Cascading failures in ac electricity grids.

Sudden failure of a single transmission element in a power grid can induce a domino effect of cascading failures, which can lead to the isolation of a large number of consumers or even to the failure of the entire grid. Here we present results of the simulation of cascading failures in power grids, using an alternating current (AC) model. We first apply this model to a regular square grid topology. For a random placement of consumers and generators on the grid, the probability to find more than a certain number of unsupplied consumers decays as a power law and obeys a scaling law with respect to system size. Varying the transmitted power threshold above which a transmission line fails does not seem to change the power-law exponent q≈1.6. Furthermore, we study the influence of the placement of generators and consumers on the number of affected consumers and demonstrate that large clusters of generators and consumers are especially vulnerable to cascading failures. As a real-world topology, we consider the German high-voltage transmission grid. Applying the dynamic AC model and considering a random placement of consumers, we find that the probability to disconnect more than a certain number of consumers depends strongly on the threshold. For large thresholds the decay is clearly exponential, while for small ones the decay is slow, indicating a power-law decay.