We give an overview of a complex systems approach to large blackouts electric power transmission caused by cascading failure. Instead looking at the details particular blackouts, we study statistics and dynamics series with approximate global models. Blackout data from several countries suggest that frequency is governed law. The law makes risk consequential consistent system being designed operated near critical point. Power overall loading or stress relative operating limits key factor...

We analyze a 15-year time series of North American electric power transmission system blackouts for evidence self-organized criticality (SOC). The probability distribution functions various measures blackout size have tail and rescaled range analysis the shows moderate long-time correlations. Moreover, same applied to from sandpile model known be critical gives results form. Thus, data seem consistent with SOC. A qualitative explanation complex dynamics observed in is suggested.

We propose an analytically tractable model of loading-dependent cascading failure that captures some the salient features large blackouts electric power transmission systems. This leads to a new application and derivation quasibinomial distribution its generalization saturating form with extended parameter range. The number failed components has power-law region at critical loading significant probability total higher loadings.

A self-consistent model of the L to H transition is derived from coupled nonlinear envelope equations for fluctuation level and radial electric field shear ${\mathrm{E}}_{\mathrm{r}}^{\ensuremath{'}}$. These exhibit a supercritical bifurcation between dual L-mode H-mode fixed points. The occurs when turbulence large enough Reynolds stress drive overcome damping E\ifmmode\times\else\texttimes\fi{}B flow. This defines power threshold transition, which calculated found be consistent with...

We define a model for the evolution of long series electric power transmission system blackouts. The describes opposing forces, which have been conjectured to cause self-organized criticality in There is slow time scale representing forces load growth and capacity fast cascading line overloads outages. scales are coupled: leads outages lead increased capacity. result dynamic equilibrium blackouts all sizes occur. means study complex dynamics this equilibrium. Markov property briefly...

A recently introduced tool for the analysis of turbulence, wavelet bicoherence [van Milligen, Hidalgo, and Sánchez, Phys. Rev. Lett. 16, 395 (1995)], is investigated. It capable detecting phase coupling—nonlinear interactions lowest (quadratic) order—with time resolution. To demonstrate its potential, it applied to numerical models chaos turbulence real measurements. detected coupling interaction between two coupled van der Pol oscillators. When a model drift wave relevant plasma physics,...

To explore the character of transport in a plasma turbulence model with avalanche transport, motion tracer particles has been followed. Both time evolution moments distribution function particle radial positions, 〈|r(t)−r(0)|n〉, and their finite scale Lyapunov number are used to determine anomalous diffusion exponent, ν. The numerical results show that mechanism is superdiffusive an exponent ν close 0.88±0.07. exit times trapped into stochastic jets also determined. These have lowest...

Numerical evidence of nondiffusive transport in three-dimensional, resistive pressure-gradient-driven plasma turbulence is presented. It shown that the probability density function (pdf) tracer particles' radial displacements strongly non-Gaussian and exhibits algebraic decaying tails. To model these results we propose a macroscopic for pdf based on use fractional derivatives space time incorporate unified way space-time nonlocality (non-Fickian transport), non-Gaussianity, scaling. The...

Transport of tracer particles is studied in a model three-dimensional, resistive, pressure-gradient-driven plasma turbulence. It shown that this system transport anomalous and cannot be described the context standard diffusion paradigm. In particular, probability density function (pdf) radial displacements tracers strongly non-Gaussian with algebraic decaying tails, moments exhibit superdiffusive scaling. To these results we present fractional derivatives space time. The incorporates unified...

A simple model for a power transmission system is presented. In this model, disturbances of all sizes may occur. They are randomly triggered and have the characteristic behavior avalanches. single parameter describes scaling avalanche size. This combines measure closeness to maximum load, size transferred loads during an overloading event, connectivity system. The probability distribution function disturbance has power-scaling range with exponent close -1.

In order to study the complex global dynamics of a series blackouts in power transmission systems dynamical model such system has been developed. This includes simple representation evolution by incorporating growth demand, engineering response failures, and upgrade generator capacity. Two types have identified, each having different properties. One type blackout involves loss load due lines reaching their limits but no line outages. The second is associated with multiple dominance one over...

