Graph Crossings in Electric Transmission Grids

The number of times that transmission lines in a power system intersect one another without connecting electrically, that is, the number of graph crossings, gives insight into the level of non-planarity for a power grid network. This paper describes the importance of these crossings metrics and discusses challenges associated with calculating them. Example results are given for the geographic spatial embedding of actual United States power grid networks, based on public data from the U. S. Energy Information Administration. These results show that within voltage classes and removing main sources of data errors, there are up to 15% as many edge crossings as the number of lines, with fewer crossings both in the very highest voltage levels and in those closer to sub-transmission. A comparison is also made between using actual right-of-way routing and straight-line routing, with the latter circumventing more data errors and producing smaller and more consistent crossing counts.