1
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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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2
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Büttner A, Plietzsch A, Anvari M, Hellmann F. A framework for synthetic power system dynamics. CHAOS (WOODBURY, N.Y.) 2023; 33:083120. [PMID: 37549123 DOI: 10.1063/5.0155971] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/25/2023] [Accepted: 07/17/2023] [Indexed: 08/09/2023]
Abstract
We present a modular framework for generating synthetic power grids that consider the heterogeneity of real power grid dynamics but remain simple and tractable. This enables the generation of large sets of synthetic grids for a wide range of applications. For the first time, our synthetic model also includes the major drivers of fluctuations on short-time scales and a set of validators that ensure the resulting system dynamics are plausible. The synthetic grids generated are robust and show good synchronization under all evaluated scenarios, as should be expected for realistic power grids. A software package that includes an efficient Julia implementation of the framework is released as a companion to the paper.
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Affiliation(s)
- Anna Büttner
- Potsdam-Institute for Climate Impact Research, 14473 Potsdam, Germany
| | - Anton Plietzsch
- Potsdam-Institute for Climate Impact Research, 14473 Potsdam, Germany
- Fraunhofer Research Institution for Energy Infrastructures and Geothermal Systems, 03046 Cottbus, Germany
| | - Mehrnaz Anvari
- Potsdam-Institute for Climate Impact Research, 14473 Potsdam, Germany
- Fraunhofer Institute for Algorithms and Scientific Computing, 53757 Sankt Augustin, Germany
| | - Frank Hellmann
- Potsdam-Institute for Climate Impact Research, 14473 Potsdam, Germany
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3
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Qing X, He W, Zhou M, Du W. Quantifying fluctuations for dynamical power systems with stochastic excitations: A power spectral density-based method. CHAOS (WOODBURY, N.Y.) 2023; 33:2890946. [PMID: 37192392 DOI: 10.1063/5.0147018] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/18/2023] [Accepted: 04/25/2023] [Indexed: 05/18/2023]
Abstract
Fluctuations of state variables play a pivotal role in analyzing small signal stability of the power system due to the integration of renewable energy sources. This paper develops a theoretical analysis methodology by using the power spectral density (PSD) for capturing the frequency and amplitude of state variable fluctuations in heterogeneous power systems with stochastic excitations. The fluctuations in generation and consumption occurring simultaneously are modeled by stochastic Ornstein-Uhlenbeck processes. The PSDs of the state variable fluctuations can be analytically calculated. PSD-based quantities have been proposed to evaluate angle and frequency deviations. Moreover, a global performance metric has been presented to measure the synchronization stability and calculated using the PSDs of frequency deviations. The underlying mathematical relationship between the metric and the primary control effort mimicking the H2-norm performance is explained in detail. Finally, the proposed analysis methodology is numerically illustrated on the IEEE RTS-96 test case. We investigate the impact of auto-correlations of stochastic processes on stability. Our results show the metric can be an alternative quantitative index of stability. We further find that the inertia allocation does not provide significant grid stability gain under small stochastic power fluctuations.
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Affiliation(s)
- Xiangyun Qing
- Key Laboratory of Smart Manufacturing in Energy Chemical Process, Ministry of Education, East China University of Science and Technology, Shanghai 200237, China
| | - Wangli He
- Key Laboratory of Smart Manufacturing in Energy Chemical Process, Ministry of Education, East China University of Science and Technology, Shanghai 200237, China
| | - Min Zhou
- Key Laboratory of Smart Manufacturing in Energy Chemical Process, Ministry of Education, East China University of Science and Technology, Shanghai 200237, China
| | - Wenli Du
- Key Laboratory of Smart Manufacturing in Energy Chemical Process, Ministry of Education, East China University of Science and Technology, Shanghai 200237, China
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4
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Molnar S, Bradley E, Gruchalla K. Oscillatory spreading and inertia in power grids. CHAOS (WOODBURY, N.Y.) 2021; 31:123103. [PMID: 34972338 DOI: 10.1063/5.0065854] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/05/2021] [Accepted: 11/08/2021] [Indexed: 06/14/2023]
Abstract
The increase in variable renewable generators (VRGs) in power systems has altered the dynamics from a historical experience. VRGs introduce new sources of power oscillations, and the stabilizing response provided by synchronous generators (SGs, e.g., natural gas, coal, etc.), which help avoid some power fluctuations, will lessen as VRGs replace SGs. These changes have led to the need for new methods and metrics to quickly assess the likely oscillatory behavior for a particular network without performing computationally expensive simulations. This work studies the impact of a critical dynamical parameter-the inertia value-on the rest of a power system's oscillatory response to representative VRG perturbations. We use a known localization metric in a novel way to quantify the number of nodes responding to a perturbation and the magnitude of those responses. This metric allows us to relate the spread and severity of a system's power oscillations with inertia. We find that as inertia increases, the system response to node perturbations transitions from localized (only a few close nodes respond) to delocalized (many nodes across the network respond). We introduce a heuristic computed from the network Laplacian to relate this oscillatory transition to the network structure. We show that our heuristic accurately describes the spread of oscillations for a realistic power-system test case. Using a heuristic to determine the likely oscillatory behavior of a system given a set of parameters has wide applicability in power systems, and it could decrease the computational workload of planning and operation.
