<?xml version="1.0" encoding="ISO-8859-1"?><article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<front>
<journal-meta>
<journal-id>0123-921X</journal-id>
<journal-title><![CDATA[Tecnura]]></journal-title>
<abbrev-journal-title><![CDATA[Tecnura]]></abbrev-journal-title>
<issn>0123-921X</issn>
<publisher>
<publisher-name><![CDATA[Universidad Distrital Francisco José de Caldas]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S0123-921X2022000100030</article-id>
<article-id pub-id-type="doi">10.14483/22487638.18635</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[Branch Optimal Power Flow Model for DC Networks with Radial Structure: A Conic Relaxation]]></article-title>
<article-title xml:lang="es"><![CDATA[Flujo de potencia óptimo de ramas para redes DC con estructura radial: una relajación cónica]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Montoya]]></surname>
<given-names><![CDATA[Oscar Danilo]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Arias-Londoño]]></surname>
<given-names><![CDATA[Andrés]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Molina-Cabrera]]></surname>
<given-names><![CDATA[Alexander]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidad Distrital Francisco José de Caldas  ]]></institution>
<addr-line><![CDATA[Bogotá D. C]]></addr-line>
<country>Colombia</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,Institución Universitaria Pascual Bravo  ]]></institution>
<addr-line><![CDATA[Medellín ]]></addr-line>
<country>Colombia</country>
</aff>
<aff id="Af3">
<institution><![CDATA[,Universidad Tecnológica de Pereira  ]]></institution>
<addr-line><![CDATA[Pereira ]]></addr-line>
<country>Colombia</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>03</month>
<year>2022</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>03</month>
<year>2022</year>
</pub-date>
<volume>26</volume>
<numero>71</numero>
<fpage>30</fpage>
<lpage>42</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_arttext&amp;pid=S0123-921X2022000100030&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_abstract&amp;pid=S0123-921X2022000100030&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_pdf&amp;pid=S0123-921X2022000100030&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract  Objective:  This work involves a convex-based mathematical reformulation of the optimal power flow problem in DC networks. The objective of the proposed optimization model corresponds to the minimization of the power losses throughout all the network branches considering a convex conic model that ensures finding the global optimum solution.  Methodology:  This work is split into three stages. The first stage presents the mathematical model of optimal power flow for DC networks and all the geometric features that make it non-convex. The second stage presents the convex reformulation from a second-order conic relaxation. The third stage shows the main characteristics of the DC system under study, as well as the optimal solution of the power flow problem and its comparisons with some methods reported in the specialized literature.  Results:  The numerical validations demonstrate that the proposed convex optimal power flow model obtains the same solution as the exact model of the problem with an efficiency of 100%, which is in contrast with the variability of the results that are presented by the metaheuristic techniques reported as comparison methodologies.  Conclusions:  The proposed second-order conic relaxation ensured the convexity of the solution space and, therefore, the finding of the optimal solution at each execution, in addition to demonstrating that, for optimal power flow problems in DC networks, the numerical performance is better than most of the comparative metaheuristic methods and that the solution provided by the proposed relaxation is equivalent to that provided by the exact model.]]></p></abstract>
<abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen  Objetivo: Este trabajo plantea una reformulación matemática de naturaleza convexa del problema de flujo de potencia óptimo en redes de corriente continua (DC). El objetivo del modelo de optimización propuesto corresponde a la minimización de las pérdidas de potencia en todas las ramas de la red considerando un modelo cónico convexo que garantice el hallazgo de la solución óptima global.  Metodología: Este trabajo está dividido en tres etapas: la primera presenta el modelo matemático de flujo de potencia óptimo para redes DC y todas las características geométricas que lo hacen no convexo; la segunda presenta la reformulación convexa a partir de una relajación cónica de segundo orden; la tercera etapa presenta las principales características del sistema DC bajo estudio, además de la solución óptima del problema de flujo de potencia y sus comparaciones con algunos métodos reportados en la literatura especializada.  Resultados: Las validaciones numéricas demuestran que el modelo de flujo de potencia óptimo convexo propuesto encuentra la misma solución el modelo exacto del problema y tiene una eficiencia del 100%, lo cual contrasta con la variabilidad de resultados que presentan las técnicas metaheurísticas reportadas como métodos de comparación.  Conclusiones: La relajación cónica de segundo orden propuesta garantizó la convexidad del espacio de soluciones, y, por tanto, el hallazgo de la solución óptima en cada ejecución. Además, demostró que, para problemas de flujo de potencia óptimo en redes DC, tiene el mejor desempeño numérico que la mayoría de los métodos metaheurísticos comparativos; y que la solución provista por la relajación propuesta es equivalente a la proveída por el modelo exacto.]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[direct current networks]]></kwd>
<kwd lng="en"><![CDATA[second-order conic relaxation]]></kwd>
<kwd lng="en"><![CDATA[non-linear programming model]]></kwd>
<kwd lng="en"><![CDATA[convex optimization]]></kwd>
<kwd lng="es"><![CDATA[redes de corriente continua]]></kwd>
<kwd lng="es"><![CDATA[relajación cónica de segundo orden]]></kwd>
<kwd lng="es"><![CDATA[modelo de programación no lineal]]></kwd>
<kwd lng="es"><![CDATA[optimización convexa]]></kwd>
</kwd-group>
</article-meta>
</front><back>
<ref-list>
<ref id="B1">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Bahrami]]></surname>
<given-names><![CDATA[S.]]></given-names>
</name>
<name>
<surname><![CDATA[Therrien]]></surname>
<given-names><![CDATA[F.]]></given-names>
</name>
<name>
<surname><![CDATA[Wong]]></surname>
<given-names><![CDATA[V. W.]]></given-names>
</name>
<name>
<surname><![CDATA[Jatskevich]]></surname>
<given-names><![CDATA[J]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Semidefinite Relaxation of Optimal Power Flow for AC-DC Grids.]]></article-title>
<source><![CDATA[IEEE Transactions on Power Systems]]></source>
<year>2017</year>
<volume>32</volume>
<numero>1</numero>
<issue>1</issue>
<page-range>289-304</page-range></nlm-citation>
</ref>
<ref id="B2">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Benson]]></surname>
<given-names><![CDATA[H. Y.]]></given-names>
</name>
<name>
<surname><![CDATA[Saglam]]></surname>
<given-names><![CDATA[U]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Mixed-Integer Second-Order Cone Programming: A Survey]]></article-title>
<source><![CDATA[INFORMS TutORials in Operations Research]]></source>
<year>2013</year>
<page-range>13-36</page-range></nlm-citation>
</ref>
<ref id="B3">
<nlm-citation citation-type="confpro">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Farivar]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Low]]></surname>
<given-names><![CDATA[S. H]]></given-names>
</name>
</person-group>
<source><![CDATA[Branch flow model: Relaxations and convexification]]></source>
<year>2012</year>
<month>,</month>
<conf-name><![CDATA[ Conference presentation]]></conf-name>
<conf-loc>Maui, HI, USA </conf-loc>
</nlm-citation>
</ref>
<ref id="B4">
<nlm-citation citation-type="confpro">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Gupta]]></surname>
