Complex systems analysis of series of blackouts: Cascading failure, critical points, and self-organization
TL;DR: An overview of a complex systems approach to large blackouts of electric power transmission systems caused by cascading failure is given and it is suggested that power system operating margins evolve slowly to near a critical point and confirmed using a power system model.
Abstract: 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.
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01 Jan 2011
TL;DR: In this paper, a polynomial dimensional decomposition (PDD) method for global sensitivity analysis of stochastic systems subject to independent random input following arbitrary probability distributions is presented.
Abstract: This paper presents a polynomial dimensional decomposition (PDD) method for global sensitivity analysis of stochastic systems subject to independent random input following arbitrary probability distributions. The method involves Fourier-polynomial expansions of lower-variate component functions of a stochastic response by measure-consistent orthonormal polynomial bases, analytical formulae for calculating the global sensitivity indices in terms of the expansion coefficients, and dimension-reduction integration for estimating the expansion coefficients. Due to identical dimensional structures of PDD and analysis-of-variance decomposition, the proposed method facilitates simple and direct calculation of the global sensitivity indices. Numerical results of the global sensitivity indices computed for smooth systems reveal significantly higher convergence rates of the PDD approximation than those from existing methods, including polynomial chaos expansion, random balance design, state-dependent parameter, improved Sobol’s method, and sampling-based methods. However, for non-smooth functions, the convergence properties of the PDD solution deteriorate to a great extent, warranting further improvements. The computational complexity of the PDD method is polynomial, as opposed to exponential, thereby alleviating the curse of dimensionality to some extent. Mathematical modeling of complex systems often requires sensitivity analysis to determine how an output variable of interest is influenced by individual or subsets of input variables. A traditional local sensitivity analysis entails gradients or derivatives, often invoked in design optimization, describing changes in the model response due to the local variation of input. Depending on the model output, obtaining gradients or derivatives, if they exist, can be simple or difficult. In contrast, a global sensitivity analysis (GSA), increasingly becoming mainstream, characterizes how the global variation of input, due to its uncertainty, impacts the overall uncertain behavior of the model. In other words, GSA constitutes the study of how the output uncertainty from a mathematical model is divvied up, qualitatively or quantitatively, to distinct sources of input variation in the model [1].
1,296 citations
16 May 2011
TL;DR: In this article, the authors provide an overview of what PLC can deliver today by surveying its history and describing the most recent technological advances in the area and discuss the main conclusions one can draw from the literature on these subjects.
Abstract: Are Power Line Communications (PLC) a good candidate for Smart Grid applications? The objective of this paper is to address this important question. To do so, we provide an overview of what PLC can deliver today by surveying its history and describing the most recent technological advances in the area. We then address Smart Grid applications as instances of sensor networking and network control problems and discuss the main conclusions one can draw from the literature on these subjects. The application scenario of PLC within the Smart Grid is then analyzed in detail. Because a necessary ingredient of network planning is modeling, we also discuss two aspects of engineering modeling that relate to our question. The first aspect is modeling the PLC channel through fading models. The second aspect we review is the Smart Grid control and traffic modeling problem which allows us to achieve a better understanding of the communications requirements. Finally, this paper reports recent studies on the electrical and topological properties of a sample power distribution network. Power grid topological studies are very important for PLC networking as the power grid is not only the information source but also the information delivery system-a unique feature when PLC is used for the Smart Grid.
1,084 citations
TL;DR: To better understand CISs to support planning, maintenance and emergency decision making, modeling and simulation of interdependencies across CISs has recently become a key field of study and this paper reviews the studies in the field and broadly groups the existing modeling and Simulation approaches into six types.
891 citations
01 Oct 2012
TL;DR: The Global Energy Assessment (GEA) as mentioned in this paper brings together over 300 international researchers to provide an independent, scientifically based, integrated and policy-relevant analysis of current and emerging energy issues and options.
Abstract: The Global Energy Assessment (GEA) brings together over 300 international researchers to provide an independent, scientifically based, integrated and policy-relevant analysis of current and emerging energy issues and options. It has been peer-reviewed anonymously by an additional 200 international experts. The GEA assesses the major global challenges for sustainable development and their linkages to energy; the technologies and resources available for providing energy services; future energy systems that address the major challenges; and the policies and other measures that are needed to realize transformational change toward sustainable energy futures. The GEA goes beyond existing studies on energy issues by presenting a comprehensive and integrated analysis of energy chalenges, opportunities and strategies, for developing, industrialized and emerging economies. This volume is a invaluable resource for energy specialists and technologists in all sectors (academia, industry and government) as well as policymakers, development economists and practitioners in international organizations and national governments.
