A criticality approach to monitoring cascading failure risk and failure propagation in transmission systems

We consider the risk of cascading failure of electric power transmission systems as overall loading is increased. There is evidence from both abstract and power systems models of cascading failure that there is a critical loading at which the risk of cascading failure sharply increases. Moreover, as expected in a phase transition, at the critical loading there is a power tail in the probability distribution of blackout size. (This power tail is consistent with the empirical distribution of North American blackout sizes.) The importance of the critical loading is that it gives a reference point for determining the risk of cascading failure. Indeed the risk of cascading failure can be quantified and monitored by finding the closeness to the critical loading. This paper suggests and outlines ways of detecting the closeness to criticality from data produced from a generic blackout model. The increasing expected blackout size at criticality can be detected by computing expected blackout size at various loadings. Another approach uses branching process models of cascading failure to interpret the closeness to the critical loading in terms of a failure propagation parameter λ. We suggest a statistic for λ that could be applied before saturation occurs. The paper concludes with suggestions for a wider research agenda for measuring the closeness to criticality of a fixed power transmission network and for studying the complex dynamics governing the slow evolution of a transmission network.