<given-names><![CDATA[H]]></given-names>
</name>
<name>
<surname><![CDATA[Gupta]]></surname>
<given-names><![CDATA[A]]></given-names>
</name>
<name>
<surname><![CDATA[Gupta]]></surname>
<given-names><![CDATA[S. K]]></given-names>
</name>
<name>
<surname><![CDATA[Nayak]]></surname>
<given-names><![CDATA[P.]]></given-names>
</name>
<name>
<surname><![CDATA[Shrivastava]]></surname>
<given-names><![CDATA[T]]></given-names>
</name>
</person-group>
<source><![CDATA[How effective is Black Hole Algorithm?]]></source>
<year>2016</year>
<conf-name><![CDATA[ Conference presentation, 2]]></conf-name>
<conf-loc>Greater Noida, India </conf-loc>
</nlm-citation>
</ref>
<ref id="B5">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Gelani]]></surname>
<given-names><![CDATA[H.]]></given-names>
</name>
<name>
<surname><![CDATA[Dastgeer F.]]></surname>
<given-names><![CDATA[Siraj]]></given-names>
</name>
<name>
<surname><![CDATA[K.]]></surname>
<given-names><![CDATA[Nasir]]></given-names>
</name>
<name>
<surname><![CDATA[M.]]></surname>
<given-names><![CDATA[Niazi]]></given-names>
</name>
<name>
<surname><![CDATA[K.]]></surname>
<given-names><![CDATA[Yang Y]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Efficiency Comparison of AC and DC Distribution Networks for Modern Residential Localities]]></article-title>
<source><![CDATA[Applied Sciences]]></source>
<year>2019</year>
<volume>9</volume>
<numero>3</numero>
<issue>3</issue>
<page-range>582</page-range></nlm-citation>
</ref>
<ref id="B6">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Garcés]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
<name>
<surname><![CDATA[Correa]]></surname>
<given-names><![CDATA[C. A.]]></given-names>
</name>
<name>
<surname><![CDATA[Sánchez]]></surname>
<given-names><![CDATA[A]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Operación económica de dispositivos almacenadores de energía para disminución de pérdidas]]></article-title>
<source><![CDATA[Revista Tecnura,]]></source>
<year>2014</year>
<volume>18</volume>
<numero>42</numero>
<issue>42</issue>
<page-range>53-64</page-range></nlm-citation>
</ref>
<ref id="B7">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Garcés]]></surname>
<given-names><![CDATA[A]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[On the Convergence of Newtons Method in Power Flow Studies for DC Microgrids]]></article-title>
<source><![CDATA[IEEE Transactions on Power Systems]]></source>
<year>2018</year>
<volume>33</volume>
<numero>5</numero>
<issue>5</issue>
<page-range>5770-7</page-range></nlm-citation>
</ref>
<ref id="B8">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Garcés]]></surname>
<given-names><![CDATA[A]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Uniqueness of the power flow solutions in low voltage direct current grids]]></article-title>
<source><![CDATA[Electric Power Systems Research]]></source>
<year>2017</year>
<numero>151</numero>
<issue>151</issue>
<page-range>149-53</page-range></nlm-citation>
</ref>
<ref id="B9">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Gil-González]]></surname>
<given-names><![CDATA[W.]]></given-names>
</name>
<name>
<surname><![CDATA[Montoya]]></surname>
<given-names><![CDATA[O. D.]]></given-names>
</name>
<name>
<surname><![CDATA[Grisales-Noreña]]></surname>
<given-names><![CDATA[L. F.]]></given-names>
</name>
<name>
<surname><![CDATA[Ramírez-Vanegas]]></surname>
<given-names><![CDATA[C. A.]]></given-names>
</name>
<name>
<surname><![CDATA[Molina-Cabrera]]></surname>
<given-names><![CDATA[A]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Hybrid Optimization Strategy for Optimal Location and Sizing of DG in Distribution Networks]]></article-title>
<source><![CDATA[Revista Tecnura]]></source>
<year>2020</year>
<volume>24</volume>
<numero>66</numero>
<issue>66</issue>
<page-range>47-61</page-range></nlm-citation>
</ref>
<ref id="B10">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Giraldo]]></surname>
