Topological Vulnerability of the European Power Grid Under Errors and Attacks

Electronic version of an article published as "International journal of bifurcation and chaos", vol. 17, no. 7, July 2007, p. 2465-2475. DOI No: 10.1142/S0218127407018531. © Copyright World Scientific Publishing Company 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 behaviour can be logarithmically related to the power grid size. This logarithmic behaviour would suggest that, though size favours 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 facilitate and improve the power grid design and functioningPeer ReviewedPostprint (author’s final draft

Applications of Temporal Graph Metrics to Real-World Networks

Real world networks exhibit rich temporal information: friends are added and removed over time in online social networks; the seasons dictate the predator-prey relationship in food webs; and the propagation of a virus depends on the network of human contacts throughout the day. Recent studies have demonstrated that static network analysis is perhaps unsuitable in the study of real world network since static paths ignore time order, which, in turn, results in static shortest paths overestimating available links and underestimating their true corresponding lengths. Temporal extensions to centrality and efficiency metrics based on temporal shortest paths have also been proposed. Firstly, we analyse the roles of key individuals of a corporate network ranked according to temporal centrality within the context of a bankruptcy scandal; secondly, we present how such temporal metrics can be used to study the robustness of temporal networks in presence of random errors and intelligent attacks; thirdly, we study containment schemes for mobile phone malware which can spread via short range radio, similar to biological viruses; finally, we study how the temporal network structure of human interactions can be exploited to effectively immunise human populations. Through these applications we demonstrate that temporal metrics provide a more accurate and effective analysis of real-world networks compared to their static counterparts.Comment: 25 page

Context-Independent Centrality Measures Underestimate the Vulnerability of Power Grids

Power grids vulnerability is a key issue in society. A component failure may trigger cascades of failures across the grid and lead to a large blackout. Complex network approaches have shown a direction to study some of the problems faced by power grids. Within Complex Network Analysis structural vulnerabilities of power grids have been studied mostly using purely topological approaches, which assumes that flow of power is dictated by shortest paths. However, this fails to capture the real flow characteristics of power grids. We have proposed a flow redistribution mechanism that closely mimics the flow in power grids using the PTDF. With this mechanism we enhance existing cascading failure models to study the vulnerability of power grids. We apply the model to the European high-voltage grid to carry out a comparative study for a number of centrality measures. `Centrality' gives an indication of the criticality of network components. Our model offers a way to find those centrality measures that give the best indication of node vulnerability in the context of power grids, by considering not only the network topology but also the power flowing through the network. In addition, we use the model to determine the spare capacity that is needed to make the grid robust to targeted attacks. We also show a brief comparison of the end results with other power grid systems to generalise the result.Comment: Pre-Proceedings of CRITIS '1

A Critical Review of Robustness in Power Grids using Complex Networks Concepts

Complex network theory for analyzing robustness in energy gridsThis paper reviews the most relevant works that have investigated robustness in power grids using Complex Networks (CN) concepts. In this broad field there are two different approaches. The first one is based solely on topological concepts, and uses metrics such as mean path length, clustering coefficient, efficiency and betweenness centrality, among many others. The second, hybrid approach consists of introducing (into the CN framework) some concepts from Electrical Engineering (EE) in the effort of enhancing the topological approach, and uses novel, more efficient electrical metrics such as electrical betweenness, net-ability, and others. There is however a controversy about whether these approaches are able to provide insights into all aspects of real power grids. The CN community argues that the topological approach does not aim to focus on the detailed operation, but to discover the unexpected emergence of collective behavior, while part of the EE community asserts that this leads to an excessive simplification. Beyond this open debate it seems to be no predominant structure (scale-free, small-world) in high-voltage transmission power grids, the vast majority of power grids studied so far. Most of them have in common that they are vulnerable to targeted attacks on the most connected nodes and robust to random failure. In this respect there are only a few works that propose strategies to improve robustness such as intentional islanding, restricted link addition, microgrids and smart grids, for which novel studies suggest that small-world networks seem to be the best topology.This work has been partially supported by the project TIN2014-54583-C2-2-R from the Spanish Ministerial Commission of Science and Technology (MICYT), by the project S2013/ICE-2933 from Comunidad de Madrid and by the project FUTURE GRIDS-2020 from the Basque Government

