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Martins LP, Garcia-Callejas D, Lai HR, Wootton KL, Tylianakis JM. The propagation of disturbances in ecological networks. Trends Ecol Evol 2024; 39:558-570. [PMID: 38402007 DOI: 10.1016/j.tree.2024.01.009] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/14/2023] [Revised: 11/17/2023] [Accepted: 01/25/2024] [Indexed: 02/26/2024]
Abstract
Despite the development of network science, we lack clear heuristics for how far different disturbance types propagate within and across species interaction networks. We discuss the mechanisms of disturbance propagation in ecological networks, and propose that disturbances can be categorized into structural, functional, and transmission types according to their spread and effect on network structure and functioning. We describe the properties of species and their interaction networks and metanetworks that determine the indirect, spatial, and temporal extent of propagation. We argue that the sampling scale of ecological studies may have impeded predictions regarding the rate and extent that a disturbance spreads, and discuss directions to help ecologists to move towards a predictive understanding of the propagation of impacts across interacting communities and ecosystems.
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Affiliation(s)
- Lucas P Martins
- Centre for Integrative Ecology, School of Biological Sciences, University of Canterbury, Private Bag 4800, Christchurch 8140, Aotearoa New Zealand.
| | - David Garcia-Callejas
- Centre for Integrative Ecology, School of Biological Sciences, University of Canterbury, Private Bag 4800, Christchurch 8140, Aotearoa New Zealand
| | - Hao Ran Lai
- Centre for Integrative Ecology, School of Biological Sciences, University of Canterbury, Private Bag 4800, Christchurch 8140, Aotearoa New Zealand; Bioprotection Aotearoa, School of Biological Sciences, University of Canterbury, Private Bag 4800, Christchurch 8140, Aotearoa New Zealand
| | - Kate L Wootton
- Centre for Integrative Ecology, School of Biological Sciences, University of Canterbury, Private Bag 4800, Christchurch 8140, Aotearoa New Zealand
| | - Jason M Tylianakis
- Centre for Integrative Ecology, School of Biological Sciences, University of Canterbury, Private Bag 4800, Christchurch 8140, Aotearoa New Zealand; Bioprotection Aotearoa, School of Biological Sciences, University of Canterbury, Private Bag 4800, Christchurch 8140, Aotearoa New Zealand
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2
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Chen L, Zhu Y, Meng F, Liu RR. Catastrophic cascade of failures in interdependent hypergraphs. CHAOS (WOODBURY, N.Y.) 2024; 34:043148. [PMID: 38648382 DOI: 10.1063/5.0187160] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/11/2023] [Accepted: 03/29/2024] [Indexed: 04/25/2024]
Abstract
The failures of individual agents can significantly impact the functionality of associated groups in interconnected systems. To reveal these impacts, we develop a threshold model to investigate cascading failures in double-layer hypergraphs with interlayer interdependence. We hypothesize that a hyperedge disintegrates when the proportion of failed nodes within it exceeds a threshold. Due to the interdependence between a node and its replica in the other layer, the disintegrations of these hyperedges could trigger a cascade of events, leading to an iterative collapse across these two layers. We find that double-layer hypergraphs undergo abrupt, discontinuous first-order phase transitions during systemic collapse regardless of the specific threshold value. Additionally, the connectivity measured by average cardinality and hyperdegree plays a crucial role in shaping system robustness. A higher average hyperdegree always strengthens system robustness. However, the relationship between system robustness and average cardinality exhibits non-monotonic behaviors. Specifically, both excessively small and large average cardinalities undermine system robustness. Furthermore, a higher threshold value can boost the system's robustness. In summary, our study provides valuable insights into cascading failure dynamics in double-layer hypergraphs and has practical implications for enhancing the robustness of complex interdependent systems across domains.
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Affiliation(s)
- Lei Chen
- Research Center for Complexity Sciences, Hangzhou Normal University, Hangzhou 311121, Zhejiang, China
| | - Yanpeng Zhu
- Research Center for Complexity Sciences, Hangzhou Normal University, Hangzhou 311121, Zhejiang, China
| | - Fanyuan Meng
- Research Center for Complexity Sciences, Hangzhou Normal University, Hangzhou 311121, Zhejiang, China
| | - Run-Ran Liu
- Research Center for Complexity Sciences, Hangzhou Normal University, Hangzhou 311121, Zhejiang, China
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3
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Olin AB, Bergström U, Bodin Ö, Sundblad G, Eriksson BK, Erlandsson M, Fredriksson R, Eklöf JS. Predation and spatial connectivity interact to shape ecosystem resilience to an ongoing regime shift. Nat Commun 2024; 15:1304. [PMID: 38347008 PMCID: PMC10861472 DOI: 10.1038/s41467-024-45713-1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/12/2023] [Accepted: 02/02/2024] [Indexed: 02/15/2024] Open
Abstract
Ecosystem regime shifts can have severe ecological and economic consequences, making it a top priority to understand how to make systems more resilient. Theory predicts that spatial connectivity and the local environment interact to shape resilience, but empirical studies are scarce. Here, we use >7000 fish samplings from the Baltic Sea coast to test this prediction in an ongoing, spatially propagating shift in dominance from predatory fish to an opportunistic mesopredator, with cascading effects throughout the food web. After controlling for the influence of other drivers (including increasing mesopredator densities), we find that predatory fish habitat connectivity increases resilience to the shift, but only when densities of fish-eating top predators (seals, cormorants) are low. Resilience also increases with temperature, likely through boosted predatory fish growth and recruitment. These findings confirm theoretical predictions that spatial connectivity and the local environment can together shape resilience to regime shifts.
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Affiliation(s)
- Agnes B Olin
- Department of Ecology, Environment and Plant Sciences, Stockholm University, Stockholm, Sweden.
- Department of Aquatic Resources, Swedish University of Agricultural Sciences, Uppsala, Sweden.
| | - Ulf Bergström
- Department of Aquatic Resources, Swedish University of Agricultural Sciences, Uppsala, Sweden
| | - Örjan Bodin
- Stockholm Resilience Centre, Stockholm University, Stockholm, Sweden
| | - Göran Sundblad
- Department of Aquatic Resources, Swedish University of Agricultural Sciences, Uppsala, Sweden
| | - Britas Klemens Eriksson
- Groningen Institute for Evolutionary Life Sciences, University of Groningen, Groningen, the Netherlands
| | - Mårten Erlandsson
- Department of Aquatic Resources, Swedish University of Agricultural Sciences, Uppsala, Sweden
| | - Ronny Fredriksson
- Department of Aquatic Resources, Swedish University of Agricultural Sciences, Uppsala, Sweden
| | - Johan S Eklöf
- Department of Ecology, Environment and Plant Sciences, Stockholm University, Stockholm, Sweden
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4
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Engsig M, Tejedor A, Moreno Y, Foufoula-Georgiou E, Kasmi C. DomiRank Centrality reveals structural fragility of complex networks via node dominance. Nat Commun 2024; 15:56. [PMID: 38167342 PMCID: PMC10761873 DOI: 10.1038/s41467-023-44257-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/16/2023] [Accepted: 12/06/2023] [Indexed: 01/05/2024] Open
Abstract
Determining the key elements of interconnected infrastructure and complex systems is paramount to ensure system functionality and integrity. This work quantifies the dominance of the networks' nodes in their respective neighborhoods, introducing a centrality metric, DomiRank, that integrates local and global topological information via a tunable parameter. We present an analytical formula and an efficient parallelizable algorithm for DomiRank centrality, making it applicable to massive networks. From the networks' structure and function perspective, nodes with high values of DomiRank highlight fragile neighborhoods whose integrity and functionality are highly dependent on those dominant nodes. Underscoring this relation between dominance and fragility, we show that DomiRank systematically outperforms other centrality metrics in generating targeted attacks that effectively compromise network structure and disrupt its functionality for synthetic and real-world topologies. Moreover, we show that DomiRank-based attacks inflict more enduring damage in the network, hindering its ability to rebound and, thus, impairing system resilience. DomiRank centrality capitalizes on the competition mechanism embedded in its definition to expose the fragility of networks, paving the way to design strategies to mitigate vulnerability and enhance the resilience of critical infrastructures.
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Affiliation(s)
- Marcus Engsig
- Directed Energy Research Centre, Technology Innovation Institute, Abu Dhabi, UAE.
| | - Alejandro Tejedor
- Institute for Biocomputation and Physics of Complex Systems (BIFI), Universidad de Zaragoza, Zaragoza, Spain.
- Department of Theoretical Physics, University of Zaragoza, Zaragoza, Spain.
- Department of Civil and Environmental Engineering, University of California Irvine, Irvine, CA, USA.
| | - Yamir Moreno
- Institute for Biocomputation and Physics of Complex Systems (BIFI), Universidad de Zaragoza, Zaragoza, Spain
- Department of Theoretical Physics, University of Zaragoza, Zaragoza, Spain
- CENTAI Institute, Turin, Italy
| | - Efi Foufoula-Georgiou
- Department of Civil and Environmental Engineering, University of California Irvine, Irvine, CA, USA
- Department of Earth System Science, University of California Irvine, Irvine, CA, USA
| | - Chaouki Kasmi
- Directed Energy Research Centre, Technology Innovation Institute, Abu Dhabi, UAE
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5
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Wang F, Cetinay H, He Z, Liu L, Van Mieghem P, Kooij RE. Recovering Power Grids Using Strategies Based on Network Metrics and Greedy Algorithms. ENTROPY (BASEL, SWITZERLAND) 2023; 25:1455. [PMID: 37895578 PMCID: PMC10606524 DOI: 10.3390/e25101455] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/05/2023] [Revised: 09/29/2023] [Accepted: 10/07/2023] [Indexed: 10/29/2023]
Abstract
For this study, we investigated efficient strategies for the recovery of individual links in power grids governed by the direct current (DC) power flow model, under random link failures. Our primary objective was to explore the efficacy of recovering failed links based solely on topological network metrics. In total, we considered 13 recovery strategies, which encompassed 2 strategies based on link centrality values (link betweenness and link flow betweenness), 8 strategies based on the products of node centrality values at link endpoints (degree, eigenvector, weighted eigenvector, closeness, electrical closeness, weighted electrical closeness, zeta vector, and weighted zeta vector), and 2 heuristic strategies (greedy recovery and two-step greedy recovery), in addition to the random recovery strategy. To evaluate the performance of these proposed strategies, we conducted simulations on three distinct power systems: the IEEE 30, IEEE 39, and IEEE 118 systems. Our findings revealed several key insights: Firstly, there were notable variations in the performance of the recovery strategies based on topological network metrics across different power systems. Secondly, all such strategies exhibited inferior performance when compared to the heuristic recovery strategies. Thirdly, the two-step greedy recovery strategy consistently outperformed the others, with the greedy recovery strategy ranking second. Based on our results, we conclude that relying solely on a single metric for the development of a recovery strategy is insufficient when restoring power grids following link failures. By comparison, recovery strategies employing greedy algorithms prove to be more effective choices.
