{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,2]],"date-time":"2025-11-02T07:03:58Z","timestamp":1762067038452,"version":"build-2065373602"},"reference-count":31,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2022,9,22]],"date-time":"2022-09-22T00:00:00Z","timestamp":1663804800000},"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 addresses the problem of the power flow analysis of bipolar direct current (DC) networks considering unbalanced loads and the effect of a neutral wire, which may be solidly grounded or non-grounded. The power flow problem is formulated using the nodal admittance representation of the system and the hyperbolic relations between power loads and voltages in the demand nodes. Using Taylor series expansion with linear terms, a recursive power flow method with quadratic convergence is proposed. The main advantage of the hyperbolic approximation in dealing with power flow problems in DC bipolar networks is that this method can analyze radial and meshed configurations without any modifications to the power flow formula. The numerical results in three test feeders composed of 4, 21, and 85 bus systems show the efficiency of the proposed power flow method. All of the simulations were conducted in MATLAB for a comparison of the proposed approach with the well-established successive approximation method for power flow studies in distribution networks.<\/jats:p>","DOI":"10.3390\/a15100341","type":"journal-article","created":{"date-parts":[[2022,9,22]],"date-time":"2022-09-22T05:33:14Z","timestamp":1663824794000},"page":"341","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Power Flow Solution in Bipolar DC Networks Considering a Neutral Wire and Unbalanced Loads: A Hyperbolic Approximation"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9569-2067","authenticated-orcid":false,"given":"Sim\u00f3n","family":"Sep\u00falveda-Garc\u00eda","sequence":"first","affiliation":[{"name":"Department of Electric Power Engineering, Universidad Tecnol\u00f3gica de Pereira, Pereira 660003, Colombia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6051-4925","authenticated-orcid":false,"given":"Oscar Danilo","family":"Montoya","sequence":"additional","affiliation":[{"name":"Grupo de Compatibilidad e Interferencia Electromagn\u00e9tica, Facultad de Ingenier\u00eda, Universidad Distrital Francisco Jos\u00e9 de Caldas, Bogot\u00e1 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\/0000-0001-6496-0594","authenticated-orcid":false,"given":"Alejandro","family":"Garc\u00e9s","sequence":"additional","affiliation":[{"name":"Department of Electric Power Engineering, Universidad Tecnol\u00f3gica de Pereira, Pereira 660003, Colombia"}]}],"member":"1968","published-online":{"date-parts":[[2022,9,22]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"296","DOI":"10.1109\/TSG.2015.2457910","article-title":"AC Versus DC Microgrid Planning","volume":"8","author":"Lotfi","year":"2017","journal-title":"IEEE Trans. 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