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

• Published in: Mathematics (Basel) Vol. 10; no. 15; p. 2626
• Main Authors: Montoya, Oscar Danilo, Ramos-Paja, Carlos Andrés, Grisales-Noreña, Luis Fernando
• Format: Journal Article
• Language: English
• Published: Basel MDPI AG 01.08.2022
• Subjects: Alternative energy sources; Carbon footprint; Emissions; Energy costs; Energy resources; Energy storage; Feeders; Genetic algorithms; Greenhouse gases; Heuristic methods; investment and operating costs; Linear programming; Literature reviews; Maintenance costs; Mathematics; Mixed integer; mixed-integer conic optimization; Nonlinear programming; Operating costs; Optimization; Optimization models; Photovoltaic cells; photovoltaic system; Programming environments; Radial distribution; radial distribution networks; Renewable resources; Search algorithms; Substations; Wind power
• ISSN: 2227-7390; 2227-7390
• DOI: 10.3390/math10152626

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.