{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,24]],"date-time":"2026-02-24T18:29:29Z","timestamp":1771957769739,"version":"3.50.1"},"reference-count":55,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2022,1,23]],"date-time":"2022-01-23T00:00:00Z","timestamp":1642896000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>This paper discusses the minimization of the total annual operative cost for a planning period of 20 years composed by the annualized costs of the energy purchasing at the substation bus summed with the annualized investment costs in photovoltaic (PV) sources, including their maintenance costs in distribution networks based on their optimal siting and sizing. This problem is presented using a mixed-integer nonlinear programming model, which is resolved by applying a master\u2013slave methodology. The master stage, consisting of a discrete-continuous version of the Vortex Search Algorithm (DCVSA), is responsible for providing the optimal locations and sizes for the PV sources\u2014whereas the slave stage employs the Matricial Backward\/Forward Power Flow Method, which is used to determine the fitness function value for each individual provided by the master stage. Numerical results in the IEEE 33- and 69-node systems with AC and DC topologies illustrate the efficiency of the proposed approach when compared to the discrete-continuous version of the Chu and Beasley genetic algorithm with the optimal location of three PV sources. All the numerical validations were carried out in the MATLAB programming environment.<\/jats:p>","DOI":"10.3390\/s22030851","type":"journal-article","created":{"date-parts":[[2022,1,23]],"date-time":"2022-01-23T20:36:27Z","timestamp":1642970187000},"page":"851","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":35,"title":["Optimal Design of PV Systems in Electrical Distribution Networks by Minimizing the Annual Equivalent Operative Costs through the Discrete-Continuous Vortex Search Algorithm"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0294-975X","authenticated-orcid":false,"given":"Brandon","family":"Cort\u00e9s-Caicedo","sequence":"first","affiliation":[{"name":"Facultad de Ingenier\u00eda, Instituto Tecnol\u00f3gico Metropolitano, Medell\u00edn 050036, Colombia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Federico","family":"Molina-Martin","sequence":"additional","affiliation":[{"name":"Estudiante de Doctorado, Departamento de Ingenier\u00eda El\u00e9ctrica, Campus Lagunillas s\/n, University of Ja\u00e9n, Edificio A3, 23071 Ja\u00e9n, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1409-9756","authenticated-orcid":false,"given":"Luis Fernando","family":"Grisales-Nore\u00f1a","sequence":"additional","affiliation":[{"name":"Estudiante de Doctorado, Departamento de Ingenier\u00eda El\u00e9ctrica, Campus Lagunillas s\/n, University of Ja\u00e9n, Edificio A3, 23071 Ja\u00e9n, Spain"},{"name":"Department of Electromechanical and Mechatronic, Faculty of Engineering, Instituto Tecnol\u00f3gico Metropolitano, Medell\u00edn 050036, Colombia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6051-4925","authenticated-orcid":false,"given":"Oscar Danilo","family":"Montoya","sequence":"additional","affiliation":[{"name":"Facultad de Ingenier\u00eda, Universidad Distrital Francisco Jos\u00e9 de Caldas, Bogot\u00e1 110231, Colombia"},{"name":"Laboratorio Inteligente de Energ\u00eda, Universidad Tecnol\u00f3gica de Bol\u00edvar, Cartagena 131001, Colombia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9117-1689","authenticated-orcid":false,"given":"Jesus C.","family":"Hern\u00e1ndez","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering, Campus Lagunillas s\/n, University of Ja\u00e9n, Edificio A3, 23071 Ja\u00e9n, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,1,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"711","DOI":"10.1080\/13642987.2019.1671355","article-title":"Is there a universal human right to electricity?","volume":"24","year":"2020","journal-title":"Int. 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