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Affiliation(s)
- Fenghua Wang
- Faculty of Electrical Engineering, Mathematics and Computer Science, Delft University of Technology, 2628 CD Delft, The Netherlands; (L.L.); (P.V.M.); (R.E.K.)
| | - Hale Cetinay
- Asset Management, System Insights and Advanced Analytics, Stedin, 3011 TA Rotterdam, The Netherlands;
| | - Zhidong He
- DS Information Technology Co., Ltd., Shanghai 200032, China;
| | - Le Liu
- Faculty of Electrical Engineering, Mathematics and Computer Science, Delft University of Technology, 2628 CD Delft, The Netherlands; (L.L.); (P.V.M.); (R.E.K.)
| | - Piet Van Mieghem
- Faculty of Electrical Engineering, Mathematics and Computer Science, Delft University of Technology, 2628 CD Delft, The Netherlands; (L.L.); (P.V.M.); (R.E.K.)
| | - Robert E. Kooij
- Faculty of Electrical Engineering, Mathematics and Computer Science, Delft University of Technology, 2628 CD Delft, The Netherlands; (L.L.); (P.V.M.); (R.E.K.)
- Unit ICT, Strategy and Policy, Netherlands Organisation for Applied Scientific Research (TNO), 2595 DA Den Haag, The Netherlands
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6
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Jain PB, Nguyen TT, Mináč J, Muller LE, Budzinski RC. Composed solutions of synchronized patterns in multiplex networks of Kuramoto oscillators. CHAOS (WOODBURY, N.Y.) 2023; 33:103128. [PMID: 37844292 DOI: 10.1063/5.0161399] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/09/2023] [Accepted: 09/18/2023] [Indexed: 10/18/2023]
Abstract
Networks with different levels of interactions, including multilayer and multiplex networks, can display a rich diversity of dynamical behaviors and can be used to model and study a wide range of systems. Despite numerous efforts to investigate these networks, obtaining mathematical descriptions for the dynamics of multilayer and multiplex systems is still an open problem. Here, we combine ideas and concepts from linear algebra and graph theory with nonlinear dynamics to offer a novel approach to study multiplex networks of Kuramoto oscillators. Our approach allows us to study the dynamics of a large, multiplex network by decomposing it into two smaller systems: one representing the connection scheme within layers (intra-layer), and the other representing the connections between layers (inter-layer). Particularly, we use this approach to compose solutions for multiplex networks of Kuramoto oscillators. These solutions are given by a combination of solutions for the smaller systems given by the intra- and inter-layer systems, and in addition, our approach allows us to study the linear stability of these solutions.
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Affiliation(s)
- Priya B Jain
- Department of Mathematics, Western University, London, Ontario N6A 3K7, Canada
- Western Institute for Neuroscience, Western University, London, Ontario N6A 3K7, Canada
- Western Academy for Advanced Research, Western University, London, Ontario N6A 3K7, Canada
| | - Tung T Nguyen
- Department of Mathematics, Western University, London, Ontario N6A 3K7, Canada
- Western Institute for Neuroscience, Western University, London, Ontario N6A 3K7, Canada
- Western Academy for Advanced Research, Western University, London, Ontario N6A 3K7, Canada
| | - Ján Mináč
- Department of Mathematics, Western University, London, Ontario N6A 3K7, Canada
- Western Institute for Neuroscience, Western University, London, Ontario N6A 3K7, Canada
- Western Academy for Advanced Research, Western University, London, Ontario N6A 3K7, Canada
| | - Lyle E Muller
- Department of Mathematics, Western University, London, Ontario N6A 3K7, Canada
- Western Institute for Neuroscience, Western University, London, Ontario N6A 3K7, Canada
- Western Academy for Advanced Research, Western University, London, Ontario N6A 3K7, Canada
| | - Roberto C Budzinski
- Department of Mathematics, Western University, London, Ontario N6A 3K7, Canada
- Western Institute for Neuroscience, Western University, London, Ontario N6A 3K7, Canada
- Western Academy for Advanced Research, Western University, London, Ontario N6A 3K7, Canada
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7
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Khramenkov VA, Dmitrichev AS, Nekorkin VI. Bistability of operating modes and their switching in a three-machine power grid. CHAOS (WOODBURY, N.Y.) 2023; 33:103129. [PMID: 37850866 DOI: 10.1063/5.0165779] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/30/2023] [Accepted: 09/26/2023] [Indexed: 10/19/2023]
Abstract
We consider a power grid consisting of three synchronous generators supplying a common static load, in which one of the generators is located electrically much closer to the load than the others, due to a shorter transmission line with longitudinal inductance compensation. A reduced model is derived in the form of an ensemble with a star (hub) topology without parameter interdependence. We show that stable symmetric and asymmetric synchronous modes can be realized in the grid, which differ, in particular, in the ratio of currents through the second and third power supply paths. The modes of different types are not observed simultaneously, but the asymmetric modes always exist in pairs. A partition of the parameter space into regions with different dynamical regimes of the grid are obtained. Regions are highlighted where only synchronous operating modes can be established. It is shown that the grid can be highly multistable and, along with synchronous operating modes, have simultaneously various types of non-synchronous modes. We study non-local stability of the asymmetric synchronous modes and switchings between them under the influence one-time disturbances and additive noise fluctuations in the mechanical powers of the generators' turbines. The characteristics of one-time disturbances are obtained leading to either return the grid back to the initial synchronous mode or switching the grid to another synchronous mode or some non-synchronous mode. The characteristics of noise fluctuations are obtained, which provide either a more probable finding of the grid in the desirable quasi-synchronous mode, or switching to an undesirable one.
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Affiliation(s)
- V A Khramenkov
- Department of Nonlinear Dynamics, Institute of Applied Physics of RAS, 46 Ulyanov Str., 603950 Nizhny Novgorod, Russia
| | - A S Dmitrichev
- Department of Nonlinear Dynamics, Institute of Applied Physics of RAS, 46 Ulyanov Str., 603950 Nizhny Novgorod, Russia
| | - V I Nekorkin
- Department of Nonlinear Dynamics, Institute of Applied Physics of RAS, 46 Ulyanov Str., 603950 Nizhny Novgorod, Russia
- Department of Oscillation Theory and Automatic Regulation, Nizhny Novgorod State University, 23 Prospekt Gagarina, 603950 Nizhny Novgorod, Russia
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8
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Sawicki J, Berner R, Loos SAM, Anvari M, Bader R, Barfuss W, Botta N, Brede N, Franović I, Gauthier DJ, Goldt S, Hajizadeh A, Hövel P, Karin O, Lorenz-Spreen P, Miehl C, Mölter J, Olmi S, Schöll E, Seif A, Tass PA, Volpe G, Yanchuk S, Kurths J. Perspectives on adaptive dynamical systems. CHAOS (WOODBURY, N.Y.) 2023; 33:071501. [PMID: 37486668 DOI: 10.1063/5.0147231] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/20/2023] [Accepted: 05/24/2023] [Indexed: 07/25/2023]
Abstract
Adaptivity is a dynamical feature that is omnipresent in nature, socio-economics, and technology. For example, adaptive couplings appear in various real-world systems, such as the power grid, social, and neural networks, and they form the backbone of closed-loop control strategies and machine learning algorithms. In this article, we provide an interdisciplinary perspective on adaptive systems. We reflect on the notion and terminology of adaptivity in different disciplines and discuss which role adaptivity plays for various fields. We highlight common open challenges and give perspectives on future research directions, looking to inspire interdisciplinary approaches.
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Affiliation(s)
- Jakub Sawicki
- Potsdam Institute for Climate Impact Research, Telegrafenberg, 14473 Potsdam, Germany
- Akademie Basel, Fachhochschule Nordwestschweiz FHNW, Leonhardsstrasse 6, 4009 Basel, Switzerland
| | - Rico Berner
- Department of Physics, Humboldt-Universität zu Berlin, Newtonstraße 15, 12489 Berlin, Germany
| | - Sarah A M Loos
- DAMTP, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
| | - Mehrnaz Anvari
- Potsdam Institute for Climate Impact Research, Telegrafenberg, 14473 Potsdam, Germany
- Fraunhofer Institute for Algorithms and Scientific Computing, Schloss Birlinghoven, 53757 Sankt-Augustin, Germany
| | - Rolf Bader
- Institute of Systematic Musicology, University of Hamburg, Hamburg, Germany
| | - Wolfram Barfuss
- Transdisciplinary Research Area: Sustainable Futures, University of Bonn, 53113 Bonn, Germany
- Center for Development Research (ZEF), University of Bonn, 53113 Bonn, Germany
| | - Nicola Botta
- Potsdam Institute for Climate Impact Research, Telegrafenberg, 14473 Potsdam, Germany
- Department of Computer Science and Engineering, Chalmers University of Technology, 412 96 Göteborg, Sweden
| | - Nuria Brede
- Potsdam Institute for Climate Impact Research, Telegrafenberg, 14473 Potsdam, Germany
- Department of Computer Science, University of Potsdam, An der Bahn 2, 14476 Potsdam, Germany
| | - Igor Franović
- Scientific Computing Laboratory, Center for the Study of Complex Systems, Institute of Physics Belgrade, University of Belgrade, Pregrevica 118, 11080 Belgrade, Serbia
| | - Daniel J Gauthier
- Potsdam Institute for Climate Impact Research, Telegrafenberg, 14473 Potsdam, Germany
| | - Sebastian Goldt
- Department of Physics, International School of Advanced Studies (SISSA), Trieste, Italy
| | - Aida Hajizadeh
- Research Group Comparative Neuroscience, Leibniz Institute for Neurobiology, Magdeburg, Germany
| | - Philipp Hövel
- Potsdam Institute for Climate Impact Research, Telegrafenberg, 14473 Potsdam, Germany
| | - Omer Karin
- Department of Mathematics, Imperial College London, London SW7 2AZ, United Kingdom
| | - Philipp Lorenz-Spreen
- Center for Adaptive Rationality, Max Planck Institute for Human Development, Lentzeallee 94, 14195 Berlin, Germany
| | - Christoph Miehl
- Akademie Basel, Fachhochschule Nordwestschweiz FHNW, Leonhardsstrasse 6, 4009 Basel, Switzerland
| | - Jan Mölter
- Department of Mathematics, School of Computation, Information and Technology, Technical University of Munich, Boltzmannstraße 3, 85748 Garching bei München, Germany
| | - Simona Olmi
- Akademie Basel, Fachhochschule Nordwestschweiz FHNW, Leonhardsstrasse 6, 4009 Basel, Switzerland
| | - Eckehard Schöll
- Potsdam Institute for Climate Impact Research, Telegrafenberg, 14473 Potsdam, Germany
- Akademie Basel, Fachhochschule Nordwestschweiz FHNW, Leonhardsstrasse 6, 4009 Basel, Switzerland
| | - Alireza Seif
- Pritzker School of Molecular Engineering, The University of Chicago, Chicago, Illinois 60637, USA
| | - Peter A Tass
- Department of Neurosurgery, Stanford University School of Medicine, Stanford, California 94304, USA
| | - Giovanni Volpe
- Department of Physics, University of Gothenburg, Gothenburg, Sweden
| | - Serhiy Yanchuk
- Potsdam Institute for Climate Impact Research, Telegrafenberg, 14473 Potsdam, Germany
- Department of Physics, Humboldt-Universität zu Berlin, Newtonstraße 15, 12489 Berlin, Germany
| | - Jürgen Kurths
- Potsdam Institute for Climate Impact Research, Telegrafenberg, 14473 Potsdam, Germany
- Department of Physics, Humboldt-Universität zu Berlin, Newtonstraße 15, 12489 Berlin, Germany
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9
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A Simulation Study of the Resiliency of Mobile Energy Storage Networks. Processes (Basel) 2023. [DOI: 10.3390/pr11030762] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/08/2023] Open
Abstract
Resilience is regarded as an essential design objective of a wide range of systems in modern society. This work is based on a vision that networks of mobile energy storage systems could provide an alternative off-grid power system design for rural and underdeveloped regions. To evaluate the resiliency of networked energy storage systems under overload failure, a model of concurrent cascading failure and healing processes is developed and demonstrated. Two resilience metrics are used to evaluate the resilience of a real-world network, namely the recovery level at a specified time and the recovery time. The simulations generate system trajectories at each time step. We explore the dependence of the system behavior on different model parameters that capture key recovery strategies. The success probability of the recovery of a failed node needs to be high enough for the network to restore its original functionality. Similarly, the increase in recovery budget parameter also leads to faster and higher recovery levels. However, in most cases, there appears to be upper limits for both parameters, beyond which any further increase could not improve the recovery performance. There is an optimum portion of the loads of the active neighboring nodes that will be carried by the newly recovered node that results in the shortest recovery times or highest recovery levels. Our work sheds light on how to enhance networked systems resiliency by considering the optimization of various model parameters.