<given-names><![CDATA[J. A]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Optimal power flow solution in direct current grids using Sine-Cosine algorithm]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[Montoya]]></surname>
<given-names><![CDATA[O. D]]></given-names>
</name>
<name>
<surname><![CDATA[Grisales-Noreña]]></surname>
<given-names><![CDATA[L. F]]></given-names>
</name>
<name>
<surname><![CDATA[Gil-González]]></surname>
<given-names><![CDATA[W]]></given-names>
</name>
<name>
<surname><![CDATA[Holguín]]></surname>
<given-names><![CDATA[M]]></given-names>
</name>
</person-group>
<source><![CDATA[J. Journal of Physics: Conference Series]]></source>
<year>2019</year>
<numero>1403</numero>
<issue>1403</issue>
<page-range>012009</page-range></nlm-citation>
</ref>
<ref id="B11">
<nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Grisales-Noreña]]></surname>
<given-names><![CDATA[L. F.]]></given-names>
</name>
<name>
<surname><![CDATA[Garzón-Rivera]]></surname>
<given-names><![CDATA[O. D.]]></given-names>
</name>
<name>
<surname><![CDATA[Montoya]]></surname>
<given-names><![CDATA[O. D.]]></given-names>
</name>
<name>
<surname><![CDATA[Ramos-Paja]]></surname>
<given-names><![CDATA[C. A]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Hybrid Metaheuristic Optimization Methods for Optimal Location and Sizing DGs in DC Networks]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[Figueroa-García]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
<name>
<surname><![CDATA[Duarte-González]]></surname>
<given-names><![CDATA[M]]></given-names>
</name>
<name>
<surname><![CDATA[Jaramillo-Isaza]]></surname>
<given-names><![CDATA[S]]></given-names>
</name>
<name>
<surname><![CDATA[Orjuela-Cañón]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
<name>
<surname><![CDATA[Díaz-Gutiérrez]]></surname>
<given-names><![CDATA[Y]]></given-names>
</name>
</person-group>
<source><![CDATA[Communications in Computer and Information Science]]></source>
<year>2019</year>
<volume>1052</volume>
<page-range>214-25</page-range></nlm-citation>
</ref>
<ref id="B12">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Grisales-Noreña]]></surname>
<given-names><![CDATA[L.]]></given-names>
</name>
<name>
<surname><![CDATA[Garzón Rivera]]></surname>
<given-names><![CDATA[O.]]></given-names>
</name>
<name>
<surname><![CDATA[Ocampo Toro]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
<name>
<surname><![CDATA[Ramos Paja]]></surname>
<given-names><![CDATA[C.]]></given-names>
</name>
<name>
<surname><![CDATA[Rodríguez Cabal]]></surname>
<given-names><![CDATA[M]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Metaheuristic Optimization Methods for Optimal Power Flow Analysis in DC Distribution Networks]]></article-title>
<source><![CDATA[Transactions on Energy Systems and Engineering Applications]]></source>
<year>2020</year>
<volume>1</volume>
<numero>1</numero>
<issue>1</issue>
<page-range>13-31</page-range></nlm-citation>
</ref>
<ref id="B13">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Hidalgo-Mora]]></surname>
<given-names><![CDATA[C. A.]]></given-names>
</name>
<name>
<surname><![CDATA[Díaz-Aldana]]></surname>
<given-names><![CDATA[N. L.]]></given-names>
</name>
<name>
<surname><![CDATA[Trujillo-Rodríguez]]></surname>
<given-names><![CDATA[C. L]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Diseño e implementación de controladores lineales para regulación del bus DC en convertidores VSC para HVDC]]></article-title>
<source><![CDATA[Revista Tecnura]]></source>
<year>2014</year>
<volume>18</volume>
<numero>40</numero>
<issue>40</issue>
<page-range>48-61</page-range></nlm-citation>
</ref>
<ref id="B14">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Kaur]]></surname>
<given-names><![CDATA[S.]]></given-names>
</name>
<name>
<surname><![CDATA[Kumbhar]]></surname>
<given-names><![CDATA[G.]]></given-names>
</name>
<name>
<surname><![CDATA[Sharma]]></surname>
<given-names><![CDATA[J]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[A MINLP technique for optimal placement of multiple DG units in distribution systems]]></article-title>
