{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T12:38:09Z","timestamp":1777639089088,"version":"3.51.4"},"reference-count":20,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2022,4,11]],"date-time":"2022-04-11T00:00:00Z","timestamp":1649635200000},"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 analyzes the power flow solution in bipolar direct current networks with radial structures considering multiple monopolar and bipolar constant power loads. The electrical configuration of the bipolar DC grid considers that the reference pole is non-grounded along the feeder, which produces important neutral currents and voltage imbalances along the DC grid. The power flow problem is formulated through the triangular-based representation of the grid topology, which generates a recursive formulation that allows determining the voltage values in the demand nodes through an iterative procedure. The linear convergence of the triangular-based power flow method is tested through multiple load variations with respect to the nominal grid operative condition. Numerical results in the 21- and the 85-bus grids reveal the relevant variations in the voltage profiles and total grid power losses when the neutral cable is solidly grounded or not.<\/jats:p>","DOI":"10.3390\/s22082914","type":"journal-article","created":{"date-parts":[[2022,4,12]],"date-time":"2022-04-12T22:48:45Z","timestamp":1649803725000},"page":"2914","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":19,"title":["Derivative-Free Power Flow Solution for Bipolar DC Networks with Multiple Constant Power Terminals"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3924-7986","authenticated-orcid":false,"given":"\u00c1ngeles","family":"Medina-Quesada","sequence":"first","affiliation":[{"name":"Department of Electrical Engineering, University of Ja\u00e9n, Campus Lagunillas s\/n, Edificio A3, 23071 Ja\u00e9n, Spain"}],"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":"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"}],"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, University of Ja\u00e9n, Campus Lagunillas s\/n, Edificio A3, 23071 Ja\u00e9n, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,4,11]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1032","DOI":"10.1080\/15325008.2017.1318977","article-title":"Toward the universal DC distribution system","volume":"45","author":"Mackay","year":"2017","journal-title":"Electr. 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