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