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Carreras, Dobson and colleagues have studied empirical data on the sizes ofthe blackouts in real grids and modeled them by computer simulations using thedirect current approximation. They have found that the resulting blackout sizesare distributed as a power law and suggested that this is because the grids aredriven to the self-organized critical state. In contrast, more recent studiesfound that the distribution of cascades is bimodal as in a first order phasetransition, resulting in either a very small blackout or a very large blackout,engulfing a finite fraction of the system. Here we reconcile the two approachesand investigate how the distribution of the blackouts change with modelparameters, including the tolerance criteria and the dynamic rules of failureof the overloaded lines during the cascade. In addition, we study the sameproblem for the Motter and Lai model and find similar results, suggesting thatthe physical laws of flow on the network are not as important as networktopology, overload conditions, and dynamic rules of failure.

Distribution of blackouts in the power grid and the Motter and Lai model