IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v131y2017icp157-171.html
   My bibliography  Save this article

Approximation of the frequency response of power systems based on scale invariance

Author

Listed:
  • Le, Thi-Tinh-Minh
  • Retiere, Nicolas

Abstract

Power networks are complex systems composed of many heterogeneous and interacting components. Smart grids are even more complex systems due to the convergence of electrical and communication networks. In order to deal with this complexity, a mathematical model that is reduced-size, accurate, wide-band and knowledge based is required for dynamic studies. This paper introduces a novel modeling approach based on scale invariance to build an approximation of the frequency response of power systems. This approach combines an asymptotic and a resonant model. Both use the spectral dimension of the network which is a key parameter to describe its scale invariance. The resonant model is identified by using an improved vector fitting method. The improvement consists in a guess of the initial poles used for the identification which is deduced from the scale invariant distribution of the dynamic modes of the network. An application to an IEEE test transmission system is finally shown.

Suggested Citation

  • Le, Thi-Tinh-Minh & Retiere, Nicolas, 2017. "Approximation of the frequency response of power systems based on scale invariance," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 131(C), pages 157-171.
  • Handle: RePEc:eee:matcom:v:131:y:2017:i:c:p:157-171
    DOI: 10.1016/j.matcom.2015.08.015
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475415001809
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.matcom.2015.08.015?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Stanley, H.E & Amaral, L.A.N & Gopikrishnan, P & Ivanov, P.Ch & Keitt, T.H & Plerou, V, 2000. "Scale invariance and universality: organizing principles in complex systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 281(1), pages 60-68.
    2. Chaoming Song & Shlomo Havlin & Hernán A. Makse, 2005. "Self-similarity of complex networks," Nature, Nature, vol. 433(7024), pages 392-395, January.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Yao, Jialing & Sun, Bingbin & Xi, lifeng, 2019. "Fractality of evolving self-similar networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 515(C), pages 211-216.
    2. Duan, Shuyu & Wen, Tao & Jiang, Wen, 2019. "A new information dimension of complex network based on Rényi entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 516(C), pages 529-542.
    3. Ikeda, Nobutoshi, 2020. "Fractal networks induced by movements of random walkers on a tree graph," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 537(C).
    4. Sun, Bingbin & Yao, Jialing & Xi, Lifeng, 2019. "Eigentime identities of fractal sailboat networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 520(C), pages 338-349.
    5. Lu, Qing-Chang & Xu, Peng-Cheng & Zhao, Xiangmo & Zhang, Lei & Li, Xiaoling & Cui, Xin, 2022. "Measuring network interdependency between dependent networks: A supply-demand-based approach," Reliability Engineering and System Safety, Elsevier, vol. 225(C).
    6. Lambiotte, R. & Panzarasa, P., 2009. "Communities, knowledge creation, and information diffusion," Journal of Informetrics, Elsevier, vol. 3(3), pages 180-190.
    7. Zhang, Qi & Luo, Chuanhai & Li, Meizhu & Deng, Yong & Mahadevan, Sankaran, 2015. "Tsallis information dimension of complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 419(C), pages 707-717.
    8. Aldrich, Preston R. & El-Zabet, Jermeen & Hassan, Seerat & Briguglio, Joseph & Aliaj, Enela & Radcliffe, Maria & Mirza, Taha & Comar, Timothy & Nadolski, Jeremy & Huebner, Cynthia D., 2015. "Monte Carlo tests of small-world architecture for coarse-grained networks of the United States railroad and highway transportation systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 438(C), pages 32-39.
    9. Retière, N. & Sidqi, Y. & Frankhauser, P., 2022. "A steady-state analysis of distribution networks by diffusion-limited-aggregation and multifractal geometry," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 600(C).
    10. Xi, Lifeng & Wang, Lihong & Wang, Songjing & Yu, Zhouyu & Wang, Qin, 2017. "Fractality and scale-free effect of a class of self-similar networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 478(C), pages 31-40.
    11. Meng, Xiangyi & Zhou, Bin, 2023. "Scale-free networks beyond power-law degree distribution," Chaos, Solitons & Fractals, Elsevier, vol. 176(C).
    12. Yin, Likang & Deng, Yong, 2018. "Measuring transferring similarity via local information," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 498(C), pages 102-115.
    13. Fan Xu & Zeng Zhou & Sergio Fagherazzi & Andrea D’Alpaos & Ian Townend & Kun Zhao & Weiming Xie & Leicheng Guo & Xianye Wang & Zhong Peng & Zhicheng Yang & Chunpeng Chen & Guangcheng Cheng & Yuan Xu &, 2024. "Anomalous scaling of branching tidal networks in global coastal wetlands and mudflats," Nature Communications, Nature, vol. 15(1), pages 1-11, December.
    14. Rosenberg, Eric, 2018. "Generalized Hausdorff dimensions of a complex network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 511(C), pages 1-17.
    15. Xuezai Pan & Xudong Shang, 2022. "The Uniform Convergence Property of Sequence of Fractal Interpolation Functions in Complicated Networks," Mathematics, MDPI, vol. 10(20), pages 1-8, October.
    16. Ou, Ruiqiu & Yang, Jianmei, 2012. "On structural properties of scale-free networks with finite size," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(3), pages 887-894.
    17. Li, Jun-fang & Zhang, Bu-han & Liu, Yi-fang & Wang, Kui & Wu, Xiao-shan, 2012. "Spatial evolution character of multi-objective evolutionary algorithm based on self-organized criticality theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(22), pages 5490-5499.
    18. Li, Meizhu & Zhang, Qi & Deng, Yong, 2018. "Evidential identification of influential nodes in network of networks," Chaos, Solitons & Fractals, Elsevier, vol. 117(C), pages 283-296.
    19. Winkelmann, Ricarda & Donges, Jonathan F. & Smith, E. Keith & Milkoreit, Manjana & Eder, Christina & Heitzig, Jobst & Katsanidou, Alexia & Wiedermann, Marc & Wunderling, Nico & Lenton, Timothy M., 2022. "Social tipping processes towards climate action: A conceptual framework," Ecological Economics, Elsevier, vol. 192(C).
    20. Le, Anbo & Gao, Fei & Xi, Lifeng & Yin, Shuhua, 2015. "Complex networks modeled on the Sierpinski gasket," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 436(C), pages 646-657.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:matcom:v:131:y:2017:i:c:p:157-171. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.