V. E. Lynch

Complex systems analysis of series of blackouts: Cascading failure, critical points, and self-organization

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 large blackouts is governed by a power law. The power law makes the risk of large blackouts consequential and is consistent with the power system being a complex system designed and operated near a critical point. Power system overall loading or stress relative to operating limits is a key factor affecting the risk of cascading failure. Power system blackout models and abstract models of cascading failure show critical points with power law behavior as load is increased. To explain why the power system is operated near these critical points and inspired by concepts from self-organized criticality, we suggest that power system operating margins evolve slowly to near a critical point and confirm this idea using a power system model. The slow evolution of the power system is driven by a steady increase in electric loading, economic pressures to maximize the use of the grid, and the engineering responses to blackouts that upgrade the system. Mitigation of blackout risk should account for dynamical effects in complex self-organized critical systems. For example, some methods of suppressing small blackouts could ultimately increase the risk of large blackouts.

Critical points and transitions in an electric power transmission model for cascading failure blackouts

Cascading failures in large-scale electric power transmission systems are an important cause of blackouts. Analysis of North American blackout data has revealed power law (algebraic) tails in the blackout size probability distribution which suggests a dynamical origin. With this observation as motivation, we examine cascading failure in a simplified transmission system model as load power demand is increased. The model represents generators, loads, the transmission line network, and the operating limits on these components. Two types of critical points are identified and are characterized by transmission line flow limits and generator capability limits, respectively. Results are obtained for tree networks of a regular form and a more realistic 118-node network. It is found that operation near critical points can produce power law tails in the blackout size probability distribution similar to those observed. The complex nature of the solution space due to the interaction of the two critical points is examined.(c) 2002 American Institute of Physics.

Mantid—Data analysis and visualization package for neutron scattering and μ SR experiments

The Mantid framework is a software solution developed for the analysis and visualization of neutron scattering and muon spin measurements. The framework is jointly developed by software engineers and scientists at the ISIS Neutron and Muon Facility and the Oak Ridge National Laboratory. The objectives, functionality and novel design aspects of Mantid are described.

An initial model fo complex dynamics in electric power system blackouts

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 representing cascading line overloads and outages. The time scales are coupled: load growth leads to outages and outages lead to increased system capacity. The opposing forces result in a dynamic equilibrium in which blackouts of all sizes occur. The model is a means to study the complex dynamics of this dynamic equilibrium. The Markov property of the model is briefly discussed. The model dynamic equilibrium is illustrated using initial results from the 73-bus IEEE reliability test system.

Complex dynamics of blackouts in power transmission systems

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 types of blackouts have been identified, each having different dynamical properties. One type of blackout involves the loss of load due to transmission 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 blackout over the other depends on operational conditions and the proximity of the system to one of its two critical points. The model displays characteristics such as a probability distribution of blackout sizes with power tails similar to that observed in real blackout data from North America.

Anomalous diffusion and exit time distribution of particle tracers in plasma turbulence model

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

Fractional diffusion in plasma turbulence

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

A model realization of self‐organized criticality for plasma confinement

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

Blackout mitigation assessment in power transmission systems

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 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.

Fluctuation‐induced flux at the plasma edge in toroidal devices

Fluctuation‐induced fluxes have a bursty character. As a consequence, a significant part of the total particle flux is carried out by sporadic, large transport bursts. The local flux distribution function is consistent with a near‐Gaussian character of the fluctuations. The radial dependence of the statistical properties of plasma fluctuations and induced fluxes have been investigated in the plasma boundary region of the TJ‐I tokamak [I. Garcia‐Cortes et al., Phys. Fluids B 4, 4007 (1992)] and the TJ‐IU torsatron [E. Ascasibar et al., in Plasma Physics and Controlled Fusion Research, Proceedings of the 15th Conference on Plasma Physics and Controlled Nuclear Fusion Research, Seville (International Atomic Energy Agency, Vienna, in press)]. There is a striking similarity between the statistical properties of turbulent transport in both devices.