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A Graph-Based Power Flow Method for Balanced Distribution Systems

Author

Listed:
  • Tao Shen

    (School of Information and Electrical Engineering, Zhejiang University City College, Hangzhou 310030, China
    College of Control Science and Engineering, Zhejiang University, Hangzhou 310027, China
    These authors contributed equally to this work.)

  • Yanjun Li

    (School of Information and Electrical Engineering, Zhejiang University City College, Hangzhou 310030, China
    These authors contributed equally to this work.)

  • Ji Xiang

    (College of Electrical Engineering, Zhejiang University, Hangzhou 310027, China
    These authors contributed equally to this work.)

Abstract

A power flow method based on graph theory is presented for three-phase balanced distribution systems. The graph theory is used to describe the power network and facilitate the derivation of the relationship between bus C urrents and the bus V oltage B ias from the feeder bus (the CVB equation). A distinctive feature of the CVB equation is its unified form for both radial and meshed networks. The method requires neither a tricky numbering and layering of nodes nor breaking meshes and loop-analysis, which are both necessary in previous works for meshed networks. The convergence of the proposed method is proven using the Banach fixed-point theorem.

Suggested Citation

  • Tao Shen & Yanjun Li & Ji Xiang, 2018. "A Graph-Based Power Flow Method for Balanced Distribution Systems," Energies, MDPI, vol. 11(3), pages 1-11, February.
    • Handle: RePEc:gam:jeners:v:11:y:2018:i:3:p:511-:d:133732
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    Citations

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    Cited by:

    1. Oscar Danilo Montoya & Francisco David Moya & Arul Rajagopalan, 2022. "Annual Operating Costs Minimization in Electrical Distribution Networks via the Optimal Selection and Location of Fixed-Step Capacitor Banks Using a Hybrid Mathematical Formulation," Mathematics, MDPI, vol. 10(9), pages 1-14, May.
    2. Brandon Cortés-Caicedo & Laura Sofía Avellaneda-Gómez & Oscar Danilo Montoya & Lazaro Alvarado-Barrios & Harold R. Chamorro, 2021. "Application of the Vortex Search Algorithm to the Phase-Balancing Problem in Distribution Systems," Energies, MDPI, vol. 14(5), pages 1-35, February.
    3. Walter Gil-González & Oscar Danilo Montoya & Arul Rajagopalan & Luis Fernando Grisales-Noreña & Jesus C. Hernández, 2020. "Optimal Selection and Location of Fixed-Step Capacitor Banks in Distribution Networks Using a Discrete Version of the Vortex Search Algorithm," Energies, MDPI, vol. 13(18), pages 1-21, September.
    4. Oscar Danilo Montoya & Walter Gil-González & Jesus C. Hernández, 2023. "Optimal Power Flow Solution for Bipolar DC Networks Using a Recursive Quadratic Approximation," Energies, MDPI, vol. 16(2), pages 1-17, January.
    5. Oscar Danilo Montoya & Luis Fernando Grisales-Noreña & Diego Armando Giral-Ramírez, 2022. "Optimal Placement and Sizing of PV Sources in Distribution Grids Using a Modified Gradient-Based Metaheuristic Optimizer," Sustainability, MDPI, vol. 14(6), pages 1-19, March.
    6. Zahid Javid & Ulas Karaagac & Ilhan Kocar & Ka Wing Chan, 2021. "Laplacian Matrix-Based Power Flow Formulation for LVDC Grids with Radial and Meshed Configurations," Energies, MDPI, vol. 14(7), pages 1-21, March.
    7. Oscar Danilo Montoya & Jorge Alexander Alarcon-Villamil & Jesus C. Hernández, 2021. "Operating Cost Reduction in Distribution Networks Based on the Optimal Phase-Swapping including the Costs of the Working Groups and Energy Losses," Energies, MDPI, vol. 14(15), pages 1-22, July.
    8. O. D. Montoya & W. Gil-González & J. C. Hernández & D. A. Giral-Ramírez & A. Medina-Quesada, 2020. "A Mixed-Integer Nonlinear Programming Model for Optimal Reconfiguration of DC Distribution Feeders," Energies, MDPI, vol. 13(17), pages 1-22, August.
    9. Oscar Danilo Montoya & Luis Fernando Grisales-Noreña & Alberto-Jesus Perea-Moreno, 2021. "Optimal Investments in PV Sources for Grid-Connected Distribution Networks: An Application of the Discrete–Continuous Genetic Algorithm," Sustainability, MDPI, vol. 13(24), pages 1-19, December.
    10. Juhani Rantaniemi & Jaakko Jääskeläinen & Jukka Lassila & Samuli Honkapuro, 2022. "A Study on the Impact of Distance-Based Value Loss on Transmission Network Power Flow Using Synthetic Networks," Energies, MDPI, vol. 15(2), pages 1-12, January.

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