{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,17]],"date-time":"2026-06-17T08:22:34Z","timestamp":1781684554565,"version":"3.54.5"},"reference-count":31,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2021,6,24]],"date-time":"2021-06-24T00:00:00Z","timestamp":1624492800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The problem of the optimal load redistribution in electrical three-phase medium-voltage grids is addressed in this research from the point of view of mixed-integer convex optimization. The mathematical formulation of the load redistribution problem is developed in terminals of the distribution node by accumulating all active and reactive power loads per phase. These loads are used to propose an objective function in terms of minimization of the average unbalanced (asymmetry) grade of the network with respect to the ideal mean consumption per-phase. The objective function is defined as the l1-norm which is a convex function. As the constraints consider the binary nature of the decision variable, each node is conformed by a 3\u00d73 matrix where each row and column have to sum 1, and two equations associated with the load redistribution at each phase for each of the network nodes. Numerical results demonstrate the efficiency of the proposed mixed-integer convex model to equilibrate the power consumption per phase in regards with the ideal value in three different test feeders, which are composed of 4, 15, and 37 buses, respectively.<\/jats:p>","DOI":"10.3390\/sym13071124","type":"journal-article","created":{"date-parts":[[2021,6,24]],"date-time":"2021-06-24T23:22:14Z","timestamp":1624576934000},"page":"1124","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["Optimal Demand Reconfiguration in Three-Phase Distribution Grids Using an MI-Convex Model"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6051-4925","authenticated-orcid":false,"given":"Oscar Danilo","family":"Montoya","sequence":"first","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":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6210-3449","authenticated-orcid":false,"given":"Andres","family":"Arias-Londo\u00f1o","sequence":"additional","affiliation":[{"name":"Facultad de Ingenier\u00eda, Instituci\u00f3n Universitaria Pascual Bravo, Campus Robledo, Medell\u00edn 050036, Colombia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"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, Medell\u00edn 050036, Colombia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1573-0300","authenticated-orcid":false,"given":"Jos\u00e9 \u00c1ngel","family":"Barrios","sequence":"additional","affiliation":[{"name":"Universidad Polit\u00e9cnica de Garc\u00eda, Prolongaci\u00f3n 16 de Septiembre, Col. Valles de San Jos\u00e9, Garc\u00eda 66004, NL, Mexico"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1746-5560","authenticated-orcid":false,"given":"Harold R.","family":"Chamorro","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering at KTH, Royal Institute of Technology, SE-100 44 Stockholm, Sweden"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2021,6,24]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"817","DOI":"10.1016\/j.ijepes.2010.12.003","article-title":"Three-phase unbalance of distribution systems: Complementary analysis and experimental case study","volume":"33","author":"Bina","year":"2011","journal-title":"Int. J. Electr. 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