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10
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Dias J, Montanari AN, Macau EEN. Power-grid vulnerability and its relation with network structure. CHAOS (WOODBURY, N.Y.) 2023; 33:033122. [PMID: 37003838 DOI: 10.1063/5.0137919] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/06/2022] [Accepted: 02/20/2023] [Indexed: 06/19/2023]
Abstract
Interconnected systems with critical infrastructures can be affected by small failures that may trigger a large-scale cascade of failures, such as blackouts in power grids. Vulnerability indices provide quantitative measures of a network resilience to component failures, assessing the break of information or energy flow in a system. Here, we focus on a network vulnerability analysis, that is, indices based solely on the network structure and its static characteristics, which are reliably available for most complex networks. This work studies the structural connectivity of power grids, assessing the main centrality measures in network science to identify vulnerable components (transmission lines or edges) to attacks and failures. Specifically, we consider centrality measures that implicitly model the power flow distribution in power systems. This framework allow us to show that the efficiency of the power flow in a grid can be highly sensitive to attacks on specific (central) edges. Numerical results are presented for randomly generated power-grid models and established power-grid benchmarks, where we demonstrate that the system's energy efficiency is more vulnerable to attacks on edges that are central to the power flow distribution. We expect that the vulnerability indices investigated in our work can be used to guide the design of structurally resilient power grids.
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Affiliation(s)
- Jussara Dias
- Associated Laboratory for Computing and Applied Mathematics, National Institute for Space Research, Sao José dos Campos, SP 12243-010, Brazil
| | - Arthur N Montanari
- Luxembourg Centre for Systems Biomedicine, University of Luxembourg, Belvaux L-4367, Luxembourg
| | - Elbert E N Macau
- Institute of Science and Technology, Federal University of Sao Paulo, Sao José dos Campos, SP 12247-014, Brazil
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11
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Zhong C, Xing Y, Fan Y, Zeng A. Predicting the cascading dynamics in complex networks via the bimodal failure size distribution. CHAOS (WOODBURY, N.Y.) 2023; 33:023137. [PMID: 36859195 DOI: 10.1063/5.0119902] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/10/2022] [Accepted: 02/03/2023] [Indexed: 06/18/2023]
Abstract
Cascading failure as a systematic risk occurs in a wide range of real-world networks. Cascade size distribution is a basic and crucial characteristic of systemic cascade behaviors. Recent research works have revealed that the distribution of cascade sizes is a bimodal form indicating the existence of either very small cascades or large ones. In this paper, we aim to understand the properties and formation characteristics of such bimodal distribution in complex networks and further predict the final cascade size. We first find that the bimodal distribution is ubiquitous under certain conditions in both synthetic and real networks. Moreover, the large cascades distributed in the right peak of bimodal distribution are resulted from either the failure of nodes with high load at the first step of the cascade or multiple rounds of cascades triggered by the initial failure. Accordingly, we propose a hybrid load metric (HLM), which combines the load of the initial broken node and the load of failed nodes triggered by the initial failure, to predict the final size of cascading failures. We validate the effectiveness of HLM by computing the accuracy of identifying the cascades belonging to the right and left peaks of the bimodal distribution. The results show that HLM is a better predictor than commonly used network centrality metrics in both synthetic and real-world networks. Finally, the influence of network structure on the optimal HLM is discussed.
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Affiliation(s)
- Chongxin Zhong
- School of Systems Science, Beijing Normal University, Beijing 100875, People's Republic of China
| | - Yanmeng Xing
- School of Systems Science, Beijing Normal University, Beijing 100875, People's Republic of China
| | - Ying Fan
- School of Systems Science, Beijing Normal University, Beijing 100875, People's Republic of China
| | - An Zeng
- School of Systems Science, Beijing Normal University, Beijing 100875, People's Republic of China
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12
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Jhun B, Choi H, Lee Y, Lee J, Kim CH, Kahng B. Prediction and mitigation of nonlocal cascading failures using graph neural networks. CHAOS (WOODBURY, N.Y.) 2023; 33:013115. [PMID: 36725647 DOI: 10.1063/5.0107420] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/05/2022] [Accepted: 12/13/2022] [Indexed: 06/18/2023]
Abstract
Cascading failures in electrical power grids, comprising nodes and links, propagate nonlocally. After a local disturbance, successive resultant can be distant from the source. Since avalanche failures can propagate unexpectedly, care must be taken when formulating a mitigation strategy. Herein, we propose a strategy for mitigating such cascading failures. First, to characterize the impact of each node on the avalanche dynamics, we propose a novel measure, that of Avalanche Centrality (AC). Then, based on the ACs, nodes potentially needing reinforcement are identified and selected for mitigation. Compared with heuristic measures, AC has proven to be efficient at reducing avalanche size; however, due to nonlocal propagation, calculating ACs can be computationally burdensome. To resolve this problem, we use a graph neural network (GNN). We begin by training a GNN using a large number of small networks; then, once trained, the GNN can predict ACs efficiently in large networks and real-world topological power grids in manageable computational time. Thus, under our strategy, mitigation in large networks is achieved by reinforcing nodes with large ACs. The framework developed in this study can be implemented in other complex processes that require longer computational time to simulate large networks.
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Affiliation(s)
- Bukyoung Jhun
- CCSS and CTP, Seoul National University, Seoul 08826, South Korea
| | - Hoyun Choi
- CCSS and CTP, Seoul National University, Seoul 08826, South Korea
| | - Yongsun Lee
- CCSS and CTP, Seoul National University, Seoul 08826, South Korea
| | - Jongshin Lee
- CCSS and CTP, Seoul National University, Seoul 08826, South Korea
| | - Cook Hyun Kim
- CCSS and CTP, Seoul National University, Seoul 08826, South Korea
| | - B Kahng
- Center for Complex Systems and KI for Grid Modernization, Korea Institute of Energy Technology, Naju, Jeonnam 58217, South Korea
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13
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Wu H, Meng X, Danziger MM, Cornelius SP, Tian H, Barabási AL. Fragmentation of outage clusters during the recovery of power distribution grids. Nat Commun 2022; 13:7372. [PMID: 36450824 PMCID: PMC9712383 DOI: 10.1038/s41467-022-35104-9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/07/2022] [Accepted: 11/17/2022] [Indexed: 12/05/2022] Open
Abstract
The understanding of recovery processes in power distribution grids is limited by the lack of realistic outage data, especially large-scale blackout datasets. By analyzing data from three electrical companies across the United States, we find that the recovery duration of an outage is connected with the downtime of its nearby outages and blackout intensity (defined as the peak number of outages during a blackout), but is independent of the number of customers affected. We present a cluster-based recovery framework to analytically characterize the dependence between outages, and interpret the dominant role blackout intensity plays in recovery. The recovery of blackouts is not random and has a universal pattern that is independent of the disruption cause, the post-disaster network structure, and the detailed repair strategy. Our study reveals that suppressing blackout intensity is a promising way to speed up restoration.
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Affiliation(s)
- Hao Wu
- State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, Beijing, 100876, China
- Center for Complex Networks Research, Department of Physics, Northeastern University, Boston, 02115, USA
| | - Xiangyi Meng
- Center for Complex Networks Research, Department of Physics, Northeastern University, Boston, 02115, USA
| | - Michael M Danziger
- Center for Complex Networks Research, Department of Physics, Northeastern University, Boston, 02115, USA
| | - Sean P Cornelius
- Department of Physics, Ryerson University, 350 Victoria Street, M5B 2K3, Toronto, Canada
| | - Hui Tian
- State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, Beijing, 100876, China.
| | - Albert-László Barabási
- Center for Complex Networks Research, Department of Physics, Northeastern University, Boston, 02115, USA
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14
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Al-Aqqad W, Hayajneh HS, Zhang X. Dynamics and resiliency of networks with concurrent cascading failure and self-healing. PLoS One 2022; 17:e0277490. [PMID: 36378677 PMCID: PMC9665362 DOI: 10.1371/journal.pone.0277490] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/15/2022] [Accepted: 10/27/2022] [Indexed: 11/16/2022] Open
Abstract
Local attacks in networked systems can often propagate and trigger cascading failures. Designing effective healing mechanisms to counter cascading failures is critical to enhance system resiliency. This work proposes a self-healing algorithm for networks undergoing load-based cascading failure. To advance understanding of the dynamics of networks with concurrent cascading failure and self-healing, a general discrete-time simulation framework is developed, and the resiliency is evaluated using two metrics, i.e., the system impact and the recovery time. This work further explores the effects of the multiple model parameters on the resiliency metrics. It is found that two parameters (reactivated node load parameter and node healing certainty level) span a phase plane for network dynamics where three regimes exist. To ensure full network recovery, the two parameters need to be moderate. This work lays the foundation for subsequent studies on optimization of model parameters to maximize resiliency, which will have implications to many real-world scenarios.
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Affiliation(s)
- Waseem Al-Aqqad
- Department of Electrical Engineering and Computer Science, Texas A&M University-Kingsville, Kingsville, Texas, United States of America
| | - Hassan S. Hayajneh
- Department of Engineering Technology, Purdue University Northwest, Hammond, Indiana, United States of America
| | - Xuewei Zhang
- Department of Electrical Engineering and Computer Science, Texas A&M University-Kingsville, Kingsville, Texas, United States of America
- * E-mail:
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15
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Yang L, Gu Z, Dang Y, He P. Analysis of Vulnerability on Weighted Power Networks under Line Breakdowns. ENTROPY 2022; 24:1449. [PMCID: PMC9601383 DOI: 10.3390/e24101449] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/13/2022] [Accepted: 10/05/2022] [Indexed: 06/18/2023]
Abstract
Vulnerability is a major concern for power networks. Malicious attacks have the potential to trigger cascading failures and large blackouts. The robustness of power networks against line failure has been of interest in the past several years. However, this scenario cannot cover weighted situations in the real world. This paper investigates the vulnerability of weighted power networks. Firstly, we propose a more practical capacity model to investigate the cascading failure of weighted power networks under different attack strategies. Results show that the smaller threshold of the capacity parameter can enhance the vulnerability of weighted power networks. Furthermore, a weighted electrical cyber-physical interdependent network is developed to study the vulnerability and failure dynamics of the entire power network. We perform simulations in the IEEE 118 Bus case to evaluate the vulnerability under various coupling schemes and different attack strategies. Simulation results show that heavier loads increase the likelihood of blackouts and that different coupling strategies play a crucial role in the cascading failure performance.