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Affiliation(s)
- Samantha Molnar
- Computer Science Department, University of Colorado Boulder, Boulder, Colorado 80309, USA
| | - Elizabeth Bradley
- Computer Science Department, University of Colorado Boulder, Boulder, Colorado 80309, USA
| | - Kenny Gruchalla
- Computational Science Center, National Renewable Energy Lab, Golden, Colorado 80401, USA
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5
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Stability analysis of T–S fuzzy coupled oscillator systems influenced by stochastic disturbance. Neural Comput Appl 2020. [DOI: 10.1007/s00521-020-05116-x] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
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6
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Anvari M, Hellmann F, Zhang X. Introduction to Focus Issue: Dynamics of modern power grids. CHAOS (WOODBURY, N.Y.) 2020; 30:063140. [PMID: 32611078 DOI: 10.1063/5.0016372] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/03/2020] [Accepted: 06/03/2020] [Indexed: 06/11/2023]
Affiliation(s)
- Mehrnaz Anvari
- Research Department 4 Complexity Science, Potsdam Institute for Climate Impact Research, Telegraphenberg A 31, 14473 Potsdam, Brandenburg, Germany
| | - Frank Hellmann
- Research Department 4 Complexity Science, Potsdam Institute for Climate Impact Research, Telegraphenberg A 31, 14473 Potsdam, Brandenburg, Germany
| | - Xiaozhu Zhang
- Chair for Network Dynamics, Institute for Theoretical Physics and Center for Advancing Electronics Dresden (cfaed), Cluster of Excellence Physics of Life, Technical University of Dresden, 01062 Dresden, Germany
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7
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Strenge L, Schultz P, Kurths J, Raisch J, Hellmann F. A multiplex, multi-timescale model approach for economic and frequency control in power grids. CHAOS (WOODBURY, N.Y.) 2020; 30:033138. [PMID: 32237782 DOI: 10.1063/1.5132335] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/18/2019] [Accepted: 03/12/2020] [Indexed: 06/11/2023]
Abstract
Power systems are subject to fundamental changes due to the increasing infeed of decentralized renewable energy sources and storage. The decentralized nature of the new actors in the system requires new concepts for structuring the power grid and achieving a wide range of control tasks ranging from seconds to days. Here, we introduce a multiplex dynamical network model covering all control timescales. Crucially, we combine a decentralized, self-organized low-level control and a smart grid layer of devices that can aggregate information from remote sources. The safety-critical task of frequency control is performed by the former and the economic objective of demand matching dispatch by the latter. Having both aspects present in the same model allows us to study the interaction between the layers. Remarkably, we find that adding communication in the form of aggregation does not improve the performance in the cases considered. Instead, the self-organized state of the system already contains the information required to learn the demand structure in the entire grid. The model introduced here is highly flexible and can accommodate a wide range of scenarios relevant to future power grids. We expect that it is especially useful in the context of low-energy microgrids with distributed generation.
