmission grids

Power transmission grids play a crucial role as a critical infrastructure by assuring the proper functioning of power systems. In particular, they secure the loads supplied by power generation plants and help avoid blackouts that can have a disastrous impact on society. The power grid structure (number of nodes and lines, their connections, and their physical properties and operational constraints) is one of the key issues (along with generation availability) to assure power system security; consequently, it deserves special attention. A promising approach for the structural analysis of transmission grids with respect to their vulnerabilities is to use metrics and approaches derived from complex network (CN) theory that are shared with other infrastructures such as the World-Wide Web, telecommunication networks, and oil and gas pipelines. These approaches, based on metrics such as global efficiency, degree and betweenness, are purely topological because they study structural vulnerabilities based on the graphical representation of a network as a set of vertices connected by a set of edges. Unfortunately, these approaches fail to capture the physical properties and operational constraints of power systems and, therefore, cannot provide meaningful analyses. This paper proposes an extended topological approach that includes the definitions of traditional topological metrics (e.g., degrees of nodes and global efficiency) as well as the physical/operational behavior of power grids in terms of real power-flow allocation over lines and line flow limits. This approach provides two new metrics, entropic degree and net-ability, that can be used to assess structural vulnerabilities in power systems. The new metrics are applied to test systems as well as real power grids to demonstrate their performance and to contrast them with traditional, purely topological metrics.