<source><![CDATA[International Journal of Electrical Power &amp; Energy Systems,]]></source>
<year>2014</year>
<numero>63</numero>
<issue>63</issue>
<page-range>609-17</page-range></nlm-citation>
</ref>
<ref id="B15">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Li]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
<name>
<surname><![CDATA[Liu]]></surname>
<given-names><![CDATA[F.]]></given-names>
</name>
<name>
<surname><![CDATA[Wang]]></surname>
<given-names><![CDATA[Z.]]></given-names>
</name>
<name>
<surname><![CDATA[Low]]></surname>
<given-names><![CDATA[S. H.]]></given-names>
</name>
<name>
<surname><![CDATA[Mei]]></surname>
<given-names><![CDATA[S]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Optimal Power Flow in Stand-Alone DC Microgrids]]></article-title>
<source><![CDATA[IEEE Transactions on Power Systems]]></source>
<year>2018</year>
<volume>33</volume>
<numero>5</numero>
<issue>5</issue>
<page-range>5496-506</page-range></nlm-citation>
</ref>
<ref id="B16">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Lotfi]]></surname>
<given-names><![CDATA[H.]]></given-names>
</name>
<name>
<surname><![CDATA[Khodaei]]></surname>
<given-names><![CDATA[A]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[AC Versus DC Microgrid Planning]]></article-title>
<source><![CDATA[IEEE Transactions on Smart Grid]]></source>
<year>2017</year>
<volume>8</volume>
<numero>1</numero>
<issue>1</issue>
<page-range>296-304</page-range></nlm-citation>
</ref>
<ref id="B17">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Montoya]]></surname>
<given-names><![CDATA[O. D.]]></given-names>
</name>
<name>
<surname><![CDATA[Gil-González]]></surname>
<given-names><![CDATA[W]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[A MIQP model for optimal location and sizing of dispatchable DGs in DC networks]]></article-title>
<source><![CDATA[Energy Systems]]></source>
<year>2021</year>
<numero>12</numero>
<issue>12</issue>
<page-range>181-202</page-range></nlm-citation>
</ref>
<ref id="B18">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Montoya]]></surname>
<given-names><![CDATA[O. D.]]></given-names>
</name>
<name>
<surname><![CDATA[Gil-González]]></surname>
<given-names><![CDATA[W.]]></given-names>
</name>
<name>
<surname><![CDATA[Garcés]]></surname>
<given-names><![CDATA[A]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Power flow approximation for DC networks with constant power loads via logarithmic transform of voltage magnitudes]]></article-title>
<source><![CDATA[Electric Power Systems Research]]></source>
<year>2019</year>
<month>a</month>
<numero>175</numero>
<issue>175</issue>
<page-range>105887</page-range></nlm-citation>
</ref>
<ref id="B19">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Montoya]]></surname>
<given-names><![CDATA[O. D.]]></given-names>
</name>
<name>
<surname><![CDATA[Gil-González]]></surname>
<given-names><![CDATA[W.]]></given-names>
</name>
<name>
<surname><![CDATA[Holguín]]></surname>
<given-names><![CDATA[M]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Optimal power flow studies in direct current grids: An application of the bio-inspired elephant swarm water search algorithm]]></article-title>
<source><![CDATA[Journal of Physics: Conference Series]]></source>
<year>2019</year>
<month>b</month>
<numero>1403</numero>
<issue>1403</issue>
<page-range>012010</page-range></nlm-citation>
</ref>
<ref id="B20">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Montoya]]></surname>
<given-names><![CDATA[O. D.]]></given-names>
</name>
<name>
<surname><![CDATA[Serra]]></surname>
<given-names><![CDATA[F. M.]]></given-names>
</name>
<name>
<surname><![CDATA[de Angelo]]></surname>
<given-names><![CDATA[C. H]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[On the Efficiency in Electrical Networks with AC and DC Operation Technologies: A Comparative Study at the Distribution Stage]]></article-title>
<source><![CDATA[Electronics]]></source>
<year>2020</year>
<month>a</month>
<volume>9</volume>
<numero>9</numero>