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Affiliation(s)
- Lia Strenge
- Control Systems Group at Technische Universität Berlin, Einsteinufer 17, 10587 Berlin, Germany
| | - Paul Schultz
- Research Department 4 Complexity Science, Potsdam Institute for Climate Impact Research, Telegraphenberg A 31, 14473 Potsdam, Brandenburg, Germany
| | - Jürgen Kurths
- Research Department 4 Complexity Science, Potsdam Institute for Climate Impact Research, Telegraphenberg A 31, 14473 Potsdam, Brandenburg, Germany
| | - Jörg Raisch
- Control Systems Group at Technische Universität Berlin, Einsteinufer 17, 10587 Berlin, Germany
| | - Frank Hellmann
- Research Department 4 Complexity Science, Potsdam Institute for Climate Impact Research, Telegraphenberg A 31, 14473 Potsdam, Brandenburg, Germany
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8
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Wienand JF, Eidmann D, Kremers J, Heitzig J, Hellmann F, Kurths J. Impact of network topology on the stability of DC microgrids. CHAOS (WOODBURY, N.Y.) 2019; 29:113109. [PMID: 31779358 DOI: 10.1063/1.5110348] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/16/2019] [Accepted: 10/13/2019] [Indexed: 06/10/2023]
Abstract
We probe the stability of Watts-Strogatz DC microgrids, in which droop-controlled producers and constant power load consumers are homogeneously distributed and obey Kirchhoff's circuit laws. The concept of survivability is employed to evaluate the system's response to Dirac-delta voltage perturbations at single nodes. A fixed point analysis of the power grid model yields that there is only one relevant attractor. Using a set of simulations with random networks, we investigate correlations between survivability and three topological network measures: the share of producers in the network and the degree and the average neighbor degree of the perturbed node. Depending on the imposed voltage and current limits, the stability is optimized for low node degrees or a specific share of producers. Based on our findings, we provide an insight into the local dynamics of the perturbed system and derive explicit guidelines for the design of resilient DC power grids.
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Affiliation(s)
- J F Wienand
- Faculty of Physics, Ludwig-Maximilians-Universität München, Schellingstraße 4, 80799 Munich, Germany
| | - D Eidmann
- Department of Civil and Environmental Engineering Sciences, Technische Universität Darmstadt, Karolinenplatz 5, 64283 Darmstadt, Germany
| | - J Kremers
- Laboratory of Geo-information Science and Remote Sensing, Wageningen University and Research, Droevendaalsesteeg 3, 6708PB Wageningen, The Netherlands
| | - J Heitzig
- Potsdam Institute for Climate Impact Research, PO Box 60 12 03, Potsdam 14412, Germany
| | - F Hellmann
- Potsdam Institute for Climate Impact Research, PO Box 60 12 03, Potsdam 14412, Germany
| | - J Kurths
- Potsdam Institute for Climate Impact Research, PO Box 60 12 03, Potsdam 14412, Germany
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9
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Peron T, Messias F de Resende B, Mata AS, Rodrigues FA, Moreno Y. Onset of synchronization of Kuramoto oscillators in scale-free networks. Phys Rev E 2019; 100:042302. [PMID: 31770973 DOI: 10.1103/physreve.100.042302] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/10/2019] [Indexed: 06/10/2023]
Abstract
Despite the great attention devoted to the study of phase oscillators on complex networks in the last two decades, it remains unclear whether scale-free networks exhibit a nonzero critical coupling strength for the onset of synchronization in the thermodynamic limit. Here, we systematically compare predictions from the heterogeneous degree mean-field (HMF) and the quenched mean-field (QMF) approaches to extensive numerical simulations on large networks. We provide compelling evidence that the critical coupling vanishes as the number of oscillators increases for scale-free networks characterized by a power-law degree distribution with an exponent 2<γ≤3, in line with what has been observed for other dynamical processes in such networks. For γ>3, we show that the critical coupling remains finite, in agreement with HMF calculations and highlight phenomenological differences between critical properties of phase oscillators and epidemic models on scale-free networks. Finally, we also discuss at length a key choice when studying synchronization phenomena in complex networks, namely, how to normalize the coupling between oscillators.