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16
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Budnick B, Biham O, Katzav E. Structure of networks that evolve under a combination of growth and contraction. Phys Rev E 2022; 106:044305. [PMID: 36397461 DOI: 10.1103/physreve.106.044305] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/03/2022] [Accepted: 09/15/2022] [Indexed: 06/16/2023]
Abstract
We present analytical results for the emerging structure of networks that evolve via a combination of growth (by node addition and random attachment) and contraction (by random node deletion). To this end we consider a network model in which at each time step a node addition and random attachment step takes place with probability P_{add} and a random node deletion step takes place with probability P_{del}=1-P_{add}. The balance between the growth and contraction processes is captured by the parameter η=P_{add}-P_{del}. The case of pure network growth is described by η=1. In the case that 0<η<1, the rate of node addition exceeds the rate of node deletion and the overall process is of network growth. In the opposite case, where -1<η<0, the overall process is of network contraction, while in the special case of η=0 the expected size of the network remains fixed, apart from fluctuations. Using the master equation and the generating function formalism, we obtain a closed-form expression for the time-dependent degree distribution P_{t}(k). The degree distribution P_{t}(k) includes a term that depends on the initial degree distribution P_{0}(k), which decays as time evolves, and an asymptotic distribution P_{st}(k) which is independent of the initial condition. In the case of pure network growth (η=1), the asymptotic distribution P_{st}(k) follows an exponential distribution, while for -1<η<1 it consists of a sum of Poisson-like terms and exhibits a Poisson-like tail. In the case of overall network growth (0<η<1) the degree distribution P_{t}(k) eventually converges to P_{st}(k). In the case of overall network contraction (-1<η<0) we identify two different regimes. For -1/3<η<0 the degree distribution P_{t}(k) quickly converges towards P_{st}(k). In contrast, for -1<η<-1/3 the convergence of P_{t}(k) is initially very slow and it gets closer to P_{st}(k) only shortly before the network vanishes. Thus, the model exhibits three phase transitions: a structural transition between two functional forms of P_{st}(k) at η=1, a transition between an overall growth and overall contraction at η=0, and a dynamical transition between fast and slow convergence towards P_{st}(k) at η=-1/3. The analytical results are found to be in very good agreement with the results obtained from computer simulations.
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Affiliation(s)
- Barak Budnick
- Racah Institute of Physics, The Hebrew University, Jerusalem 9190401, Israel
| | - Ofer Biham
- Racah Institute of Physics, The Hebrew University, Jerusalem 9190401, Israel
| | - Eytan Katzav
- Racah Institute of Physics, The Hebrew University, Jerusalem 9190401, Israel
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17
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Steinacker C, Storch DM, Timme M, Schröder M. Demand-driven design of bicycle infrastructure networks for improved urban bikeability. NATURE COMPUTATIONAL SCIENCE 2022; 2:655-664. [PMID: 38177262 DOI: 10.1038/s43588-022-00318-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/13/2022] [Accepted: 08/12/2022] [Indexed: 01/06/2024]
Abstract
Cycling is crucial for sustainable urban transportation. Promoting cycling critically relies on sufficiently developed infrastructure; however, designing efficient bike path networks constitutes a complex problem that requires balancing multiple constraints. Here we propose a framework for generating efficient bike path networks, explicitly taking into account cyclists' demand distribution and route choices based on safety preferences. By reversing the network formation, we iteratively remove bike paths from an initially complete bike path network and continually update cyclists' route choices to create a sequence of networks adapted to the cycling demand. We illustrate the applicability of this demand-driven approach for two cities. A comparison of the resulting bike path networks with those created for homogenized demand enables us to quantify the importance of the demand distribution for network planning. The proposed framework may thus enable quantitative evaluation of the structure of current and planned cycling networks, and support the demand-driven design of efficient infrastructures.
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Affiliation(s)
- Christoph Steinacker
- Chair for Network Dynamics, Center for Advancing Electronics Dresden (cfaed) and Institute for Theoretical Physics, Technische Universität Dresden, Dresden, Germany.
| | - David-Maximilian Storch
- Chair for Network Dynamics, Center for Advancing Electronics Dresden (cfaed) and Institute for Theoretical Physics, Technische Universität Dresden, Dresden, Germany
| | - Marc Timme
- Chair for Network Dynamics, Center for Advancing Electronics Dresden (cfaed) and Institute for Theoretical Physics, Technische Universität Dresden, Dresden, Germany
- Lakeside Labs, 9020 Klagenfurt, Austria
| | - Malte Schröder
- Chair for Network Dynamics, Center for Advancing Electronics Dresden (cfaed) and Institute for Theoretical Physics, Technische Universität Dresden, Dresden, Germany.
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18
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Ódor G, Deng S, Hartmann B, Kelling J. Synchronization dynamics on power grids in Europe and the United States. Phys Rev E 2022; 106:034311. [PMID: 36266845 DOI: 10.1103/physreve.106.034311] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/31/2022] [Accepted: 08/16/2022] [Indexed: 06/16/2023]
Abstract
Dynamical simulation of the cascade failures on the Europe and United States (U.S.) high-voltage power grids has been done via solving the second-order Kuramoto equation. We show that synchronization transition happens by increasing the global coupling parameter K with metasatble states depending on the initial conditions so that hysteresis loops occur. We provide analytic results for the time dependence of frequency spread in the large-K approximation and by comparing it with numerics of d=2,3 lattices, we find agreement in the case of ordered initial conditions. However, different power-law (PL) tails occur, when the fluctuations are strong. After thermalizing the systems we allow a single line cut failure and follow the subsequent overloads with respect to threshold values T. The PDFs p(N_{f}) of the cascade failures exhibit PL tails near the synchronization transition point K_{c}. Near K_{c} the exponents of the PLs for the U.S. power grid vary with T as 1.4≤τ≤2.1, in agreement with the empirical blackout statistics, while on the Europe power grid we find somewhat steeper PLs characterized by 1.4≤τ≤2.4. Below K_{c}, we find signatures of T-dependent PLs, caused by frustrated synchronization, reminiscent of Griffiths effects. Here we also observe stability growth following the blackout cascades, similar to intentional islanding, but for K>K_{c} this does not happen. For T<T_{c}, bumps appear in the PDFs with large mean values, known as "dragon king" blackout events. We also analyze the delaying or stabilizing effects of instantaneous feedback or increased dissipation and show how local synchronization behaves on geographic maps.
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Affiliation(s)
- Géza Ódor
- Centre for Energy Research, Institute of Technical Physics and Materials Science, H-1525 Budapest, Hungary
| | - Shengfeng Deng
- Centre for Energy Research, Institute of Technical Physics and Materials Science, H-1525 Budapest, Hungary
| | - Bálint Hartmann
- Centre for Energy Research, Institute for Energy Security and Environmental Safety, H-1525 Budapest, Hungary
| | - Jeffrey Kelling
- Faculty of Natural Sciences, Technische Universität Chemnitz, 09111 Chemnitz, Germany
- Department of Information Services and Computing, Helmholtz-Zentrum Dresden-Rossendorf, 01314 Dresden, Germany
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19
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Long YS, Zhai ZM, Tang M, Liu Y, Lai YC. Structural position vectors and symmetries in complex networks. CHAOS (WOODBURY, N.Y.) 2022; 32:093132. [PMID: 36182361 DOI: 10.1063/5.0107583] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/06/2022] [Accepted: 08/11/2022] [Indexed: 06/16/2023]
Abstract
Symmetries, due to their fundamental importance to dynamical processes on networks, have attracted a great deal of current research. Finding all symmetric nodes in large complex networks typically relies on automorphism groups from algebraic-group theory, which are solvable in quasipolynomial time. We articulate a conceptually appealing and computationally extremely efficient approach to finding and characterizing all symmetric nodes by introducing a structural position vector (SPV) for each node in networks. We establish the mathematical result that symmetric nodes must have the same SPV value and demonstrate, using six representative complex networks from the real world, that all symmetric nodes in these networks can be found in linear time. Furthermore, the SPVs not only characterize the similarity of nodes but also quantify the nodal influences in propagation dynamics. A caveat is that the proved mathematical result relating the SPV values to nodal symmetries is not sufficient; i.e., nodes having the same SPV values may not be symmetric, which arises in regular networks or networks with a dominant regular component. We point out with an analysis that this caveat is, in fact, shared by the known existing approaches to finding symmetric nodes in the literature. We further argue, with the aid of a mathematical analysis, that our SPV method is generally effective for finding the symmetric nodes in real-world networks that typically do not have a dominant regular component. Our SPV-based framework, therefore, provides a physically intuitive and computationally efficient way to uncover, understand, and exploit symmetric structures in complex networks arising from real-world applications.
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Affiliation(s)
- Yong-Shang Long
- School of Physics and Electronic Science, East China Normal University, Shanghai 200241, China
| | - Zheng-Meng Zhai
- School of Electrical, Computer and Energy Engineering, Arizona State University, Tempe, Arizona 85287, USA
| | - Ming Tang
- School of Physics and Electronic Science, East China Normal University, Shanghai 200241, China
| | - Ying Liu
- School of Computer Science, Southwest Petroleum University, Chengdu 610500, China
| | - Ying-Cheng Lai
- School of Electrical, Computer and Energy Engineering, Arizona State University, Tempe, Arizona 85287, USA
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20
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Qiang R, Yang J. Influential Spreader Identification in Complex Networks Based on Network Connectivity and Efficiency. WIRELESS COMMUNICATIONS AND MOBILE COMPUTING 2022. [DOI: https://doi.org/10.1155/2022/7896380] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/15/2023]
Abstract
Influential spreader identification is a vital research area in complex network theory, which has important influence on application and popularization. Each of the existing methods has its own advantages and disadvantages, and there are still various methods proposed to solve this issue. In this paper, we come up with a new centrality of influential spreader identification based on network connectivity and efficiency (CEC). The consequences of spreader deletion can be generally divided into two parts, one is that the connectivity of network topology is destroyed, and the other is that network’s performance is degraded, which makes the network unable to meet the functional requirement. Therefore, the relative changes of connectivity and efficiency of network before and after removing spreaders are used to present the influence of spreaders. We adopt susceptible-infected (SI) model, a well-known infectious disease model, to verify the effectiveness of CEC through the spreading ability simulation of spreaders in actual networks. And the simulation results demonstrate the superiority of CEC.