A general paradigm, based on the concept of self-organized criticality (SOC), for turbulent transport in magnetically confined plasmas, has been recently suggested as an explanation some apparent discrepancies between most theoretical models and experimental observations plasmas. This model describes dynamics without relying underlying local fluctuation mechanisms. Computations a cellular automata realization such have found that noise-driven SOC systems can maintain average profiles are...

A model for plasma transport near marginal stability is presented. The based on subcri- tical resistive pressure-gradient-driven turbulence. Three-dimensional nonlinear calculations this show effective subcritical mean profiles. This exhibits some of the characteristic properties self-organized criticality. Perturbative techniques are used to elucidate properties. Propagation positive and negative pulses studied. observed results suggest a possible explanation apparent nonlocal effects ob-...

The use of reaction-diffusion models rests on the key assumption that diffusive process is Gaussian. However, a growing number studies have pointed out presence anomalous diffusion, and there need to understand reactive systems in this type non-Gaussian diffusion. Here we study front dynamics where diffusion due asymmetric Levy flights. Our approach consists replacing Laplacian operator by fractional order alpha, whose fundamental solutions are alpha-stable distributions exhibit power law...

Transport is the outstanding physics issue in quest for fusion by magnetic confinement. In spite of intrinsic difficulty, a great deal progress has been made past 25 years. Experiments have gone from being dominated high anomalous losses, order Bohm diffusion to operation with no transport. This success due combination improved experimental infrastructure and degree knowledge on how control plasma discharges, Both it possible access enhanced confinement regimes unravel new effects physics....

Cascading transmission line outages contribute to widespread blackouts. Engineers respond the risk of cascading by applying policies such as n-1 criterion and upgrading lines involved in recent outages. The grid slowly evolves these are applied maintain reliability while load grows. We suggest how assess long-term effect on simulating both slow evolution grid. effects probability distribution outage size utilization computed for IEEE 118-bus test system. results show complex system...

Electric power transmission systems are a key infrastructure, and blackouts of these have major consequences for the economy national security. Analyses blackout data suggest that size distributions law form over much their range. This result is an indication behave as complex dynamical system. We use simulation upgrading system to investigate how dynamics impact assessment mitigation risk. The failures in needs be approached with care. efforts can move new dynamic equilibrium while...

We use North American Electric Reliability Corporation historical data to give improved estimates of distributions blackout size, time correlations, and waiting times for the Eastern Western interconnections grid. then explain estimate implications power law region (heavy tails) in empirical distribution size interconnection. Annual mean has high variability risk large blackouts exceeds medium blackouts. Ways communicate are discussed.

We examine correlations in a time series of electric power system blackout sizes using scaled window variance analysis and R/S statistics. The data shows some evidence long has Hurst exponent near 0.7. Large blackouts tend to correlate with further large after interval. Similar effects are also observed many other complex systems exhibiting self-organized criticality. discuss this initial possible explanations for criticality blackouts. Self-organized criticality, if fully confirmed systems,...

Analysis of the edge plasma fluctuation in several confinement devices reveals self-similar character fluctuations through presence long-range time correlations. These results show that tail autocorrelation function decays as a power law for lags longer than decorrelation and long times on order particle diffusion time. The algebraic decay correlations is consistent with transport characterized by self-organized criticality.

The Advanced Toroidal Facility (ATF), now under construction at Oak Ridge National Laboratory, will be the world’s largest stellarator experiment when it begins operation in early 1987. It have a 2.1-m major radius and 0.3-m average plasma radius, magnetic field capability of up to 2 T for 5-s pulse 1 steady state, 5 MW heating. ATF is designed study wide range toroidal confinement issues, including stability high-beta plasmas, low-collisionality transport, impurity behavior, configuration...

Catastrophic disruptions of large, interconnected infrastructure systems are often due to cascading failure. For example, large blackouts electric power typically caused by failure heavily loaded system components. We introduce the CASCADE model a with many identical components randomly loaded. An initial disturbance causes some fail exceeding their loading limit. Failure component fixed load increase for other As fail, becomes more and further likely. The probability distribution number...

Networked infrastructures operated under highly loaded conditions are vulnerable to catastrophic cascading failures. For example, electric power transmission systems must be designed and reduce the risk of widespread blackouts caused by failure. There is a need for analytically tractable models understand quantify risks We study probabilistic model loading dependent failure approximating propagation failures as Poisson branching process. This leads criticality condition propagation. At there...