812 citations
TL;DR: The Bak–Tang–Wiesenfeld sandpile model is studied on modular random graphs and on graphs based on actual, interdependent power grids and it is shown that asymmetric capacity among interdependent networks affects the optimal connectivity that each prefers and may lead to an arms race for greater capacity.
Abstract: Understanding how interdependence among systems affects cascading behaviors is increasingly important across many fields of science and engineering. Inspired by cascades of load shedding in coupled electric grids and other infrastructure, we study the Bak–Tang–Wiesenfeld sandpile model on modular random graphs and on graphs based on actual, interdependent power grids. Starting from two isolated networks, adding some connectivity between them is beneficial, for it suppresses the largest cascades in each system. Too much interconnectivity, however, becomes detrimental for two reasons. First, interconnections open pathways for neighboring networks to inflict large cascades. Second, as in real infrastructure, new interconnections increase capacity and total possible load, which fuels even larger cascades. Using a multitype branching process and simulations we show these effects and estimate the optimal level of interconnectivity that balances their trade-offs. Such equilibria could allow, for example, power grid owners to minimize the largest cascades in their grid. We also show that asymmetric capacity among interdependent networks affects the optimal connectivity that each prefers and may lead to an arms race for greater capacity. Our multitype branching process framework provides building blocks for better prediction of cascading processes on modular random graphs and on multitype networks in general.
525 citations
References
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TL;DR: In this paper, a simple model based on the power-law degree distribution of real networks was proposed, which was able to reproduce the power law degree distribution in real networks and to capture the evolution of networks, not just their static topology.
Abstract: The emergence of order in natural systems is a constant source of inspiration for both physical and biological sciences. While the spatial order characterizing for example the crystals has been the basis of many advances in contemporary physics, most complex systems in nature do not offer such high degree of order. Many of these systems form complex networks whose nodes are the elements of the system and edges represent the interactions between them.
Traditionally complex networks have been described by the random graph theory founded in 1959 by Paul Erdohs and Alfred Renyi. One of the defining features of random graphs is that they are statistically homogeneous, and their degree distribution (characterizing the spread in the number of edges starting from a node) is a Poisson distribution. In contrast, recent empirical studies, including the work of our group, indicate that the topology of real networks is much richer than that of random graphs. In particular, the degree distribution of real networks is a power-law, indicating a heterogeneous topology in which the majority of the nodes have a small degree, but there is a significant fraction of highly connected nodes that play an important role in the connectivity of the network.
The scale-free topology of real networks has very important consequences on their functioning. For example, we have discovered that scale-free networks are extremely resilient to the random disruption of their nodes. On the other hand, the selective removal of the nodes with highest degree induces a rapid breakdown of the network to isolated subparts that cannot communicate with each other.
The non-trivial scaling of the degree distribution of real networks is also an indication of their assembly and evolution. Indeed, our modeling studies have shown us that there are general principles governing the evolution of networks. Most networks start from a small seed and grow by the addition of new nodes which attach to the nodes already in the system. This process obeys preferential attachment: the new nodes are more likely to connect to nodes with already high degree. We have proposed a simple model based on these two principles wich was able to reproduce the power-law degree distribution of real networks. Perhaps even more importantly, this model paved the way to a new paradigm of network modeling, trying to capture the evolution of networks, not just their static topology.
18,415 citations
TL;DR: Developments in this field are reviewed, including such concepts as the small-world effect, degree distributions, clustering, network correlations, random graph models, models of network growth and preferential attachment, and dynamical processes taking place on networks.
Abstract: Inspired by empirical studies of networked systems such as the Internet, social networks, and biological networks, researchers have in recent years developed a variety of techniques and models to help us understand or predict the behavior of these systems. Here we review developments in this field, including such concepts as the small-world effect, degree distributions, clustering, network correlations, random graph models, models of network growth and preferential attachment, and dynamical processes taking place on networks.
17,647 citations
TL;DR: The major concepts and results recently achieved in the study of the structure and dynamics of complex networks are reviewed, and the relevant applications of these ideas in many different disciplines are summarized, ranging from nonlinear science to biology, from statistical mechanics to medicine and engineering.
9,441 citations
"Complex systems analysis of series ..." refers background in this paper
...There is an extensive literature on cascading in graphs [48, 9 ] that is partially motivated by idealized models of propagation of failures in infrastructure networks such as the internet....
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TL;DR: It is shown that dynamical systems with spatial degrees of freedom naturally evolve into a self-organized critical point, and flicker noise, or 1/f noise, can be identified with the dynamics of the critical state.
Abstract: We show that dynamical systems with spatial degrees of freedom naturally evolve into a self-organized critical point. Flicker noise, or 1/f noise, can be identified with the dynamics of the critical state. This picture also yields insight into the origin of fractal objects.
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