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-dependent01805nas a2200205 4500008003900000020001800039245006500057210006500122260003900187300001100226520117200237653001301409653001001422653001001432100002701442700001601469700002201485700001601507856007601523 2003 d a0-7695-1874-500aBlackout mitigation assessment in power transmission systems0 aBlackout mitigation assessment in power transmission systems aBig Island, HI, USAbIEEEc01/2003 a10 pp.3 aElectric power transmission systems are a key infrastructure and blackouts of these systems have major direct and indirect consequences on the economy and national security. Analysis of North American Electrical Reliability Council blackout data suggests the existence of blackout size distributions with power tails. This is an indication that blackout dynamics behave as a complex dynamical system. Here, we investigate how these complex system dynamics impact the assessment and mitigation of blackout risk. The mitigation of failures in complex systems needs to be approached with care. The mitigation efforts can move the system to a new dynamic equilibrium while remaining near criticality and preserving the power tails. Thus, while the absolute frequency of disruptions of all sizes may be reduced, the underlying forces can still cause the relative frequency of large disruptions to small disruptions to remain the same. Moreover, in some cases, efforts to mitigate small disruptions can even increase the frequency of large disruptions. This occurs because the large and small disruptions are not independent but are strongly coupled by the dynamics.

10aAA01-00110aCERTS10aRTINA1 aCarreras, Benjamin, A.1 aLynch, V.E.1 aNewman, David, E.1 aDobson, Ian uhttps://certs.lbl.gov/publications/blackout-mitigation-assessment-power02028nas 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-model01762nas a2200193 4500008003900000245010400039210006900143260001200212300000700224520114500231653001301376653000901389653001001398653002601408100002701434700001601461700002201477856006901499 2002 d00aDynamics, Criticality, and Self-organization in a Model for Blackouts in Power Transmission Systems0 aDynamics Criticality and Selforganization in a Model for Blackou c01/2002 a103 aCatastrophic 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.

10aAA01-00110aAARD10aCERTS10aSystem Security Tools1 aCarreras, Benjamin, A.1 aDobson, Ian1 aNewman, David, E. uhttps://certs.lbl.gov/publications/dynamics-criticality-and-self01271nas a2200217 4500008003900000245008400039210006900123260001200192300000700204520060700211653001300818653000900831653001000840653002600850100001600876700001400892700002100906700002700927700002200954856007700976 2002 d00aExamining Criticality of Blackouts in Power System Models with Cascading Events0 aExamining Criticality of Blackouts in Power System Models with C c01/2002 a103 aAs power system loading increases, larger blackouts due to cascading outages become more likely. We investigate a critical loading at which the average size of blackouts increases sharply to examine whether the probability distribution of blackout sizes shows the power tails observed in real blackout data. Three different models are used, including two simulations of cascading outages in electric power transmission systems. We also derive and use a new, analytically solvable model of probabilistic cascading failure which represents the progressive system weakening as the cascade proceeds.

10aAA01-00110aAARD10aCERTS10aSystem Security Tools1 aDobson, Ian1 aChen, Jie1 aThorp, James, S.1 aCarreras, Benjamin, A.1 aNewman, David, E. uhttps://certs.lbl.gov/publications/examining-criticality-blackouts-power01236nas a2200193 4500008003900000245009600039210006900135260002800204300000600232520060800238653001300846653000900859653002600868100001600894700002200910700002700932700002200959856006100981 2002 d00aAn Initial Complex Systems Analysis of the Risks of Blackouts in Power Transmission Systems0 aInitial Complex Systems Analysis of the Risks of Blackouts in Po aBeijing, Chinac09/2002 a73 aElectric power transmission systems are a key infrastructure and blackouts of these systems have major direct and indirect consequences on the economy and national security. In particular, electric power blackouts have cascading effects on other vital infrastructures. While it is useful to analyze the detailed causes of individual blackouts, in this paper we focus on the intrinsic dynamics of series of blackouts and how this complex system dynamics impacts the assessment and mitigation of blackout risk. Indeed, the mitigation of failures in complex systems needs to be approached with care.

10aAA01-00110aAARD10aSystem Security Tools1 aDobson, Ian1 aNewman, David, E.1 aCarreras, Benjamin, A.1 aLynch, Vickie, E. uhttp://iandobson.ece.iastate.edu/PAPERS/dobsonCRIS02.pdf