We generalize an analytically solvable probabilistic model of cascading failure in which failing components interact with other components by increasing their load and hence their chance of failure. In the generalized model, instead of a failing component increasing the load of all components, it increases the load of a random sample of the components. The size of the sample describes the extent of component interactions within the system. The generalized model is approximated by a saturating branching process and this leads to a criticality condition for cascading failure propagation that depends on the size of the sample. The criticality condition shows how the extent of component interactions controls the proximity to catastrophic cascading failure. Implications for the complexity of power transmission system design to avoid cascading blackouts are briefly discussed.

10aAA01-00110aAARD10aCERTS10aSystem Security Tools1 aDobson, Ian1 aCarreras, Benjamin, A.1 aNewman, David, E. uhttps://certs.lbl.gov/publications/probabilistic-load-dependent02028nas a2200217 4500008003900000245010500039210006900144260001200213300000600225520134500231653001301576653000901589653001001598653002401608653001001632653002601642100001601668700002701684700002201711856007701733 2003 d00aA Probabilistic Loading-dependent Model of Cascading Failure and Possible Implications for Blackouts0 aProbabilistic Loadingdependent Model of Cascading Failure and Po c01/2003 a93 aA model has been developed to study the global complex dynamics of a series of blackouts in power transmission systems. This model has included a simple level of self-organization by incorporating the growth of power demand and the engineering response to system failures. Two types of blackouts have been identified with different dynamical properties. One type of blackout involves loss of load due to lines reaching their load limits but no line outages. The second type of blackout is associated with multiple line outages. The dominance of one type of blackouts versus the other depends on operational conditions and the proximity of the system to one of its two critical points. The first critical point is characterized by operation with lines close to their line limits. The second critical point is characterized by the maximum in the fluctuations of the load demand being near the generator margin capability. The identification of this second critical point is an indication that the increase of the generator capability as a response to the increase of the load demand must be included in the dynamical model to achieve a higher degree of self-organization. When this is done, the model shows a probability distribution of blackout sizes with power tails similar to that observed in real blackout data from North America.

10aAA01-00110aAARD10aCERTS10apower interruptions10aRTGRM10aSystem Security Tools1 aDobson, Ian1 aCarreras, Benjamin, A.1 aNewman, David, E. uhttps://certs.lbl.gov/publications/probabilistic-loading-dependent-model