Line-graph based modeling for assessing the vulnerability of transmission lines

The aim of this paper is to evaluate the ability of the line-graph based model (LGBM) to assess the vulnerability of power systems as part of complex network theory. The nodes in the line graph are the transmission lines, thus emphasizing their vulnerability. We derive and compute line-graph corresponding to several standard IEEE test cases and well as to the Western Systems Coordinating Council (WSCC) power grid. In each case, we compute various graph-theoretic measures, and we compared to the measures corresponding to standard topologies of complex networks (random, scale-free, and small world). We also compare LGBM topological characteristics with those of the bus-based model (BBM). Moreover, we examine the vulnerability of the LGBM nodes (transmission lines) are removed randomly or targeted by a malicious opponent. In both the IEEE models and the WSCC, simulations show that when the network size is large, and the BBM behaves like a scale-free network, the pattern of LGBM node degree distribution is distinct from that of BBM. The LGBM seems to possess a higher clustering coefficient, almost double, suggesting that transmission lines are more tightly connected and interdependent than buses, at least from a topological point of view. In general, our simulations show that attacking transmission lines seem to be more detrimental to the power grid than attacking buses.