IDEAS home Printed from https://ideas.repec.org/a/gam/jeners/v16y2023i2p589-d1024641.html
   My bibliography  Save this article

Optimal Power Flow Solution for Bipolar DC Networks Using a Recursive Quadratic Approximation

Author

Listed:
  • Oscar Danilo Montoya

    (Grupo de Compatibilidad e Interferencia Electromagnética (GCEM), Facultad de Ingeniería, Universidad Distrital Francisco José de Caldas, Bogotá 110231, Colombia
    Laboratorio Inteligente de Energía, Facultad de Ingeniería, Universidad Tecnológica de Bolívar, Cartagena 131001, Colombia)

  • Walter Gil-González

    (Department of Electrical Engineering, Universidad Tecnológica de Pereira, Pereira 660003, Colombia)

  • Jesus C. Hernández

    (Department of Electrical Engineering, University of Jaén, Campus Lagunillas s/n, Edificio A3, 23071 Jaén, Spain)

Abstract

The problem regarding of optimal power flow in bipolar DC networks is addressed in this paper from the recursive programming stand of view. A hyperbolic relationship between constant power terminals and voltage profiles is used to resolve the optimal power flow in bipolar DC networks. The proposed approximation is based on the Taylors’ Taylor series expansion. In addition, nonlinear relationships between dispersed generators and voltage profiles are relaxed based on the small voltage voltage-magnitude variations in contrast with power output. The resulting optimization model transforms the exact nonlinear non-convex formulation into a quadratic convex approximation. The main advantage of the quadratic convex reformulation lies in finding the optimum global via recursive programming, which adjusts the point until the desired convergence is reached. Two test feeders composed of 21 and 33 buses are employed for all the numerical validations. The effectiveness of the proposed recursive convex model is verified through the implementation of different metaheuristic algorithms. All the simulations are carried out in the MATLAB programming environment using the convex disciplined tool known as CVX with the SEDUMI and SDPT3 solvers.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jeners:v:16:y:2023:i:2:p:589-:d:1024641
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/1996-1073/16/2/589/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/1996-1073/16/2/589/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Oscar Danilo Montoya & Farhad Zishan & Diego Armando Giral-Ramírez, 2022. "Recursive Convex Model for Optimal Power Flow Solution in Monopolar DC Networks," Mathematics, MDPI, vol. 10(19), pages 1-14, October.
    2. Luis Fernando Grisales-Noreña & Daniel Gonzalez Montoya & Carlos Andres Ramos-Paja, 2018. "Optimal Sizing and Location of Distributed Generators Based on PBIL and PSO Techniques," Energies, MDPI, vol. 11(4), pages 1-27, April.
    3. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Walter Gil-González & Oscar Danilo Montoya & Jesús C. Hernández, 2023. "Optimal Neutral Grounding in Bipolar DC Networks with Asymmetric Loading: A Recursive Mixed-Integer Quadratic Formulation," Energies, MDPI, vol. 16(9), pages 1-18, April.
    2. Oscar Danilo Montoya & Luis Fernando Grisales-Noreña & Jesús C. Hernández, 2023. "A Recursive Conic Approximation for Solving the Optimal Power Flow Problem in Bipolar Direct Current Grids," Energies, MDPI, vol. 16(4), pages 1-19, February.

