Martí Rosas-Casals

TOPOLOGICAL VULNERABILITY OF THE EUROPEAN POWER GRID UNDER ERRORS AND ATTACKS

We present an analysis of the topological structure and static tolerance to errors and attacks of the September 2003 actualization of the Union for the Coordination of Transport of Electricity (UCTE) power grid, involving thirty-three different networks. Though every power grid studied has exponential degree distribution and most of them lack typical small-world topology, they display patterns of reaction to node loss similar to those observed in scale-free networks. We have found that the node removal behavior can be logarithmically related to the power grid size. This logarithmic behavior would suggest that, though size favors fragility, growth can reduce it. We conclude that, with the ever-growing demand for power and reliability, actual planning strategies to increase transmission systems would have to take into account this relative increase in vulnerability with size, in order to facilitate and improve the power grid design and functioning.

Robustness of the European power grids under intentional attack

The power grid defines one of the most important technological networks of our times and sustains our complex society. It has evolved for more than a century into an extremely huge and seemingly robust and well understood system. But it becomes extremely fragile as well, when unexpected, usually minimal, failures turn into unknown dynamical behaviours leading, for example, to sudden and massive blackouts. Here we explore the fragility of the European power grid under the effect of selective node removal. A mean field analysis of fragility against attacks is presented together with the observed patterns. Deviations from the theoretical conditions for network percolation (and fragmentation) under attacks are analysed and correlated with non topological reliability measures.

Power Grids as Complex Networks: Topology and Fragility

We almost certainly agree that the harnessing of electricity can be considered the most important technological advance of the twentieth century. The development that allows this control is the power grid, an intricate system composed of generators, substations and transformers connected by cable lines hundreds of kilometers long. Its presence is nowadays so intertwined with ours, and so much taken for granted, that we are only capable of sensing its absence, disguised as a cascading failure or a blackout in its extreme form. Since these extreme phenomena seem to have increased in recent years and new actors, like highly liberalized markets or environmental and social constraints, are taking a leading role, different paths other than traditional engineering ones have been explored. In the last ten years, and mainly due to increasing computational capability and accessibility to data, the conceptual frame of complex networks has allowed different approaches in order to understand the usual (and not-so-usual) outcomes of this system. This paper considers power grids as complex networks. It presents some recent results that correlate their topology with their fragility, together with major malfunctions analysis, and for the European transmission power grid in particular.

Assessing European power grid reliability by means of topological measures

Publicat originalment a: WIT transactions on ecology and the environment, 2009, vol. 121, p. 527-537

Knowing power grids and understanding complexity science

Complex networks theory has been well established as a useful framework for studying and analysing structure, dynamics and evolution of many complex systems. Infrastructural and man-made systems like power grids, gas and water networks and the internet, have been also included in this network framework, albeit sometimes ignoring the huge historical body of knowledge surrounding them. Although there seems to exist clear evidence that both complexity approach in general, and complex networks in particular, can be useful, it is necessary and profitable to put forward some of the limits that this scheme is facing when dealing with not so complex but rather complicated systems like the power grid. In this introductory paper, we offer a critical revision of the usefulness of the complexity and complex networks’ approach in this later case, highlighting both its strengths and weaknesses. At the same time we emphasise the disconnection between the so called complex and the more traditional engineering communities as one of the major drawbacks in the advent of a true body of understanding, more than simply knowing the subtleties of this kind of complex systems.

Correlating empirical data and extended topological measures in power grid networks

Power grids have entered the complex networks realm for quite a long time now. Their structure (i.e., topology) and dynamics have been thoroughly studied and many topological measures have been used in order to classify them, evaluate their behavior in terms of robustness or model their dynamic response to malfunctions. Generally speaking, results have been mainly theoretical and sound correlations between real grid’s dynamical behavior (i.e., malfunctions and major events) and any of the mentioned before measures have not yet been found. In recent years, though, new extended topological measures have been used to quantify the ability of a network in sustaining its basic functions. In this paper we present a first attempt to correlate these new measures with real malfunction data for some major European power transmission grids. Similar behavior is found, in terms of robustness to selected attacks to buses, between different networks. This is measured by means of extended topological indexes electrically better defined. These behaviors can be (weakly) correlated with similar probability distributions of major events, identifying similar dynamical response among topologically similar grids. This would raise hopes in finding a more meaningful and significant linkage between structural measures and the real dynamical output (i.e., major events) of a grid.

Spatial and Performance Optimality in Power Distribution Networks

Complex network theory has been widely used in vulnerability analysis of power networks, especially for power transmission ones. With the development of the smart grid concept, power distribution networks are becoming increasingly relevant. In this paper, we model power distribution systems as spatial networks. Topological and spatial properties of 14 European power distribution networks are analyzed, together with the relationship between geographical constraints and performance optimization, taking into account economic and vulnerability issues. Supported by empirical reliability data, our results suggest that power distribution networks are influenced by spatial constraints which clearly affect their overall performance.

Network Hierarchy Evolution and System Vulnerability in Power Grids

The seldom addressed network hierarchy property and its relationship with vulnerability analysis for power transmission grids from a complex-systems point of view are given in this paper. We analyze and compare the evolution of network hierarchy for the dynamic vulnerability evaluation of four different power transmission grids of real cases. Several meaningful results suggest that the vulnerability of power grids can be assessed by means of a network hierarchy evolution analysis. First, the network hierarchy evolution may be used as a novel measurement to quantify the robustness of power grids. Second, an antipyramidal structure appears in the most robust network when quantifying cascading failures by the proposed hierarchy metric. Furthermore, the analysis results are also validated and proved by empirical reliability data. We show that our proposed hierarchy evolution analysis methodology could be used to assess the vulnerability of power grids or even other networks from a complex-systems point of view.

Obsolescence in Urban Energy Infrastructures: The Influence of Scaling Laws on Consumption Forecasting

Abstract Cities can be considered complex systems, constantly changing and adapting to new economic, social, and cultural dynamics. They exist in many forms and over a wide range of sizes. In spite of this, researchers have discovered regularities in the form of simple scaling laws that emerge when urban outputs of many types, such as income, patents, or energy consumption, are correlated with population size. This article briefly presents some facts and figures on scaling correlations in urban contexts and how this evidence can determine and influence the obsolescence of energy infrastructures. It finally suggests several strategies which could be used to ameliorate the impacts of this on the assessment of urban consumption forecasting.

Modification of the Perrine–Baum Diagram to Improve the Calculation of High-Voltage Transmission Lines

Throughout the history of electrical engineering education, vector and phasor diagrams have been used as a fundamental learning tool. Currently, computational power has replaced these with long data lists, the result of solving equation systems with numerical methods. In this sense, diagrams have been relegated to an academic background topic that, although theoretically explained, is not used in practice. This fact may work against the understanding of the complex behavior of electrical power systems by students. This paper proposes a modification of the classic Perrine-Baum diagram construction to allow both a more practical representation and a better understanding of the behavior of a high-voltage transmission line under different load levels. A tool capable of evaluating the moment in time when demand exceeds the lines carrying capacity is also introduced. In addition, the impact of this tool on the learning process is evaluated.