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Affiliation(s)
- Rong Qiang
- School of Computer and Information Science, Southwest University, Chongqing 400715, China
| | - Jianshe Yang
- Basic Medical School, Gansu Medical College, Pingliang 744000, China
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21
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Thümler M, Zhang X, Timme M. Absence of pure voltage instabilities in the third-order model of power grid dynamics. CHAOS (WOODBURY, N.Y.) 2022; 32:043105. [PMID: 35489857 DOI: 10.1063/5.0080284] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/30/2021] [Accepted: 03/16/2022] [Indexed: 06/14/2023]
Abstract
Secure operation of electric power grids fundamentally relies on their dynamical stability properties. For the third-order model, a paradigmatic model that captures voltage dynamics, three routes to instability are established in the literature: a pure rotor angle instability, a pure voltage instability, and one instability induced by the interplay of both. Here, we demonstrate that one of these routes, the pure voltage instability, requires infinite voltage amplitudes and is, thus, nonphysical. We show that voltage collapse dynamics nevertheless exist in the absence of any voltage instabilities.
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Affiliation(s)
- Moritz Thümler
- Chair for Network Dynamics, Institute for Theoretical Physics and Center for Advancing Electronics Dresden (cfaed), Technische Universität Dresden, 01069 Dresden, Germany
| | - Xiaozhu Zhang
- Chair for Network Dynamics, Institute for Theoretical Physics and Center for Advancing Electronics Dresden (cfaed), Technische Universität Dresden, 01069 Dresden, Germany
| | - Marc Timme
- Chair for Network Dynamics, Institute for Theoretical Physics and Center for Advancing Electronics Dresden (cfaed), Technische Universität Dresden, 01069 Dresden, Germany
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22
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Smith O, Cattell O, Farcot E, O’Dea RD, Hopcraft KI. The effect of renewable energy incorporation on power grid stability and resilience. SCIENCE ADVANCES 2022; 8:eabj6734. [PMID: 35235363 PMCID: PMC8890699 DOI: 10.1126/sciadv.abj6734] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 05/25/2021] [Accepted: 01/05/2022] [Indexed: 06/14/2023]
Abstract
Contemporary proliferation of renewable power generation is causing an overhaul in the topology, composition, and dynamics of electrical grids. These low-output, intermittent generators are widely distributed throughout the grid, including at the household level. It is critical for the function of modern power infrastructure to understand how this increasingly distributed layout affects network stability and resilience. This paper uses dynamical models, household power consumption, and photovoltaic generation data to show how these characteristics vary with the level of distribution. It is shown that resilience exhibits daily oscillations as the grid's effective structure and the power demand fluctuate. This can lead to a substantial decrease in grid resilience, explained by periods of highly clustered generator output. Moreover, the addition of batteries, while enabling consumer self-sufficiency, fails to ameliorate these problems. The methodology identifies a grid's susceptibility to disruption resulting from its network structure and modes of operation.
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23
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Goekoop R, de Kleijn R. Permutation Entropy as a Universal Disorder Criterion: How Disorders at Different Scale Levels Are Manifestations of the Same Underlying Principle. ENTROPY (BASEL, SWITZERLAND) 2021; 23:1701. [PMID: 34946007 PMCID: PMC8700347 DOI: 10.3390/e23121701] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 07/04/2021] [Revised: 12/10/2021] [Accepted: 12/13/2021] [Indexed: 12/12/2022]
Abstract
What do bacteria, cells, organs, people, and social communities have in common? At first sight, perhaps not much. They involve totally different agents and scale levels of observation. On second thought, however, perhaps they share everything. A growing body of literature suggests that living systems at different scale levels of observation follow the same architectural principles and process information in similar ways. Moreover, such systems appear to respond in similar ways to rising levels of stress, especially when stress levels approach near-lethal levels. To explain such communalities, we argue that all organisms (including humans) can be modeled as hierarchical Bayesian controls systems that are governed by the same biophysical principles. Such systems show generic changes when taxed beyond their ability to correct for environmental disturbances. Without exception, stressed organisms show rising levels of 'disorder' (randomness, unpredictability) in internal message passing and overt behavior. We argue that such changes can be explained by a collapse of allostatic (high-level integrative) control, which normally synchronizes activity of the various components of a living system to produce order. The selective overload and cascading failure of highly connected (hub) nodes flattens hierarchical control, producing maladaptive behavior. Thus, we present a theory according to which organic concepts such as stress, a loss of control, disorder, disease, and death can be operationalized in biophysical terms that apply to all scale levels of organization. Given the presumed universality of this mechanism, 'losing control' appears to involve the same process anywhere, whether involving bacteria succumbing to an antibiotic agent, people suffering from physical or mental disorders, or social systems slipping into warfare. On a practical note, measures of disorder may serve as early warning signs of system failure even when catastrophic failure is still some distance away.
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Affiliation(s)
- Rutger Goekoop
- Parnassia Group, PsyQ Parnassia Academy, Department of Anxiety Disorders, Early Detection and Intervention Team (EDIT), Lijnbaan 4, 2512 VA Den Haag, The Netherlands
| | - Roy de Kleijn
- Cognitive Psychology Unit, Institute of Psychology & Leiden Institute for Brain and Cognition, Leiden University, Wassenaarseweg 52, 2333 AK Leiden, The Netherlands;
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24
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Yang SG, Kim BJ, Son SW, Kim H. Power-grid stability predictions using transferable machine learning. CHAOS (WOODBURY, N.Y.) 2021; 31:123127. [PMID: 34972349 DOI: 10.1063/5.0058001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/26/2021] [Accepted: 11/19/2021] [Indexed: 06/14/2023]
Abstract
Complex network analyses have provided clues to improve power-grid stability with the help of numerical models. The high computational cost of numerical simulations, however, has inhibited the approach, especially when it deals with the dynamic properties of power grids such as frequency synchronization. In this study, we investigate machine learning techniques to estimate the stability of power-grid synchronization. We test three different machine learning algorithms-random forest, support vector machine, and artificial neural network-training them with two different types of synthetic power grids consisting of homogeneous and heterogeneous input-power distribution, respectively. We find that the three machine learning models better predict the synchronization stability of power-grid nodes when they are trained with the heterogeneous input-power distribution rather than the homogeneous one. With the real-world power grids of Great Britain, Spain, France, and Germany, we also demonstrate that the machine learning algorithms trained on synthetic power grids are transferable to the stability prediction of the real-world power grids, which implies the prospective applicability of machine learning techniques on power-grid studies.
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Affiliation(s)
- Seong-Gyu Yang
- Asia Pacific Center for Theoretical Physics, Pohang 37673, Republic of Korea
| | - Beom Jun Kim
- Department of Physics, Sungkyunkwan University, Suwon 16419, Republic of Korea
| | - Seung-Woo Son
- Asia Pacific Center for Theoretical Physics, Pohang 37673, Republic of Korea
| | - Heetae Kim
- Department of Energy Technology, Korea Institute of Energy Technology, Naju 58330, Republic of Korea
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25
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Network isolators inhibit failure spreading in complex networks. Nat Commun 2021; 12:3143. [PMID: 34035263 PMCID: PMC8149673 DOI: 10.1038/s41467-021-23292-9] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/26/2020] [Accepted: 04/19/2021] [Indexed: 11/08/2022] Open
Abstract
In our daily lives, we rely on the proper functioning of supply networks, from power grids to water transmission systems. A single failure in these critical infrastructures can lead to a complete collapse through a cascading failure mechanism. Counteracting strategies are thus heavily sought after. In this article, we introduce a general framework to analyse the spreading of failures in complex networks and demostrate that not only decreasing but also increasing the connectivity of the network can be an effective method to contain damages. We rigorously prove the existence of certain subgraphs, called network isolators, that can completely inhibit any failure spreading, and we show how to create such isolators in synthetic and real-world networks. The addition of selected links can thus prevent large scale outages as demonstrated for power transmission grids.
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26
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Berner R, Yanchuk S, Schöll E. What adaptive neuronal networks teach us about power grids. Phys Rev E 2021; 103:042315. [PMID: 34005899 DOI: 10.1103/physreve.103.042315] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/11/2020] [Accepted: 04/08/2021] [Indexed: 06/12/2023]
Abstract
Power grid networks, as well as neuronal networks with synaptic plasticity, describe real-world systems of tremendous importance for our daily life. The investigation of these seemingly unrelated types of dynamical networks has attracted increasing attention over the past decade. In this paper, we provide insight into the fundamental relation between these two types of networks. For this, we consider well-established models based on phase oscillators and show their intimate relation. In particular, we prove that phase oscillator models with inertia can be viewed as a particular class of adaptive networks. This relation holds even for more general classes of power grid models that include voltage dynamics. As an immediate consequence of this relation, we discover a plethora of multicluster states for phase oscillators with inertia. Moreover, the phenomenon of cascading line failure in power grids is translated into an adaptive neuronal network.
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Affiliation(s)
- Rico Berner
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstraße 36, 10623 Berlin, Germany
- Institut für Mathematik, Technische Universität Berlin, Straße des 17. Juni 136, 10623 Berlin, Germany
| | - Serhiy Yanchuk
- Institut für Mathematik, Technische Universität Berlin, Straße des 17. Juni 136, 10623 Berlin, Germany
| | - Eckehard Schöll
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstraße 36, 10623 Berlin, Germany
- Bernstein Center for Computational Neuroscience Berlin, Humboldt-Universität, 10115 Berlin, Germany
- Potsdam Institute for Climate Impact Research, Telegrafenberg A 31, 14473 Potsdam, Germany
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27
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Abstract
Traditional power systems have been gradually shifting to power-electronic-based ones, with more power electronic devices (including converters) incorporated recently. Faced with much more complicated dynamics, it is a great challenge to uncover its physical mechanisms for system stability and/or instability (oscillation). In this paper, we first establish a nonlinear model of a multi-converter power system within the DC-link voltage timescale, from the first principle. Then, we obtain a linearized model with the associated characteristic matrix, whose eigenvalues determine the system stability, and finally get independent subsystems by using symmetry approximation conditions under the assumptions that all converters’ parameters and their susceptance to the infinite bus (Bg) are identical. Based on these mathematical analyses, we find that the whole system can be decomposed into several equivalent single-converter systems and its small-signal stability is solely determined by a simple converter system connected to an infinite bus under the same susceptance Bg. These results of large-scale multi-converter analysis help to understand the power-electronic-based power system dynamics, such as renewable energy integration. As well, they are expected to stimulate broad interests among researchers in the fields of network dynamics theory and applications.
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28
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Chen CY, Zhao Y, Gao J, Stanley HE. Nonlinear model of cascade failure in weighted complex networks considering overloaded edges. Sci Rep 2020; 10:13428. [PMID: 32778699 PMCID: PMC7417584 DOI: 10.1038/s41598-020-69775-5] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/08/2020] [Accepted: 07/16/2020] [Indexed: 11/16/2022] Open
Abstract
Considering the elasticity of the real networks, the components in the network have a redundant capacity against the load, such as power grids, traffic networks and so on. Moreover, the interaction strength between nodes is often different. This paper proposes a novel nonlinear model of cascade failure in weighted complex networks considering overloaded edges to describe the redundant capacity for edges and capture the interaction strength of nodes. We fill this gap by studying a nonlinear weighted model of cascade failure with overloaded edges over synthetic and real weighted networks. The cascading failure model is constructed for the first time according to the overload coefficient, capacity parameter, weight coefficient, and distribution coefficient. Then through theoretical analysis, the conditions for stopping failure cascades are obtained, and the analysis shows the superiority of the constructed model. Finally, the cascading invulnerability is simulated in several typical network models and the US power grid. The results show that the model is a feasible and reasonable change of weight parameters, capacity coefficient, distribution coefficient, and overload coefficient can significantly improve the destructiveness of complex networks against cascade failure. Our methodology provides an efficacious reference for the control and prevention of cascading failures in many real networks.