<issue>9</issue>
<page-range>1352</page-range></nlm-citation>
</ref>
<ref id="B21">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Montoya]]></surname>
<given-names><![CDATA[O. D.]]></given-names>
</name>
<name>
<surname><![CDATA[Gil-González]]></surname>
<given-names><![CDATA[W.]]></given-names>
</name>
<name>
<surname><![CDATA[Grisales-Noreña]]></surname>
<given-names><![CDATA[L. F]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Vortex Search Algorithm for Optimal Power Flow Analysis in DC Resistive Networks with CPLs]]></article-title>
<source><![CDATA[IEEE Transactions on Circuits and Systems II]]></source>
<year>2020</year>
<month>b</month>
<volume>67</volume>
<numero>8</numero>
<issue>8</issue>
<page-range>1439-43</page-range></nlm-citation>
</ref>
<ref id="B22">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Parhizi]]></surname>
<given-names><![CDATA[S.]]></given-names>
</name>
<name>
<surname><![CDATA[Lotfi]]></surname>
<given-names><![CDATA[H.]]></given-names>
</name>
<name>
<surname><![CDATA[Khodaei]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
<name>
<surname><![CDATA[Bahramirad]]></surname>
<given-names><![CDATA[S]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[State of the Art in Research on Microgrids: A Review]]></article-title>
<source><![CDATA[IEEE Access]]></source>
<year>2015</year>
<numero>3</numero>
<issue>3</issue>
<page-range>890-925</page-range></nlm-citation>
</ref>
<ref id="B23">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Serra]]></surname>
<given-names><![CDATA[F. M.]]></given-names>
</name>
<name>
<surname><![CDATA[de Angelo]]></surname>
<given-names><![CDATA[C. H]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Control of a battery charger for electric vehicles with unity power factor]]></article-title>
<source><![CDATA[Transactions on Energy Systems and Engineering Applications]]></source>
<year>2021</year>
<volume>2</volume>
<numero>1</numero>
<issue>1</issue>
<page-range>32-44</page-range></nlm-citation>
</ref>
<ref id="B24">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Simpson-Porco]]></surname>
<given-names><![CDATA[J. W.]]></given-names>
</name>
<name>
<surname><![CDATA[Dorfler]]></surname>
<given-names><![CDATA[F.]]></given-names>
</name>
<name>
<surname><![CDATA[Bullo]]></surname>
<given-names><![CDATA[F]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[On Resistive Networks of Constant-Power Devices]]></article-title>
<source><![CDATA[IEEE Transactions on Circuits and Systems II]]></source>
<year>2015</year>
<volume>62</volume>
<numero>8</numero>
<issue>8</issue>
<page-range>811-5</page-range></nlm-citation>
</ref>
<ref id="B25">
<nlm-citation citation-type="confpro">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Starke]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Tolbert]]></surname>
<given-names><![CDATA[L. M.]]></given-names>
</name>
<name>
<surname><![CDATA[Ozpineci]]></surname>
<given-names><![CDATA[B]]></given-names>
</name>
</person-group>
<source><![CDATA[AC vs. DC distribution: A loss comparison]]></source>
<year>2008</year>
<month>,</month>
<conf-name><![CDATA[ Conference presentation]]></conf-name>
<conf-loc>Chicago, IL, USA </conf-loc>
</nlm-citation>
</ref>
<ref id="B26">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Velásquez]]></surname>
<given-names><![CDATA[O. S.]]></given-names>
</name>
<name>
<surname><![CDATA[Montoya]]></surname>
<given-names><![CDATA[O. D.]]></given-names>
</name>
<name>
<surname><![CDATA[Garrido]]></surname>
<given-names><![CDATA[V. M.]]></given-names>
</name>
<name>
<surname><![CDATA[Grisales-Noreña]]></surname>
<given-names><![CDATA[L. F]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Optimal Power Flow in Direct-Current Power Grids via Black Hole Optimization]]></article-title>
<source><![CDATA[Advances in Electrical and Electronic Engineering]]></source>
<year>2019</year>
<volume>17</volume>
<numero>1</numero>
<issue>1</issue>
<page-range>3069</page-range></nlm-citation>
</ref>
</ref-list>
</back>
</article>