Evolution of networks

We review the recent fast progress in statistical physics of evolving networks. Interest has focused mainly on the structural properties of random complex networks in communications, biology, social sciences and economics. A number of giant artificial networks of such a kind came into existence recently. This opens a wide field for the study of their topology, evolution, and complex processes occurring in them. Such networks possess a rich set of scaling properties. A number of them are scale-free and show striking resilience against random breakdowns. In spite of large sizes of these networks, the distances between most their vertices are short -- a feature known as the ``small-world'' effect. We discuss how growing networks self-organize into scale-free structures and the role of the mechanism of preferential linking. We consider the topological and structural properties of evolving networks, and percolation in these networks. We present a number of models demonstrating the main features of evolving networks and discuss current approaches for their simulation and analytical study. Applications of the general results to particular networks in Nature are discussed. We demonstrate the generic connections of the network growth processes with the general problems of non-equilibrium physics, econophysics, evolutionary biology, etc.Comment: 67 pages, updated, revised, and extended version of review, submitted to Adv. Phy

Topological Complexity of the Electricity Transmissión Network. Implications in the Sustainability Paradigm

Aquesta tesi explora i estudia l'estructura, dinàmica i evolució de la xarxa de transmissió d'electricitat des de la perspectiva dels sistemes complexos, essent el seu principal objectiu la definició de nous criteris i eines per ajudar a un disseny més eficient i sostenible de la xarxa de transmissió de potència. Per assolir aquest objectiu, s'han estudiat i analitzat dos conjunts de dades. D'una banda, la xarxa corresponent a la Unió per la Coordinació de Transport d'Electricitat (UCTE), que associa a la majoria dels operadors de xarxes elèctriques nacionals de l'Europa continental amb la finalitat de coordinar la producció i la demanda anual d'uns 2.300 TWh d'energia per 450 milions de clients de 24 països diferents. D'altra banda, l'evolució històrica de la xarxa de transport del Gestionaire du Réseau du Transport d'Electricité (RTE), responsable de l'explotació, manteniment i desenvolupament de la xarxa nacional mésgran d'Europa, la xarxa francesa de transport d'electricitat.Els resultats obtinguts fins al moment mostren diferències estadísticament significatives en l'estructura de les xarxes elèctriques, definint clarament comportaments dinàmics particulars que ens permeten segregar les xarxes europees en dos grups, a saber, fràgil i robust. Les xarxes fràgils es caracteritzen per les topologies més estructurades, mallades i no a l'atzar, mentre que les topològiques de caràcter més robust, contraintuïtivament, tenen estructures molts més aleatòries. Les conseqüències d'aquestes troballes per a la sostenibilitat de les xarxes d'infraestructures són importants en termes de cost i avaluació d'impactes i riscos. Es presenta així mateix un model per a l'evolució temporal i espacial d'una xarxa elèctrica. En aquest sentit, suggerim que la fragilitat topològica global augmenta quan es consideren accions de connectivitat de caire local a fi d'augmentar la fiabilitat de la xarxa a escala regional.Aquests resultats suggereixen la necessitat d'aplicar nous mètodes de disseny de la xarxa elèctrica així com noves eines amb capacitat per incloure aquests nous aspectes topològics en l'avaluació de l'eficiència i la fiabilitat de lamateixa.This Thesis explores the structure, dynamics and evolution of the electricity transmission network from a complexsystems perspective, its main objective being the definition of new criteria and tools to help to design a more efficientand sustainable transmission power grid. In doing so, two data sets have been explored and analyzed. On one hand,the Union for the Coordination of Transport of Electricity (UCTE) network, which associates most of the continentalEurope national power grid operators in order to coordinate the production and demand of some annual 2300 TWh ofenergy and 450 million customers from 24 countries. On the other hand, the Gestionaire du Réseau du Transportd'Electricité (RTE) transport network historical evolution, responsible for operating, maintaining and developing thebiggest national network in Europe, the French electricity transmission network.The results obtained so far show statistically significant dissimilarities in the structure of the power grids, clearlydefining and enclosing particular dynamic behaviors that enable us to segregate European networks in two sets,namely fragile and robust. Fragile networks are characterized by meshed topologies and non random structures whilerobust ones share more randomly generated topologies. The consequences of these finding for the sustainability ofinfrastructure networks are significant in terms of cost and risk assessment. A model for the evolution of a power gridnetwork is also presented. We suggest that global topological fragility increases when local connectivity schemes areadapted in order to increase local reliability.These outcomes appeal for new power grid design methods and tools capable to include these new topologicalaspects into efficiency and reliability assessment

