A Topological Investigation of Phase Transitions of Cascading Failures   in Power Grids
  Cascading failures are one of the main reasons for blackouts in electric power transmission grids. The economic cost of such failures is in the order of tens of billion dollars annually. The loading level of power system is a key aspect to determine the amount of the damage caused by cascading failures. Existing studies show that the blackout size exhibits phase transitions as the loading level increases. This paper investigates the impact of the topology of a power grid on phase transitions in its robustness. Three spectral graph metrics are considered: spectral radius, effective graph resistance and algebraic connectivity. Experimental results from a model of cascading failures in power grids on the IEEE power systems demonstrate the applicability of these metrics to design/optimize a power grid topology for an enhanced phase transition behavior of the system. 
Yakup Ko\c{c}, Martijn Warnier, Piet Van Mieghem, Robert E. Kooij,   Frances M.T. Brazier
physics.soc-ph cond-mat.dis-nn