Quantifying the overall risk of blackout due to cascading failure and determining the corresponding safe limits for power system design and operation are challenging problems. Large blackouts involve long, complicated and diverse cascades of events that often are unlikely or unexpected. An exhaustive and detailed analysis of these cascading events before the blackout occurs is impossible because of the huge number of possible combinations of unlikely events. Despite these challenges, approaches

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... to quantify the overall risk of blackouts are emerging and we give a tutorial account reviewing these emerging approaches and their prospects. We summarize the implications for blackout risk of the powerlaw region in the observed distribution of sizes of North American blackouts. High-level probabilistic models of cascading failure and power system simulations suggest that there is a critical loading at which expected blackout size sharply increases and there is a power law in the distribution of blackout size. This critical loading could serve as a reference point for determining the "edge" for cascading failure risk. We model cascading failure as an initial disturbance that sometimes propagates to become much more widespread. The size of the initial disturbance and the average amount of propagation of the failures can be estimated from data from simulated cascades. We suggest that these estimates could be used to efficiently quantify the blackout risk. We summarize initial testing on power system simulations of cascading overloads and speculate that extending this approach to process data from series of cascades occurring in the power system could lead to direct monitoring of power system reliability.