Criticality in a cascading failure blackout model

We verify and examine criticality in a 1000 bus network with an AC blackout model that represents many of the interactions that occur in cascading failure. At the critical loading there is a sharp rise in the mean black- out size and a power law probability d istribu- tion of blackout size that indicates a s i g n i f i - cant risk of large blackouts. the product of blackout size and blackout probability, remains constant so that the risk of large blackouts is comparable to that of small blackouts.) The power law is also consistent with the observed frequency of large blackouts in North America (3). It is important to verify and compare criticality in a variety of power sys- tem blackout models to find out the extent to which it is a phenomenon universally associated with cascading failure of power systems. Models of cascading failure in power systems are described in (14, 12, 1, 10, 5, 13). We investigate criticality in a sizable network with a fairly detailed blackout model and measure blackout size by energy unserved. At a given loading level, initial outages are chosen randomly and the consequences of each initial outage are simulated to estimate the distribu- tion of blackout size. Gradually increasing the loading yields estimates of the probability distribution of black- out size at each loading. The mean blackout size is also computed at each loading. Blackouts are traditionally analyzed after the blackout by a detailed investigation of the particular sequence of failures. This is good engineering practice and very useful for finding and correcting weaknesses in the power system. We take a different and complementary approach and seek to analyze the overall probability and risk of blackouts from a global perspective. An anal- ogy can highlight this bulk systems approach and the role of phase transitions: If we seek to find out how close a beaker of water is to boiling, we do not compute in detail the vast number of individual molecule move- ments and collisions according to Newton's determinis- tic laws. A bulk statistical approach using a ther- mometer works well and we know that the phase transi- tion of boiling water occurs at 100 degrees Celsius. The analogy suggests that to manage the risk of blackouts, we first need to confirm, understand and detect the criti- cality phase transition in blackout risk that seems to occur as power systems become more stressed.