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Affiliation(s)
- Chao-Yang Chen
- School of Information and Electrical Engineering, Hunan University of Science and Technology, Xiangtan, 411201, People's Republic of China.
- Center for Polymer Studies and Department of Physics, Boston University, Boston, MA, 02215, USA.
| | - Yang Zhao
- School of Information and Electrical Engineering, Hunan University of Science and Technology, Xiangtan, 411201, People's Republic of China
| | - Jianxi Gao
- Department of Computer Science, Rensselaer Polytechnic Institute, Troy, NY, 12180, USA.
- Network Science and Technology Center, Rensselaer Polytechnic Institute, Troy, NY, 12180, USA.
| | - Harry Eugene Stanley
- Center for Polymer Studies and Department of Physics, Boston University, Boston, MA, 02215, USA.
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29
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Totz CH, Olmi S, Schöll E. Control of synchronization in two-layer power grids. Phys Rev E 2020; 102:022311. [PMID: 32942404 DOI: 10.1103/physreve.102.022311] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/22/2020] [Accepted: 07/29/2020] [Indexed: 06/11/2023]
Abstract
In this work we suggest modeling the dynamics of power grids in terms of a two-layer network, and we use the Italian high-voltage power grid as a proof-of-principle example. The first layer in our model represents the power grid consisting of generators and consumers, while the second layer represents a dynamic communication network that serves as a controller of the first layer. In particular, the dynamics of the power grid is modeled by the Kuramoto model with inertia, while the communication layer provides a control signal P_{i}^{c} for each generator to improve frequency synchronization within the power grid. We propose different realizations of the communication layer topology and different ways to calculate the control signal. Then we conduct a systematic survey of the two-layer system against a multitude of different realistic perturbation scenarios, such as disconnecting generators, increasing demand of consumers, or generators with stochastic power output. When using a control topology that allows all generators to exchange information, we find that a control scheme aimed to minimize the frequency difference between adjacent nodes operates very efficiently even against the worst scenarios with the strongest perturbations.
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Affiliation(s)
- Carl H Totz
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstraße 36, 10623 Berlin, Germany
| | - Simona Olmi
- Inria Sophia Antipolis Méditerranée Research Centre, 2004 Route des Lucioles, 06902 Valbonne, France
- CNR - Consiglio Nazionale delle Ricerche - Istituto dei Sistemi Complessi, 50019, Sesto Fiorentino, Italy
| | - Eckehard Schöll
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstraße 36, 10623 Berlin, Germany
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30
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Nesti T, Sloothaak F, Zwart B. Emergence of Scale-Free Blackout Sizes in Power Grids. PHYSICAL REVIEW LETTERS 2020; 125:058301. [PMID: 32794856 DOI: 10.1103/physrevlett.125.058301] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/12/2019] [Revised: 06/07/2020] [Accepted: 07/10/2020] [Indexed: 06/11/2023]
Abstract
We model power grids as graphs with heavy-tailed sinks, which represent demand from cities, and study cascading failures on such graphs. Our analysis links the scale-free nature of blackout sizes to the scale-free nature of city sizes, contrasting previous studies suggesting that this nature is governed by self-organized criticality. Our results are based on a new mathematical framework combining the physics of power flow with rare event analysis for heavy-tailed distributions, and are validated using various synthetic networks and the German transmission grid.
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Affiliation(s)
- Tommaso Nesti
- Centrum Wiskunde and Informatica, 1098 XG Amsterdam, Netherlands
| | - Fiona Sloothaak
- Eindhoven University of Technology, 5612 AZ Eindhoven, Netherlands
| | - Bert Zwart
- Centrum Wiskunde and Informatica, 1098 XG Amsterdam, Netherlands
- Eindhoven University of Technology, 5612 AZ Eindhoven, Netherlands
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31
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Ji Y, He W, Cheng S, Kurths J, Zhan M. Dynamic Network Characteristics of Power-electronics-based Power Systems. Sci Rep 2020; 10:9946. [PMID: 32561818 PMCID: PMC7305112 DOI: 10.1038/s41598-020-66635-0] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/18/2019] [Accepted: 05/20/2020] [Indexed: 11/10/2022] Open
Abstract
Power flow studies in traditional power systems aim to uncover the stationary relationship between voltage amplitude and phase and active and reactive powers; they are important for both stationary and dynamic power system analysis. With the increasing penetration of large-scale power electronics devices including renewable generations interfaced with converters, the power systems become gradually power-electronics-dominant and correspondingly their dynamical behavior changes substantially. Due to the fast dynamics of converters, such as AC current controller, the quasi-stationary state approximation, which has been widely used in power systems, is no longer appropriate and should be reexamined. In this paper, for a better description of network characteristics, we develop a novel concept of dynamic power flow and uncover an explicit dynamic relation between the instantaneous powers and the voltage vectors. This mathematical relation has been well verified by simulations on transient analysis of a small power-electronics-based power system, and a small-signal frequency-domain stability analysis of a voltage source converter connected to an infinitely strong bus. These results demonstrate the applicability of the proposed method and shed an improved light on our understanding of power-electronics-dominant power systems, whose dynamical nature remains obscure.
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Affiliation(s)
- Yuxi Ji
- The State Key Laboratory of Advanced Electromagnetic Engineering and Technology, School of Electrical and Electronic Engineering, Huazhong University of Science and Technology, Wuhan, 430074, China
| | - Wei He
- The State Key Laboratory of Advanced Electromagnetic Engineering and Technology, School of Electrical and Electronic Engineering, Huazhong University of Science and Technology, Wuhan, 430074, China
| | - Shijie Cheng
- The State Key Laboratory of Advanced Electromagnetic Engineering and Technology, School of Electrical and Electronic Engineering, Huazhong University of Science and Technology, Wuhan, 430074, China
| | - Jürgen Kurths
- Potsdam Institute for Climate Impact Research, Telegraphenberg, Potsdam, D-14415, Germany.,Institute of Physics, Humboldt University Berlin, Berlin, D-12489, Germany.,Saratov State University, Saratov, 4410012, Russia
| | - Meng Zhan
- The State Key Laboratory of Advanced Electromagnetic Engineering and Technology, School of Electrical and Electronic Engineering, Huazhong University of Science and Technology, Wuhan, 430074, China.
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32
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Ódor G, Hartmann B. Power-Law Distributions of Dynamic Cascade Failures in Power-Grid Models. ENTROPY 2020; 22:e22060666. [PMID: 33286438 PMCID: PMC7517205 DOI: 10.3390/e22060666] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 05/07/2020] [Revised: 06/10/2020] [Accepted: 06/11/2020] [Indexed: 11/16/2022]
Abstract
Power-law distributed cascade failures are well known in power-grid systems. Understanding this phenomena has been done by various DC threshold models, self-tuned at their critical point. Here, we attempt to describe it using an AC threshold model, with a second-order Kuramoto type equation of motion of the power-flow. We have focused on the exploration of network heterogeneity effects, starting from homogeneous two-dimensional (2D) square lattices to the US power-grid, possessing identical nodes and links, to a realistic electric power-grid obtained from the Hungarian electrical database. The last one exhibits node dependent parameters, topologically marginally on the verge of robust networks. We show that too weak quenched heterogeneity, coming solely from the probabilistic self-frequencies of nodes (2D square lattice), is not sufficient for finding power-law distributed cascades. On the other hand, too strong heterogeneity destroys the synchronization of the system. We found agreement with the empirically observed power-law failure size distributions on the US grid, as well as on the Hungarian networks near the synchronization transition point. We have also investigated the consequence of replacing the usual Gaussian self-frequencies to exponential distributed ones, describing renewable energy sources. We found a drop in the steady state synchronization averages, but the cascade size distribution, both for the US and Hungarian systems, remained insensitive and have kept the universal tails, being characterized by the exponent τ≃1.8. We have also investigated the effect of an instantaneous feedback mechanism in case of the Hungarian power-grid.
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33
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Suchithra KS, Gopalakrishnan EA, Surovyatkina E, Kurths J. Rate-induced transitions and advanced takeoff in power systems. CHAOS (WOODBURY, N.Y.) 2020; 30:061103. [PMID: 32611081 DOI: 10.1063/5.0002456] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/25/2020] [Accepted: 05/22/2020] [Indexed: 06/11/2023]
Abstract
One of the most common causes of failures in complex systems in nature or engineering is an abrupt transition from a stable to an alternate stable state. Such transitions cause failures in the dynamic power systems. We focus on this transition from a stable to an unstable manifold for a rate-dependent mechanical power input via a numerical investigation in a theoretical power system model. Our studies uncover early transitions that depend on the rate of variation of mechanical input. Furthermore, we determine the dependency of a critical rate on initial conditions of the system. Accordingly, this knowledge of the critical rate can be used in devising an effective control strategy based on artificial intelligence (AI).
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Affiliation(s)
- K S Suchithra
- Center for Computational Engineering & Networking (CEN), Amrita School of Engineering, Coimbatore, Amrita Vishwa Vidyapeetham, India
| | - E A Gopalakrishnan
- Center for Computational Engineering & Networking (CEN), Amrita School of Engineering, Coimbatore, Amrita Vishwa Vidyapeetham, India
| | | | - Jürgen Kurths
- Potsdam Institute for Climate Impact Research, Potsdam 14473, Germany
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34
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Tishby I, Biham O, Katzav E. Analysis of the convergence of the degree distribution of contracting random networks towards a Poisson distribution using the relative entropy. Phys Rev E 2020; 101:062308. [PMID: 32688589 DOI: 10.1103/physreve.101.062308] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/28/2020] [Accepted: 05/22/2020] [Indexed: 06/11/2023]
Abstract
We present analytical results for the structural evolution of random networks undergoing contraction processes via generic node deletion scenarios, namely, random deletion, preferential deletion, and propagating deletion. Focusing on configuration model networks, which exhibit a given degree distribution P_{0}(k) and no correlations, we show using a rigorous argument that upon contraction the degree distributions of these networks converge towards a Poisson distribution. To this end, we use the relative entropy S_{t}=S[P_{t}(k)||π(k|〈K〉_{t})] of the degree distribution P_{t}(k) of the contracting network at time t with respect to the corresponding Poisson distribution π(k|〈K〉_{t}) with the same mean degree 〈K〉_{t} as a distance measure between P_{t}(k) and Poisson. The relative entropy is suitable as a distance measure since it satisfies S_{t}≥0 for any degree distribution P_{t}(k), while equality is obtained only for P_{t}(k)=π(k|〈K〉_{t}). We derive an equation for the time derivative dS_{t}/dt during network contraction and show that the relative entropy decreases monotonically to zero during the contraction process. We thus conclude that the degree distributions of contracting configuration model networks converge towards a Poisson distribution. Since the contracting networks remain uncorrelated, this means that their structures converge towards an Erdős-Rényi (ER) graph structure, substantiating earlier results obtained using direct integration of the master equation and computer simulations [Tishby et al., Phys. Rev. E 100, 032314 (2019)2470-004510.1103/PhysRevE.100.032314]. We demonstrate the convergence for configuration model networks with degenerate degree distributions (random regular graphs), exponential degree distributions, and power-law degree distributions (scale-free networks).