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Affiliation(s)
- Thomas Peron
- Institute of Mathematics and Computer Science, University of São Paulo, São Carlos, São Paulo 13566-590, Brazil
- Institute for Biocomputation and Physics of Complex Systems (BIFI), University of Zaragoza, E-Zaragoza 50018, Spain
| | | | - Angélica S Mata
- Departamento de Física, Universidade Federal de Lavras, 37200-000 Lavras, Minas Gerais, Brazil
| | - Francisco A Rodrigues
- Institute of Mathematics and Computer Science, University of São Paulo, São Carlos, São Paulo 13566-590, Brazil
| | - Yamir Moreno
- Institute for Biocomputation and Physics of Complex Systems (BIFI), University of Zaragoza, E-Zaragoza 50018, Spain
- Department of Theoretical Physics, University of Zaragoza, E-Zaragoza 50009, Spain
- ISI Foundation, I-10126 Torino, Italy
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10
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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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11
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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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12
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Schmietendorf K, Kamps O, Wolff M, Lind PG, Maass P, Peinke J. Bridging between load-flow and Kuramoto-like power grid models: A flexible approach to integrating electrical storage units. CHAOS (WOODBURY, N.Y.) 2019; 29:103151. [PMID: 31675812 DOI: 10.1063/1.5099241] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/08/2019] [Accepted: 08/16/2019] [Indexed: 06/10/2023]
Abstract
In future power systems, electrical storage will be the key technology for balancing feed-in fluctuations. With increasing share of renewables and reduction of system inertia, the focus of research expands toward short-term grid dynamics and collective phenomena. Against this backdrop, Kuramoto-like power grids have been established as a sound mathematical modeling framework bridging between the simplified models from nonlinear dynamics and the more detailed models used in electrical engineering. However, they have a blind spot concerning grid components, which cannot be modeled by oscillator equations, and hence do not allow one to investigate storage-related issues from scratch. Our aim here is twofold: First, we remove this shortcoming by adopting a standard practice in electrical engineering and bring together Kuramoto-like and algebraic load-flow equations. This is a substantial extension of the current Kuramoto-like framework with arbitrary grid components. Second, we use this concept and demonstrate the implementation of a storage unit in a wind power application with realistic feed-in conditions. We show how to implement basic control strategies from electrical engineering, give insights into their potential with respect to frequency quality improvement, and point out their limitations by maximum capacity and finite-time response. With that, we provide a solid starting point for the integration of flexible storage units into Kuramoto-like grid models enabling to address current problems like smart storage control, optimal siting, and rough cost estimations.
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Affiliation(s)
- Katrin Schmietendorf
- ForWind and Institut für Physik, Universität Oldenburg, Küpkersweg 70, 26129 Oldenburg, Germany
| | - O Kamps
- Center for Nonlinear Science, Universität Münster, Correnstraße 2, 48149 Münster, Germany
| | - M Wolff
- Fachbereich Physik, Universität Osnabrück, Barbarastraße 7, 49076 Osnabrück, Germany
| | - P G Lind
- Department of Computer Science, Oslo Metropolitan University, P.O. Box 4 St. Olavs plass, N-0130 Oslo, Norway
| | - P Maass
- Fachbereich Physik, Universität Osnabrück, Barbarastraße 7, 49076 Osnabrück, Germany
| | - J Peinke
- ForWind and Institut für Physik, Universität Oldenburg, Küpkersweg 70, 26129 Oldenburg, Germany
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13
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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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14
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Zhang X, Hallerberg S, Matthiae M, Witthaut D, Timme M. Fluctuation-induced distributed resonances in oscillatory networks. SCIENCE ADVANCES 2019; 5:eaav1027. [PMID: 31392264 PMCID: PMC6669019 DOI: 10.1126/sciadv.aav1027] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 08/15/2018] [Accepted: 06/24/2019] [Indexed: 06/10/2023]
Abstract
Across physics, biology, and engineering, the collective dynamics of oscillatory networks often evolve into self-organized operating states. How such networks respond to external fluctuating signals fundamentally underlies their function, yet is not well understood. Here, we present a theory of dynamic network response patterns and reveal how distributed resonance patterns emerge in oscillatory networks once the dynamics of the oscillatory units become more than one-dimensional. The network resonances are topology specific and emerge at an intermediate frequency content of the input signals, between global yet homogeneous responses at low frequencies and localized responses at high frequencies. Our analysis reveals why these patterns arise and where in the network they are most prominent. These results may thus provide general theoretical insights into how fluctuating signals induce response patterns in networked systems and simultaneously help to develop practical guiding principles for real-world network design and control.
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Affiliation(s)
- Xiaozhu Zhang
- Chair for Network Dynamics, Institute for Theoretical Physics and Center for Advancing Electronics Dresden (cfaed), Technical University of Dresden, 01062 Dresden, Germany
| | - Sarah Hallerberg
- Faculty for Engineering and Computer Science, Hamburg University of Applied Science, 20099 Hamburg, Germany
| | - Moritz Matthiae
- Institute for Energy and Climate Research–Systems Analysis and Technology Evaluation (IEK-STE), Forschungszentrum Jülich GmbH, 52425 Jülich, Germany
| | - Dirk Witthaut
- Institute for Energy and Climate Research–Systems Analysis and Technology Evaluation (IEK-STE), Forschungszentrum Jülich GmbH, 52425 Jülich, Germany
- Institute for Theoretical Physics, University of Cologne, 50923 Köln, Germany
| | - Marc Timme
- Chair for Network Dynamics, Institute for Theoretical Physics and Center for Advancing Electronics Dresden (cfaed), Technical University of Dresden, 01062 Dresden, Germany
- Department of Physics, Technical University of Darmstadt, 64289 Darmstadt, Germany
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