Resiliency analysis for complex engineered system design

Resilience is a key driver in the design of systems that must operate in an uncertain operating environment, and is a key metric to assess the capacity for systems to perform within the specified performance envelop despite disturbances to their operating environment. This paper describes a graph spectral approach to calculate the resilience of complex engineered systems. The resilience of the design architecture of complex engineered systems is deduced from graph spectra. This is calculated from adjacency matrix representations of the physical connections between components in complex engineered systems. Furthermore, we propose a new method to identify the most vulnerable components in the design and design architectures that are robust to transmission of failures. Non-linear dynamical system (NLDS) and epidemic spreading models are used to compare the failure propagation mean time transformation. Using these metrics, we present a case study based on the Advanced Diagnostics and Prognostics Testbed (ADAPT), which is an Electrical Power System (EPS) developed at NASA Ames as a subsystem for the Ramp System of an Infantry Fighting Vehicle (IFV).Keywords: Complex System Design, Failure Density, Failure Propagation, Robust Desig

A systems approach to analyze the robustness of infrastructure networks to complex spatial hazards

Ph. D. ThesisInfrastructure networks such as water supply systems, power networks, railway networks, and road networks provide essential services that underpin modern society’s health, wealth, security, and wellbeing. However, infrastructures are susceptible to damage and disruption caused by extreme weather events such as floods and windstorms. For instance, in 2007, extensive disruption was caused by floods affecting a number of electricity substations in the United Kingdom, resulting in an estimated damage of GBP£3.18bn (US$4bn). In 2017, Hurricane Harvey hit the Southern United States, causing an approximated US$125bn (GBP£99.35bn) in damage due to the resulting floods and high winds. The magnitude of these impacts is at risk of being compounded by the effects of Climate Change, which is projected to increase the frequency of extreme weather events. As a result, it is anticipated that an estimated US$3.7tn (GBP£2.9tn) in investment will be required, per year, to meet the expected need between 2019 and 2035. A key reason for the susceptibility of infrastructure networks to extreme weather events is the wide area that needs to be covered to provide essential services. For example, in the United Kingdom alone there are over 800,000 km of overhead electricity cables, suggesting that the footprint of infrastructure networks can be as extended as that of an entire Country. These networks possess different spatial structures and attributes, as a result of their evolution over long timeframes, and respond to damage and disruption in different and complex ways. Existing approaches to understanding the impact of hazards on infrastructure networks typically either (i) use computationally expensive models, which are unable to support the investigation of enough events and scenarios to draw general insights, or (ii) use low complexity representations of hazards, with little or no consideration of their spatial properties. Consequently, this has limited the understanding of the relationship between spatial hazards, the spatial form and connectivity of infrastructure networks, and infrastructure reliability. This thesis investigates these aspects through a systemic modelling approach, applied to a synthetic and a real case study, to evaluate the response of infrastructure networks to spatially complex hazards against a series of robustness metrics. In the first case study, non-deterministic spatial hazards are generated by a fractal method which allows to control their spatial variability, resulting in spatial configurations that very closely resemble natural phenomena such as floods or windstorms. These hazards are then superimposed on a range of synthetic network layouts, which have spatial structures consistent with real infrastructure networks reported in the literature. Failure of network components is initially determined as a function of hazard intensity, and cascading failure of further components is also investigated. The performance of different infrastructure configurations is captured by an array of metrics which cover different aspects of robustness, ranging from the proneness to partitioning to the ability to process flows in the face of disruptions. Whereas analyses to date have largely adopted low complexity representations of hazards, this thesis shows that consideration of a high complexity representation which includes hazard spatial variability can reduce the robustness of the infrastructure network by nearly 40%. A “small-world” network, in which each node is within a limited number of steps from any other node, is shown to be the most robust of all the modelled networks to the different structures of spatial hazard. The second case study uses real data to assess the robustness of a power supply network operating in the Hull region in the United Kingdom, which is split in high and low voltage lines. The spatial hazard is represented by a high-resolution wind gust model and tested under current and future climate scenarios. The analysis reveals how the high and low voltage lines interact with each other in the event of faults, which lines would benefit the most from increased robustness, and which are most exposed to cascading failures. The second case study also reveals the importance of the spatial footprint of the hazard relative to the location of the infrastructure, and how particular hazard patterns can affect low voltage lines that are more often located in exposed areas at the edge of the network. The impact of Climate Change on windstorms is highly uncertain, although it could further reduce network robustness due to more severe events. Overall the two case studies provide important insights for infrastructure designers, asset managers, the academic sector, and practitioners in general. In fact, in the first case study, this thesis defines important design principles, such as the adoption of a small-world network layout, that can integrate the traditional design drivers of demand, efficiency, and cost. In the second case study, this thesis lays out a methodology that can help identify assets requiring increased robustness and protection against cascading failures, resulting in more effective prioritized infrastructure investments and adaptation plans