A probabilistic loading-dependent model of cascading failure and possible implications for blackouts

Catastrophic disruptions of large, interconnected infrastructure systems are often due to cascading failure. For example, large blackouts of electric power systems are typically caused by cascading failure of heavily loaded system components. We introduce the CASCADE model of cascading failure of a system with many identical components randomly loaded. An initial disturbance causes some components to fail by exceeding their loading limit. Failure of a component causes a fixed load increase for other components. As components fail, the system becomes more loaded and cascading failure of further components becomes likely. The probability distribution of the number of failed components is an extended quasibinomial distribution. Explicit formulas for the extended quasibinomial distribution are derived using a recursion. The CASCADE model in a restricted parameter range gives a new model yielding the quasibinomial distribution. Some qualitative behaviors of the extended quasibinomial distribution are illustrated, including regimes with power tails, exponential tails, and significant probabilities of total system failure.