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An Efficient Methodology for Locating and Sizing PV Generators in Radial Distribution Networks Using a Mixed-Integer Conic Relaxation

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  • Oscar Danilo Montoya

    (Grupo de Compatibilidad e Interferencia Electromagnética, 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
    These authors contributed equally to this work.)

  • Carlos Andrés Ramos-Paja

    (Facultad de Minas, Universidad Nacional de Colombia, Medellín 050034, Colombia
    These authors contributed equally to this work.)

  • Luis Fernando Grisales-Noreña

    (Facultad de Ingeniería, Institución Universitaria Pascual Bravo, Campus Robledo, Medellín 050036, Colombia
    These authors contributed equally to this work.)

Abstract

This paper proposes a new solution methodology based on a mixed-integer conic formulation to locate and size photovoltaic (PV) generation units in AC distribution networks with a radial structure. The objective function comprises the annual expected energy costs of the conventional substation in addition to the investment and operating costs of PV sources. The original optimization model that represents this problem belongs to the family of mixed-integer nonlinear programming (MINLP); however, the complexity of the power balance constraints make it difficult to find the global optimum. In order to improve the quality of the optimization model, a mixed-integer conic (MIC) formulation is proposed in this research in order to represent the studied problem. Numerical results in two test feeders composed of 33 and 69 nodes demonstrate the effectiveness of the proposed MIC model when compared to multiple metaheuristic optimizers such as the Chu and Beasley Genetic Algorithm, the Newton Metaheuristic Algorithm, the Vortex Search Algorithm, the Gradient-Based Metaheuristic Optimization Algorithm, and the Arithmetic Optimization Algorithm, among others. The final results obtained with the MIC model show improvements greater than USD 100,000 per year of operation. All simulations were run in the MATLAB programming environment, using its own scripts for all the metaheuristic algorithms and the disciplined convex tool known as CVX with the Gurobi solver in order to solve the proposed MIC model.

Suggested Citation

  • Oscar Danilo Montoya & Carlos Andrés Ramos-Paja & Luis Fernando Grisales-Noreña, 2022. "An Efficient Methodology for Locating and Sizing PV Generators in Radial Distribution Networks Using a Mixed-Integer Conic Relaxation," Mathematics, MDPI, vol. 10(15), pages 1-17, July.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:15:p:2626-:d:873106
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    References listed on IDEAS

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    1. Betakova, Vendula & Vojar, Jiri & Sklenicka, Petr, 2015. "Wind turbines location: How many and how far?," Applied Energy, Elsevier, vol. 151(C), pages 23-31.
    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. Bjørnebye, Henrik & Hagem, Cathrine & Lind, Arne, 2018. "Optimal location of renewable power," Energy, Elsevier, vol. 147(C), pages 1203-1215.
    4. 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.
    5. Faissal Jelti & Amine Allouhi & Mahmut Sami Büker & Rachid Saadani & Abdelmajid Jamil, 2021. "Renewable Power Generation: A Supply Chain Perspective," Sustainability, MDPI, vol. 13(3), pages 1-22, January.
    6. Sarah Feron, 2016. "Sustainability of Off-Grid Photovoltaic Systems for Rural Electrification in Developing Countries: A Review," Sustainability, MDPI, vol. 8(12), pages 1-26, December.
    7. Gregorio Fernández & Noemi Galan & Daniel Marquina & Diego Martínez & Alberto Sanchez & Pablo López & Hans Bludszuweit & Jorge Rueda, 2020. "Photovoltaic Generation Impact Analysis in Low Voltage Distribution Grids," Energies, MDPI, vol. 13(17), pages 1-27, August.
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    Cited by:

    1. David Steveen Guzmán-Romero & Brandon Cortés-Caicedo & Oscar Danilo Montoya, 2023. "Development of a MATLAB-GAMS Framework for Solving the Problem Regarding the Optimal Location and Sizing of PV Sources in Distribution Networks," Resources, MDPI, vol. 12(3), pages 1-19, March.
    2. Árpád Bűrmen & Tadej Tuma, 2022. "Preface to the Special Issue on “Optimization Theory and Applications”," Mathematics, MDPI, vol. 10(24), pages 1-3, December.
    3. Brandon Cortés-Caicedo & Luis Fernando Grisales-Noreña & Oscar Danilo Montoya & Miguel Angel Rodriguez-Cabal & Javier Alveiro Rosero, 2022. "Energy Management System for the Optimal Operation of PV Generators in Distribution Systems Using the Antlion Optimizer: A Colombian Urban and Rural Case Study," Sustainability, MDPI, vol. 14(23), pages 1-35, December.
    4. Luis Fernando Grisales-Noreña & Oscar Danilo Montoya & Brandon Cortés-Caicedo & Farhad Zishan & Javier Rosero-García, 2023. "Optimal Power Dispatch of PV Generators in AC Distribution Networks by Considering Solar, Environmental, and Power Demand Conditions from Colombia," Mathematics, MDPI, vol. 11(2), pages 1-20, January.

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