Long-range response in ac electricity grids.

Local changes in the topology of electricity grids can cause overloads far away from the disturbance [D. Witthaut and M. Timme, Eur. Phys. J. B 86, 377 (2013)EPJBFY1434-602810.1140/epjb/e2013-40469-4], making the prediction of the robustness against changes in the topology-for example, caused by power outages or grid extensions-a challenging task. The impact of single-line additions on the long-range response of dc electricity grids has recently been studied [D. Labavić, R. Suciu, H. Meyer-Ortmanns, and S. Kettemann, Eur. Phys. J.: Spec. Top. 223, 2517 (2014)1951-635510.1140/epjst/e2014-02273-0]. By solving the real part of the static ac load flow equations, we conduct a similar investigation for ac grids. In a regular two-dimensional grid graph with cyclic boundary conditions, we find a power law decay for the change of power flow as a function of distance to the disturbance over a wide range of distances. The power exponent increases and saturates for large system sizes. By applying the same analysis to the German transmission grid topology, we show that also in real-world topologies a long-ranged response can be found.