IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v188y2024ics0960077924010634.html
   My bibliography  Save this article

Explicit formulas for the asymptotic variance of a linearized model of a Gaussian disturbance driven power system with a uniform damping-inertia ratio

Author

Listed:
  • Wu, Xian
  • Xi, Kaihua
  • Cheng, Aijie
  • Lin, Hai Xiang
  • van Schuppen, Jan H.
  • Zhang, Chenghui

Abstract

Serious fluctuations caused by disturbances may lead to instability of power systems. With the disturbance modeled by a Brownian motion process, the fluctuations are often described by the asymptotic variance at the invariant probability distribution of an associated Gaussian stochastic process. Here, we derive the explicit formula of the variance matrix for the system with a uniform damping-inertia ratio at all the nodes, which enables us to analyze the influences of the system parameters on the fluctuations and investigate the fluctuation propagation in the network. With application to systems with complete graphs and star graphs, it is found that the variance of the frequency at the disturbed node is significantly bigger than those at all the other nodes. It is also shown that adding new nodes may prevent the propagation of fluctuations from the disturbed node to all the others. Finally, it is proven theoretically that larger line capacities accelerate the propagation of the frequency fluctuation and larger inertia of synchronous machines help suppress the fluctuations of the phase differences, however, these acceleration and suppression are quite limited.

Suggested Citation

  • Wu, Xian & Xi, Kaihua & Cheng, Aijie & Lin, Hai Xiang & van Schuppen, Jan H. & Zhang, Chenghui, 2024. "Explicit formulas for the asymptotic variance of a linearized model of a Gaussian disturbance driven power system with a uniform damping-inertia ratio," Chaos, Solitons & Fractals, Elsevier, vol. 188(C).
    • Handle: RePEc:eee:chsofr:v:188:y:2024:i:c:s0960077924010634
    DOI: 10.1016/j.chaos.2024.115511
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077924010634
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2024.115511?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. Peter J. Menck & Jobst Heitzig & Jürgen Kurths & Hans Joachim Schellnhuber, 2014. "How dead ends undermine power grid stability," Nature Communications, Nature, vol. 5(1), pages 1-8, September.
    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. Arinushkin, P.A. & Vadivasova, T.E., 2021. "Nonlinear damping effects in a simplified power grid model based on coupled Kuramoto-like oscillators with inertia," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    2. Acotto, Francesca & Venturino, Ezio & Viscardi, Alberto, 2024. "Does a marginal contact with a native species living in a complex domain with a fractional dimension boundary represent a sufficient invasive mechanism for the establishment of a migrating population?," Chaos, Solitons & Fractals, Elsevier, vol. 184(C).
    3. Rybalova, E. & Averyanov, V. & Lozi, R. & Strelkova, G., 2024. "Peculiarities of the spatio-temporal dynamics of a Hénon–Lozi map network in the presence of Lévy noise," Chaos, Solitons & Fractals, Elsevier, vol. 184(C).
    4. Shepelev, I.A. & Bukh, A.V. & Strelkova, G.I., 2022. "Anti-phase synchronization of waves in a multiplex network of van der Pol oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    5. Ye, Jiachen & Ji, Peng & Waxman, David & Lin, Wei & Moreno, Yamir, 2020. "Impact of intra and inter-cluster coupling balance on the performance of nonlinear networked systems," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    6. Khramenkov, Vladislav & Dmitrichev, Aleksei & Nekorkin, Vladimir, 2021. "Partial stability criterion for a heterogeneous power grid with hub structures," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    7. Biswas, Debabrata & Mandal, Tapas & Banerjee, Tanmoy, 2024. "Transition among oscillation death, amplitude death, and revival of oscillation in coupled time-delayed systems with diffusivity and common environment," Chaos, Solitons & Fractals, Elsevier, vol. 188(C).
    8. Zhang, Ding-Xue & Zhao, Dan & Guan, Zhi-Hong & Wu, Yonghong & Chi, Ming & Zheng, Gui-Lin, 2016. "Probabilistic analysis of cascade failure dynamics in complex network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 461(C), pages 299-309.
    9. Xiaoge Bao & Qitong Hu & Peng Ji & Wei Lin & Jürgen Kurths & Jan Nagler, 2022. "Impact of basic network motifs on the collective response to perturbations," Nature Communications, Nature, vol. 13(1), pages 1-8, December.
    10. Rybalova, E.V. & Zakharova, A. & Strelkova, G.I., 2021. "Interplay between solitary states and chimeras in multiplex neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 148(C).
    11. Rybalova, E.V. & Strelkova, G.I. & Anishchenko, V.S., 2021. "Impact of sparse inter-layer coupling on the dynamics of a heterogeneous multilayer network of chaotic maps," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    12. Wei, Mengke & Han, Xiujing, 2024. "Fast–slow dynamics related to sharp transition behaviors in the Rayleigh oscillator with two slow square wave excitations," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    13. Ferré, M.A., 2023. "Critical visit to the chimera world," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    14. Lee, Yongsun & Choi, Hoyun & Pagnier, Laurent & Kim, Cook Hyun & Lee, Jongshin & Jhun, Bukyoung & Kim, Heetae & Kurths, Jürgen & Kahng, B., 2024. "Reinforcement learning optimizes power dispatch in decentralized power grid," Chaos, Solitons & Fractals, Elsevier, vol. 186(C).
    15. Lacerda, Juliana C. & Freitas, Celso & Macau, Elbert E.N., 2022. "Elementary changes in topology and power transmission capacity can induce failures in power grids," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 590(C).
    16. Li, Fan & Liu, Shuai & Li, Xiaola, 2023. "Effect of phase shift on the dynamics of a single-machine infinite-bus power system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 616(C).

    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:chsofr:v:188:y:2024:i:c:s0960077924010634. 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: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    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.