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Affiliation(s)
- Ido Tishby
- Racah Institute of Physics, The Hebrew University, Jerusalem 9190401, Israel
| | - Ofer Biham
- Racah Institute of Physics, The Hebrew University, Jerusalem 9190401, Israel
| | - Eytan Katzav
- Racah Institute of Physics, The Hebrew University, Jerusalem 9190401, Israel
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35
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Krönke J, Wunderling N, Winkelmann R, Staal A, Stumpf B, Tuinenburg OA, Donges JF. Dynamics of tipping cascades on complex networks. Phys Rev E 2020; 101:042311. [PMID: 32422827 DOI: 10.1103/physreve.101.042311] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/09/2019] [Accepted: 03/18/2020] [Indexed: 01/02/2023]
Abstract
Tipping points occur in diverse systems in various disciplines such as ecology, climate science, economy, and engineering. Tipping points are critical thresholds in system parameters or state variables at which a tiny perturbation can lead to a qualitative change of the system. Many systems with tipping points can be modeled as networks of coupled multistable subsystems, e.g., coupled patches of vegetation, connected lakes, interacting climate tipping elements, and multiscale infrastructure systems. In such networks, tipping events in one subsystem are able to induce tipping cascades via domino effects. Here, we investigate the effects of network topology on the occurrence of such cascades. Numerical cascade simulations with a conceptual dynamical model for tipping points are conducted on Erdős-Rényi, Watts-Strogatz, and Barabási-Albert networks. Additionally, we generate more realistic networks using data from moisture-recycling simulations of the Amazon rainforest and compare the results to those obtained for the model networks. We furthermore use a directed configuration model and a stochastic block model which preserve certain topological properties of the Amazon network to understand which of these properties are responsible for its increased vulnerability. We find that clustering and spatial organization increase the vulnerability of networks and can lead to tipping of the whole network. These results could be useful to evaluate which systems are vulnerable or robust due to their network topology and might help us to design or manage systems accordingly.
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Affiliation(s)
- Jonathan Krönke
- Earth System Analysis, Potsdam Institute for Climate Impact Research, Member of the Leibniz Association, 14473 Potsdam, Germany.,Institute of Physics and Astronomy, University of Potsdam, 14476 Potsdam, Germany
| | - Nico Wunderling
- Earth System Analysis, Potsdam Institute for Climate Impact Research, Member of the Leibniz Association, 14473 Potsdam, Germany.,Institute of Physics and Astronomy, University of Potsdam, 14476 Potsdam, Germany.,Department of Physics, Humboldt University of Berlin, 12489 Berlin, Germany
| | - Ricarda Winkelmann
- Earth System Analysis, Potsdam Institute for Climate Impact Research, Member of the Leibniz Association, 14473 Potsdam, Germany.,Institute of Physics and Astronomy, University of Potsdam, 14476 Potsdam, Germany
| | - Arie Staal
- Stockholm Resilience Centre, Stockholm University, 10691 Stockholm, Sweden
| | - Benedikt Stumpf
- Earth System Analysis, Potsdam Institute for Climate Impact Research, Member of the Leibniz Association, 14473 Potsdam, Germany.,Department of Physics, Free University Berlin, 14195 Berlin, Germany
| | - Obbe A Tuinenburg
- Stockholm Resilience Centre, Stockholm University, 10691 Stockholm, Sweden.,Copernicus Institute, Faculty of Geosciences, Utrecht University, 3584 CB Utrecht, The Netherlands
| | - Jonathan F Donges
- Earth System Analysis, Potsdam Institute for Climate Impact Research, Member of the Leibniz Association, 14473 Potsdam, Germany.,Stockholm Resilience Centre, Stockholm University, 10691 Stockholm, Sweden
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36
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Smith O, Crowe J, Farcot E, O'Dea RD, Hopcraft KI. Cascading failures in networks of heterogeneous node behavior. Phys Rev E 2020; 101:020301. [PMID: 32168662 DOI: 10.1103/physreve.101.020301] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/03/2019] [Accepted: 02/11/2020] [Indexed: 06/10/2023]
Abstract
Variability in the dynamical function of nodes comprising a complex network impacts upon cascading failures that can compromise the network's ability to operate. Node types correspond to sources, sinks, or passive conduits of a current flow, applicable to renewable electrical power microgrids containing a variable number of intermittently operating generators and consumers of power. The resilience to cascading failures of ensembles of synthetic networks with different topology is examined as a function of the edge current carrying capacity and mix of node types, together with exemplar real-world networks. While a network with a homogeneous composition of node types can be resilient to failure, onewith an identical topology but with heterogeneous nodes can be strongly susceptible to failure. For networks with similar numbers of sources, sinks, and passive nodes the mean resilience decreases as networks become more disordered. Nevertheless all network topologies have enhanced regions of resilience, accessible by the manipulation of node composition and functionality.
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Affiliation(s)
- O Smith
- School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD, United Kingdom
| | - J Crowe
- Faculty of Engineering, University of Nottingham, Nottingham NG7 2RD, United Kingdom
| | - E Farcot
- School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD, United Kingdom
| | - R D O'Dea
- School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD, United Kingdom
| | - K I Hopcraft
- School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD, United Kingdom
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37
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Taher H, Olmi S, Schöll E. Enhancing power grid synchronization and stability through time-delayed feedback control. Phys Rev E 2019; 100:062306. [PMID: 31962463 DOI: 10.1103/physreve.100.062306] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/21/2019] [Indexed: 06/10/2023]
Abstract
We study the synchronization and stability of power grids within the Kuramoto phase oscillator model with inertia with a bimodal natural frequency distribution representing the generators and the loads. The Kuramoto model describes the dynamics of the ac voltage phase and allows for a comprehensive understanding of fundamental network properties capturing the essential dynamical features of a power grid on coarse scales. We identify critical nodes through solitary frequency deviations and Lyapunov vectors corresponding to unstable Lyapunov exponents. To cure dangerous deviations from synchronization we propose time-delayed feedback control, which is an efficient control concept in nonlinear dynamic systems. Different control strategies are tested and compared with respect to the minimum number of controlled nodes required to achieve synchronization and Lyapunov stability. As a proof of principle, this fast-acting control method is demonstrated for different networks (the German and the Italian power transmission grid), operating points, configurations, and models. In particular, an extended version of the Kuramoto model with inertia is considered that includes the voltage dynamics, thus taking into account the interplay of amplitude and phase typical of the electrodynamical behavior of a machine.
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Affiliation(s)
- Halgurd Taher
- Inria Sophia Antipolis Méditerranée Research Centre, 06902 Valbonne, France
- Institut für Theoretische Physik, Technische Universität Berlin, 10623 Berlin, Germany
| | - Simona Olmi
- Inria Sophia Antipolis Méditerranée Research Centre, 06902 Valbonne, France
- CNR, Consiglio Nazionale delle Ricerche, Istituto dei Sistemi Complessi, 50019 Sesto Fiorentino, Italy
| | - Eckehard Schöll
- Institut für Theoretische Physik, Technische Universität Berlin, 10623 Berlin, Germany
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38
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Ding L, Liu SY, Yang Q, Xu XK. Uncovering the Dependence of Cascading Failures on Network Topology by Constructing Null Models. ENTROPY 2019; 21:1119. [PMCID: PMC7514463 DOI: 10.3390/e21111119] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/10/2019] [Accepted: 11/14/2019] [Indexed: 06/17/2023]
Abstract
Cascading failures are the significant cause of network breakdowns in a variety of complex infrastructure systems. Given such a system, uncovering the dependence of cascading failures on its underlying topology is essential but still not well explored in the field of complex networks. This study offers an original approach to systematically investigate the association between cascading failures and topological variation occurring in realistic complex networks by constructing different types of null models. As an example of its application, we study several standard Internet networks in detail. The null models first transform the original network into a series of randomized networks representing alternate realistic topologies, while taking its basic topological characteristics into account. Then considering the routing rule of shortest-path flow, it is sought to determine the implications of different topological circumstances, and the findings reveal the effects of micro-scale (such as degree distribution, assortativity, and transitivity) and meso-scale (such as rich-club and community structure) features on the cascade damage caused by deliberate node attacks. Our results demonstrate that the proposed method is suitable and promising to comprehensively analyze realistic influence of various topological properties, providing insight into designing the networks to make them more robust against cascading failures.
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Affiliation(s)
- Lin Ding
- School of Computer, University of South China, Hengyang 421001, China; (L.D.); (Q.Y.)
| | - Si-Yuan Liu
- College of Information and Communication Engineering, Dalian Minzu University, Dalian 116600, China;
| | - Quan Yang
- School of Computer, University of South China, Hengyang 421001, China; (L.D.); (Q.Y.)
| | - Xiao-Ke Xu
- College of Information and Communication Engineering, Dalian Minzu University, Dalian 116600, China;
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39
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Duan D, Lv C, Si S, Wang Z, Li D, Gao J, Havlin S, Stanley HE, Boccaletti S. Universal behavior of cascading failures in interdependent networks. Proc Natl Acad Sci U S A 2019; 116:22452-22457. [PMID: 31624122 PMCID: PMC6842597 DOI: 10.1073/pnas.1904421116] [Citation(s) in RCA: 44] [Impact Index Per Article: 8.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/25/2023] Open
Abstract
Catastrophic and major disasters in real-world systems, such as blackouts in power grids or global failures in critical infrastructures, are often triggered by minor events which originate a cascading failure in interdependent graphs. We present here a self-consistent theory enabling the systematic analysis of cascading failures in such networks and encompassing a broad range of dynamical systems, from epidemic spreading, to birth-death processes, to biochemical and regulatory dynamics. We offer testable predictions on breakdown scenarios, and, in particular, we unveil the conditions under which the percolation transition is of the first-order or the second-order type, as well as prove that accounting for dynamics in the nodes always accelerates the cascading process. Besides applying directly to relevant real-world situations, our results give practical hints on how to engineer more robust networked systems.
