{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,8]],"date-time":"2026-03-08T10:14:16Z","timestamp":1772964856522,"version":"3.50.1"},"reference-count":32,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2022,8,5]],"date-time":"2022-08-05T00:00:00Z","timestamp":1659657600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>This paper focuses on minimizing the annual operative costs in monopolar DC distribution networks with the inclusion of solar photovoltaic (PV) generators while considering a planning period of 20 years. This problem is formulated through a mixed-integer nonlinear programming (MINLP) model, in which binary variables define the nodes where the PV generators must be located, and continuous variables are related to the power flow solution and the optimal sizes of the PV sources. The implementation of a master\u2013slave optimization approach is proposed in order to address the complexity of the MINLP formulation. In the master stage, the discrete-continuous generalized normal distribution optimizer (DCGNDO) is implemented to define the nodes for the PV sources along with their sizes. The slave stage corresponds to a specialized power flow approach for monopolar DC networks known as the successive approximation power flow method, which helps determine the total energy generation at the substation terminals and its expected operative costs in the planning period. Numerical results in the 33- and 69-bus grids demonstrate the effectiveness of the DCGNDO optimizer compared to the discrete-continuous versions of the Chu and Beasley genetic algorithm and the vortex search algorithm.<\/jats:p>","DOI":"10.3390\/a15080277","type":"journal-article","created":{"date-parts":[[2022,8,7]],"date-time":"2022-08-07T21:03:50Z","timestamp":1659906230000},"page":"277","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["Solar Photovoltaic Integration in Monopolar DC Networks via the GNDO Algorithm"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6051-4925","authenticated-orcid":false,"given":"Oscar Danilo","family":"Montoya","sequence":"first","affiliation":[{"name":"Grupo de Compatibilidad e Interferencia Electromagn\u00e9tica, Facultad de Ingenier\u00eda, Universidad Distrital Francisco Jos\u00e9 de Caldas, Bogota 110231, Colombia"},{"name":"Laboratorio Inteligente de Energ\u00eda, Facultad de Ingenier\u00eda, Universidad Tecnol\u00f3gica de Bol\u00edvar, Cartagena 131001, Colombia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7609-1197","authenticated-orcid":false,"given":"Walter","family":"Gil-Gonz\u00e1lez","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering, Universidad Tecnol\u00f3gica de Pereira, Pereira 660003, Colombia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1409-9756","authenticated-orcid":false,"given":"Luis Fernando","family":"Grisales-Nore\u00f1a","sequence":"additional","affiliation":[{"name":"Facultad de Ingenier\u00eda, Instituci\u00f3n Universitaria Pascual Bravo, Campus Robledo, Medellin 050036, Colombia"}]}],"member":"1968","published-online":{"date-parts":[[2022,8,5]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"5496","DOI":"10.1109\/TPWRS.2018.2801280","article-title":"Optimal Power Flow in Stand-Alone DC Microgrids","volume":"33","author":"Li","year":"2018","journal-title":"IEEE Trans. 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