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In order to study the complex global dynamics of a series of blackouts in power transmission systems a dynamical model of such a system has been developed. This model includes a simple representation of the dynamical evolution by incorporating the growth of power demand, the engineering response to system failures, and the upgrade of generator capacity. Two(More)
We define a model for the evolution of a long series of electric power transmission system blackouts. The model describes opposing forces which have been conjectured to cause self-organized criticality in power system blackouts. There is a slow time scale representing the opposing forces of load growth and growth in system capacity and a fast time scale(More)
Electric 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(More)
We introduce branching process models in discrete and continuous time for the exponentially increasing phase of cascading blackouts. Cumulative line trips from real blackout data have portions consistent with these branching process models. Some initial calculations identifying parameters and using a branching process model to estimate blackout(More)
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We give an overview of a complex systems approach to large blackouts of electric power transmission systems caused by cascading failure. Instead of looking at the details of particular blackouts, we study the statistics and dynamics of series of blackouts with approximate global models. Blackout data from several countries suggest that the frequency of(More)
— We analyze a 15-year time series of North American electric power transmission system blackouts for evidence of self-organized criticality. The probability distribution functions of various measures of blackout size have a power tail and R/S analysis of the time series shows moderate long time correlations. Moreover, the same analysis applied to a time(More)
We analyze a 15-year time series of North American electric power system blackouts for evidence of self-organized criticality. Scaled window variance and R/S analysis of the time series shows moderate long time correlations. The probability distribution functions of various measures of blackout size have a power tail. Moreover, the same analysis applied to(More)
A model for blackouts in electric power transmission systems is implemented and studied in simple networks with a regular structure. The model describes load demand and network improvements evolving on a slow timescale as well as the fast dynamics of cascading overloads and outages. The model dynamics are demonstrated on the simple power system networks.(More)
algorithms time complexity ROM space special condition modulo adder size PI wg 4 > n2 no n*M PI wg 4 2 yes 2 " PI O(n) &n " , no M New algorithm 000~ nl O(n) no <M 1001 in the figure are the same. Each cell in the tree performs the findno algorithm. In the diagram, the RNS representation is used as input to the first level of cells in pair, i.e. is the(More)