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Affiliation(s)
- Dongli Duan
- School of Mechanical Engineering, Northwestern Polytechnical University, Xi'an 710072, China
- School of Information and Control Engineering, Xi'an University of Architecture and Technology, Xi'an 710311, China
| | - Changchun Lv
- School of Mechanical Engineering, Northwestern Polytechnical University, Xi'an 710072, China
| | - Shubin Si
- School of Mechanical Engineering, Northwestern Polytechnical University, Xi'an 710072, China;
| | - Zhen Wang
- School of Mechanical Engineering, Northwestern Polytechnical University, Xi'an 710072, China;
- Center for OPTical IMagery Analysis and Learning, Northwestern Polytechnical University, Xi'an 710072, China
| | - Daqing Li
- School of Reliability and Systems Engineering, Beihang University, Beijing 100191, China
| | - Jianxi Gao
- Department of Computer Science, Rensselaer Polytechnic Institute, Troy, NY 12180
- Network Science and Technology Center, Rensselaer Polytechnic Institute, Troy, NY 12180
| | - Shlomo Havlin
- Department of Physics, Bar-Ilan University, Ramat-Gan 52900, Israel
| | - H Eugene Stanley
- Center for Polymer Studies, Department of Physics, Boston University, Boston, MA 02215;
| | - Stefano Boccaletti
- Institute of Complex Systems, Consiglio Nazionale delle Ricerche, Florence 50019, Italy
- Unmanned Systems Research Institute, Northwestern Polytechnical University, Xi'an 710072, China
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40
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Bourne J, O'Sullivan A, Arcaute E. Don't go chasing artificial waterfalls: Artificial line limits and cascading failures in power grids. CHAOS (WOODBURY, N.Y.) 2019; 29:113117. [PMID: 31779362 DOI: 10.1063/1.5115493] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/18/2019] [Accepted: 10/17/2019] [Indexed: 06/10/2023]
Abstract
Research on cascading failures in power-transmission networks requires detailed data on the capacity of individual transmission lines. However, these data are often unavailable to researchers. Consequently, line limits are often modeled by assuming that they are proportional to some average load. However, there is scarce research to support this assumption as being realistic. In this paper, we analyze the proportional loading (PL) approach and compare it to two linear models that use voltage and initial power flow as variables and are trained on the line limits of a real power network that we have access to. We compare these artificial line-limit methods using four tests: the ability to model true line limits, the damage done during an attack, the order in which edges are lost, and accuracy ranking the relative performance of different attack strategies. We find that the linear models are the top-performing method or are close to the top in all the tests we perform. In comparison, the tolerance value that produces the best PL limits changes depending on the test. The PL approach was a particularly poor fit when the line tolerance was less than two, which is the most commonly used value range in cascading failure research. We also find indications that the accuracy of modeling line limits does not indicate how well a model will represent grid collapse. The findings of this paper provide an understanding of the weaknesses of the PL approach and offer an alternative method of line-limit modeling.
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Affiliation(s)
- J Bourne
- UCL Energy Institute, University College London, Gower Street, London WC1E 6BT, United Kingdom
| | - A O'Sullivan
- UCL Energy Institute, University College London, Gower Street, London WC1E 6BT, United Kingdom
| | - E Arcaute
- Centre for Advanced Spatial Analysis (CASA), University College London, Gower St, London WC1E 6BT, United Kingdom
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41
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Wolff MF, Schmietendorf K, Lind PG, Kamps O, Peinke J, Maass P. Heterogeneities in electricity grids strongly enhance non-Gaussian features of frequency fluctuations under stochastic power input. CHAOS (WOODBURY, N.Y.) 2019; 29:103149. [PMID: 31675815 DOI: 10.1063/1.5122986] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/01/2019] [Accepted: 10/08/2019] [Indexed: 06/10/2023]
Abstract
Stochastic feed-in of fluctuating renewable energies is steadily increasing in modern electricity grids, and this becomes an important risk factor for maintaining power grid stability. Here, we study the impact of wind power feed-in on the short-term frequency fluctuations in power grids based on an Institute of Electrical and Electronics Engineers test grid structure, the swing equation for the dynamics of voltage phase angles, and a series of measured wind speed data. External control measures are accounted for by adjusting the grid state to the average power feed-in on a time scale of 1 min. The wind power is injected at a single node by replacing one of the conventional generator nodes in the test grid by a wind farm. We determine histograms of local frequencies for a large number of 1-min wind speed sequences taken from the measured data and for different injection nodes. These histograms exhibit a common type of shape, which can be described by a Gaussian distribution for small frequencies and a nearly exponentially decaying tail part. Non-Gaussian features become particularly pronounced for wind power injection at locations, which are weakly connected to the main grid structure. This effect is only present when taking into account the heterogeneities in transmission line and node properties of the grid, while it disappears upon homogenizing of these features. The standard deviation of the frequency fluctuations increases linearly with the average injected wind power.
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Affiliation(s)
- Matthias F Wolff
- Fachbereich Physik, Universität Osnabrück, Barbarastraße 7, 49076 Osnabrück, Germany
| | - Katrin Schmietendorf
- Institut für Theoretische Physik, Westfälische Wilhelms-Universität Münster, Wilhelm-Klemm-Straße 9, 48149 Münster, Germany
| | - Pedro G Lind
- Department of Computer Science, OsloMet-Oslo Metropolitan University, Pilestredet 35, 0166 Oslo, Norway
| | - Oliver Kamps
- Institut für Theoretische Physik, Westfälische Wilhelms-Universität Münster, Wilhelm-Klemm-Straße 9, 48149 Münster, Germany
| | - Joachim Peinke
- Institut für Physik & ForWind, Universität Oldenburg, Küpkersweg 70, 26129 Oldenburg, Germany
| | - Philipp Maass
- Fachbereich Physik, Universität Osnabrück, Barbarastraße 7, 49076 Osnabrück, Germany
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Kim H, Lee MJ, Lee SH, Son SW. On structural and dynamical factors determining the integrated basin instability of power-grid nodes. CHAOS (WOODBURY, N.Y.) 2019; 29:103132. [PMID: 31675814 DOI: 10.1063/1.5115532] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/19/2019] [Accepted: 10/02/2019] [Indexed: 06/10/2023]
Abstract
In electric power systems delivering alternating current, it is essential to maintain its synchrony of the phase with the rated frequency. The synchronization stability that quantifies how well the power-grid system recovers its synchrony against perturbation depends on various factors. As an intrinsic factor that we can design and control, the transmission capacity of the power grid affects the synchronization stability. Therefore, the transition pattern of the synchronization stability with the different levels of transmission capacity against external perturbation provides the stereoscopic perspective to understand the synchronization behavior of power grids. In this study, we extensively investigate the factors affecting the synchronization stability transition by using the concept of basin stability as a function of the transmission capacity. For a systematic approach, we introduce the integrated basin instability, which literally adds up the instability values as the transmission capacity increases. We first take simple 5-node motifs as a case study of building blocks of power grids, and a more realistic IEEE 24-bus model to highlight the complexity of decisive factors. We find that both structural properties such as gate keepers in network topology and dynamical properties such as large power input/output at nodes cause synchronization instability. The results suggest that evenly distributed power generation and avoidance of bottlenecks can improve the overall synchronization stability of power-grid systems.
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Affiliation(s)
- Heetae Kim
- Department of Industrial Engineering, Universidad de Talca, Curicó 3341717, Chile
| | - Mi Jin Lee
- Department of Physics, Inha University, Incheon 22212, South Korea
| | - Sang Hoon Lee
- Department of Liberal Arts, Gyeongnam National University of Science and Technology, Jinju 52725, South Korea
| | - Seung-Woo Son
- Asia Pacific Center for Theoretical Physics, Pohang 37673, South Korea
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Tishby I, Biham O, Katzav E. Convergence towards an Erdős-Rényi graph structure in network contraction processes. Phys Rev E 2019; 100:032314. [PMID: 31640068 DOI: 10.1103/physreve.100.032314] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/08/2019] [Indexed: 11/07/2022]
Abstract
In a highly influential paper twenty years ago, Barabási and Albert [Science 286, 509 (1999)SCIEAS0036-807510.1126/science.286.5439.509] showed that networks undergoing generic growth processes with preferential attachment evolve towards scale-free structures. In any finite system, the growth eventually stalls and is likely to be followed by a phase of network contraction due to node failures, attacks, or epidemics. Using the master equation formulation and computer simulations, we analyze the structural evolution of networks subjected to contraction processes via random, preferential, and propagating node deletions. We show that the contracting networks converge towards an Erdős-Rényi network structure whose mean degree continues to decrease as the contraction proceeds. This is manifested by the convergence of the degree distribution towards a Poisson distribution and the loss of degree-degree correlations.
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Affiliation(s)
- Ido Tishby
- Racah Institute of Physics, The Hebrew University, Jerusalem 91904, Israel
| | - Ofer Biham
- Racah Institute of Physics, The Hebrew University, Jerusalem 91904, Israel
| | - Eytan Katzav
- Racah Institute of Physics, The Hebrew University, Jerusalem 91904, Israel
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Schäfer B, Yalcin GC. Dynamical modeling of cascading failures in the Turkish power grid. CHAOS (WOODBURY, N.Y.) 2019; 29:093134. [PMID: 31575158 DOI: 10.1063/1.5110974] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/22/2019] [Accepted: 09/11/2019] [Indexed: 06/10/2023]
Abstract
A reliable supply of electricity is critical for our modern society, and any large-scale disturbance of the electrical system causes substantial costs. In 2015, one overloaded transmission line caused a cascading failure in the Turkish power grid, affecting about 75×106 people. Here, we analyze the Turkish power grid and its dynamical and statistical properties. Specifically, we propose, for the first time, a model that incorporates the dynamical properties and the complex network topology of the Turkish power grid to investigate cascading failures. We find that the network damage depends on the load and generation distribution in the network with centralized generation being more susceptible to failures than a decentralized one. Furthermore, economic considerations on transmission line capacity are shown to conflict with stability.
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Affiliation(s)
- Benjamin Schäfer
- School of Mathematical Sciences, Queen Mary University of London, London E1 4NS, United Kingdom
| | - G Cigdem Yalcin
- Department of Physics, Istanbul University, Vezneciler, 34134 Istanbul, Turkey
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Hassanibesheli F, Donner RV. Network inference from the timing of events in coupled dynamical systems. CHAOS (WOODBURY, N.Y.) 2019; 29:083125. [PMID: 31472517 DOI: 10.1063/1.5110881] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/21/2019] [Accepted: 08/09/2019] [Indexed: 06/10/2023]
Abstract
Spreading phenomena like opinion formation or disease propagation often follow the links of some underlying network structure. While the effects of network topology on spreading efficiency have already been vastly studied, we here address the inverse problem of whether we can infer an unknown network structure from the timing of events observed at different nodes. For this purpose, we numerically investigate two types of event-based stochastic processes. On the one hand, a generic model of event propagation on networks is considered where the nodes exhibit two types of eventlike activity: spontaneous events reflecting mutually independent Poisson processes and triggered events that occur with a certain probability whenever one of the neighboring nodes exhibits any of these two kinds of events. On the other hand, we study a variant of the well-known SIRS model from epidemiology and record only the timings of state switching events of individual nodes, irrespective of the specific states involved. Based on simulations of both models on different prototypical network architectures, we study the pairwise statistical similarity between the sequences of event timings at all nodes by means of event synchronization and event coincidence analysis (ECA). By taking strong mutual similarities of event sequences (functional connectivity) as proxies for actual physical links (structural connectivity), we demonstrate that both approaches can lead to reasonable prediction accuracy. In general, sparser networks can be reconstructed more accurately than denser ones, especially in the case of larger networks. In such cases, ECA is shown to commonly exhibit the better reconstruction accuracy.
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Affiliation(s)
- Forough Hassanibesheli
- Research Domain IV-Complexity Science, Potsdam Institute for Climate Impact Research-Member of the Leibniz Society, Telegrafenberg A31, 14473 Potsdam, Germany
| | - Reik V Donner
- Research Domain IV-Complexity Science, Potsdam Institute for Climate Impact Research-Member of the Leibniz Society, Telegrafenberg A31, 14473 Potsdam, Germany
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