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

Oscar Danilo Montoya, Carlos Andrés Ramos-Paja and Luis Fernando Grisales-Noreña
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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
Carlos Andrés Ramos-Paja: Facultad de Minas, Universidad Nacional de Colombia, Medellín 050034, Colombia
Luis Fernando Grisales-Noreña: Facultad de Ingeniería, Institución Universitaria Pascual Bravo, Campus Robledo, Medellín 050036, Colombia

Mathematics, 2022, vol. 10, issue 15, 1-17

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.

Keywords: photovoltaic system; investment and operating costs; mixed-integer conic optimization; radial distribution networks (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

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