IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v7y2019i1p106-d199307.html
   My bibliography  Save this article

Calculating Nodal Voltages Using the Admittance Matrix Spectrum of an Electrical Network

Author

Listed:
  • Ioannis Dassios

    (School of Electrical and Electronic Engineering, University College Dublin, Dublin 4, Ireland)

  • Andrew Keane

    (School of Electrical and Electronic Engineering, University College Dublin, Dublin 4, Ireland)

  • Paul Cuffe

    (School of Electrical and Electronic Engineering, University College Dublin, Dublin 4, Ireland)

Abstract

Calculating nodal voltages and branch current flows in a meshed network is fundamental to electrical engineering. This work demonstrates how such calculations can be performed using the eigenvalues and eigenvectors of the Laplacian matrix which describes the connectivity of the electrical network. These insights should permit the functioning of electrical networks to be understood in the context of spectral analysis.

Suggested Citation

  • Ioannis Dassios & Andrew Keane & Paul Cuffe, 2019. "Calculating Nodal Voltages Using the Admittance Matrix Spectrum of an Electrical Network," Mathematics, MDPI, vol. 7(1), pages 1-6, January.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:1:p:106-:d:199307
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/7/1/106/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/7/1/106/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Pagani, Giuliano Andrea & Aiello, Marco, 2013. "The Power Grid as a complex network: A survey," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(11), pages 2688-2700.
    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. Lu Pang & Cheng Hu & Juan Yu & Haijun Jiang, 2022. "Fixed-Time Synchronization for Fuzzy-Based Impulsive Complex Networks," Mathematics, MDPI, vol. 10(9), pages 1-16, May.
    2. Gianluca Fulli & Marcelo Masera & Catalin Felix Covrig & Francesco Profumo & Ettore Bompard & Tao Huang, 2017. "The EU Electricity Security Decision-Analytic Framework: Status and Perspective Developments," Energies, MDPI, vol. 10(4), pages 1-20, March.
    3. Ma, Li & Wang, Lingfeng & Liu, Zhaoxi, 2021. "Multi-level trading community formation and hybrid trading network construction in local energy market," Applied Energy, Elsevier, vol. 285(C).
    4. Claudio M. Rocco & Kash Barker & Jose Moronta, 2022. "Determining the best algorithm to detect community structures in networks: application to power systems," Environment Systems and Decisions, Springer, vol. 42(2), pages 251-264, June.
    5. Gangwal, Utkarsh & Singh, Mayank & Pandey, Pradumn Kumar & Kamboj, Deepak & Chatterjee, Samrat & Bhatia, Udit, 2022. "Identifying early-warning indicators of onset of sudden collapse in networked infrastructure systems against sequential disruptions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 591(C).
    6. Goddet, Etienne & Retière, Nicolas & Stojanović, Vojislav & Dieudonné, Anca & Genoulaz, Jérôme & Guichon, Jean-Michel, 2019. "Maximizing the algebraic connectivity of meshed electrical pathways used as current return network," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 158(C), pages 18-31.
    7. Ram, J.S. & Muni, S.S. & Shepelev, I.A., 2024. "Spatiotemporal patterns in a 2D lattice of Hindmarsh–Rose neurons induced by high-amplitude pulses," Chaos, Solitons & Fractals, Elsevier, vol. 189(P1).
    8. Xiao, Guanping & Zheng, Zheng & Wang, Haoqin, 2017. "Evolution of Linux operating system network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 466(C), pages 249-258.
    9. Espejo, Rafael & Lumbreras, Sara & Ramos, Andres, 2018. "Analysis of transmission-power-grid topology and scalability, the European case study," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 509(C), pages 383-395.
    10. Hu, Jianqiang & Yu, Jie & Cao, Jinde & Ni, Ming & Yu, Wenjie, 2014. "Topological interactive analysis of power system and its communication module: A complex network approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 416(C), pages 99-111.
    11. Kashyap, G. & Ambika, G., 2019. "Link deletion in directed complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 514(C), pages 631-643.
    12. Kashin Sugishita & Yasuo Asakura, 2021. "Vulnerability studies in the fields of transportation and complex networks: a citation network analysis," Public Transport, Springer, vol. 13(1), pages 1-34, March.
    13. Rocchetta, Roberto, 2022. "Enhancing the resilience of critical infrastructures: Statistical analysis of power grid spectral clustering and post-contingency vulnerability metrics," Renewable and Sustainable Energy Reviews, Elsevier, vol. 159(C).
    14. Pagani, Giuliano Andrea & Aiello, Marco, 2016. "From the grid to the smart grid, topologically," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 449(C), pages 160-175.
    15. Wu, Chengxing & Duan, Dongli, 2024. "Collapse process prediction of mutualistic dynamical networks with k-core and dimension reduction method," Chaos, Solitons & Fractals, Elsevier, vol. 180(C).
    16. Andrey Karpachevskiy & German Titov & Oksana Filippova, 2021. "Development of A Spatiotemporal Database for Evolution Analysis of the Moscow Backbone Power Grid," Data, MDPI, vol. 6(12), pages 1-14, November.
    17. Abdullah Almaatouq, 2016. "Complex Systems and a Computational Social Science Perspective on the Labor Market," Papers 1606.08562, arXiv.org.
    18. Xu, Yan & Gurfinkel, Aleks Jacob & Rikvold, Per Arne, 2014. "Architecture of the Florida power grid as a complex network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 401(C), pages 130-140.
    19. Wang, Wensheng & Karimi, Faezeh & Khalilpour, Kaveh & Green, David & Varvarigos, Manos, 2023. "Robustness analysis of electricity networks against failure or attack: The case of the Australian National Electricity Market (NEM)," International Journal of Critical Infrastructure Protection, Elsevier, vol. 41(C).
    20. Zhang, Wei-qi & Zhang, Xin-yan & Huang, Shao-wei & Xia, Yu-kai & Fan, Xiao-chao & Mei, Sheng-wei, 2017. "Evolution of a transmission network with high proportion of renewable energy in the future," Renewable Energy, Elsevier, vol. 102(PB), pages 372-379.

    More about this item

    Keywords

    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    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:gam:jmathe:v:7:y:2019:i:1:p:106-:d:199307. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.