    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. 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.
    2. 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.
    3. 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.
    4. 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.
    5. Andrés Alfonso Rosales-Muñoz & Luis Fernando Grisales-Noreña & Jhon Montano & Oscar Danilo Montoya & Alberto-Jesus Perea-Moreno, 2021. "Application of the Multiverse Optimization Method to Solve the Optimal Power Flow Problem in Direct Current Electrical Networks," Sustainability, MDPI, vol. 13(16), pages 1-28, August.
    6. Iraj Faraji Davoudkhani & Farhad Zishan & Saeedeh Mansouri & Farzad Abdollahpour & Luis Fernando Grisales-Noreña & Oscar Danilo Montoya, 2023. "Allocation of Renewable Energy Resources in Distribution Systems While Considering the Uncertainty of Wind and Solar Resources via the Multi-Objective Salp Swarm Algorithm," Energies, MDPI, vol. 16(1), pages 1-17, January.
    7. Oscar Danilo Montoya & Farhad Zishan & Diego Armando Giral-Ramírez, 2022. "Recursive Convex Model for Optimal Power Flow Solution in Monopolar DC Networks," Mathematics, MDPI, vol. 10(19), pages 1-14, October.
    8. Shanmugarajah Vinothine & Lidula N. Widanagama Arachchige & Athula D. Rajapakse & Roshani Kaluthanthrige, 2022. "Microgrid Energy Management and Methods for Managing Forecast Uncertainties," Energies, MDPI, vol. 15(22), pages 1-22, November.
    9. Ghaeth Fandi & Ibrahim Ahmad & Famous O. Igbinovia & Zdenek Muller & Josef Tlusty & Vladimir Krepl, 2018. "Voltage Regulation and Power Loss Minimization in Radial Distribution Systems via Reactive Power Injection and Distributed Generation Unit Placement," Energies, MDPI, vol. 11(6), pages 1-17, May.
    10. Mateusz Andrychowicz, 2021. "RES and ES Integration in Combination with Distribution Grid Development Using MILP," Energies, MDPI, vol. 14(2), pages 1-19, January.
    11. Mateusz Andrychowicz, 2020. "Comparison of the Use of Energy Storages and Energy Curtailment as an Addition to the Allocation of Renewable Energy in the Distribution System in Order to Minimize Development Costs," Energies, MDPI, vol. 13(14), pages 1-20, July.
    12. Mahesh Kumar & Amir Mahmood Soomro & Waqar Uddin & Laveet Kumar, 2022. "Optimal Multi-Objective Placement and Sizing of Distributed Generation in Distribution System: A Comprehensive Review," Energies, MDPI, vol. 15(21), pages 1-48, October.
    13. 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.
    14. 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.
    15. Luis Fernando Grisales-Noreña & Oscar Danilo Montoya & Ricardo Alberto Hincapié-Isaza & Mauricio Granada Echeverri & Alberto-Jesus Perea-Moreno, 2021. "Optimal Location and Sizing of DGs in DC Networks Using a Hybrid Methodology Based on the PPBIL Algorithm and the VSA," Mathematics, MDPI, vol. 9(16), pages 1-18, August.
    16. Mohsin Shahzad & Waseem Akram & Muhammad Arif & Uzair Khan & Barkat Ullah, 2021. "Optimal Siting and Sizing of Distributed Generators by Strawberry Plant Propagation Algorithm," Energies, MDPI, vol. 14(6), pages 1-13, March.
    17. Jinxin Wang & Zhongwei Wang & Xiuzhen Ma & Guojin Feng & Chi Zhang, 2020. "Locating Sensors in Complex Engineering Systems for Fault Isolation Using Population-Based Incremental Learning," Energies, MDPI, vol. 13(2), pages 1-14, January.
    18. 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.
    19. Nissim Amar & Aaron Shmaryahu & Michael Coletti & Ilan Aharon, 2021. "Sizing Procedure for System Hybridization Based on Experimental Source Modeling in Grid Application," Energies, MDPI, vol. 14(15), pages 1-19, August.
    20. Walter Gil-González & Oscar Danilo Montoya & Luis Fernando Grisales-Noreña & Alberto-Jesus Perea-Moreno & Quetzalcoatl Hernandez-Escobedo, 2020. "Optimal Placement and Sizing of Wind Generators in AC Grids Considering Reactive Power Capability and Wind Speed Curves," Sustainability, MDPI, vol. 12(7), pages 1-20, April.

    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:jeners:v:16:y:2023:i:2:p:589-:d:1024641. 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.