{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,19]],"date-time":"2026-01-19T11:00:13Z","timestamp":1768820413459,"version":"3.49.0"},"reference-count":21,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2020,4,23]],"date-time":"2020-04-23T00:00:00Z","timestamp":1587600000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100007637","name":"Departamento Administrativo de Ciencia, Tecnolog\u00eda e Innovaci\u00f3n (COLCIENCIAS)","doi-asserted-by":"publisher","award":["727-2015"],"award-info":[{"award-number":["727-2015"]}],"id":[{"id":"10.13039\/100007637","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Here, we explore the possibility of employing proportional-integral passivity-based control (PI-PBC) to support active and reactive power in alternating current (AC) distribution networks by using a supercapacitor energy storage system. A direct power control approach is proposed by taking advantage of the Park\u2019s reference frame transform direct and quadrature currents (    i d     and     i q    ) into active and reactive powers (p and q). Based on the open-loop Hamiltonian model of the system, we propose a closed-loop PI-PBC controller that takes advantage of Lyapunov\u2019s stability to design a global tracking controller. Numerical simulations in MATLAB\/Simulink demonstrate the efficiency and robustness of the proposed controller, especially for parametric uncertainties.<\/jats:p>","DOI":"10.3390\/sym12040666","type":"journal-article","created":{"date-parts":[[2020,4,23]],"date-time":"2020-04-23T10:46:22Z","timestamp":1587638782000},"page":"666","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Direct Power Compensation in AC Distribution Networks with SCES Systems via PI-PBC Approach"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7609-1197","authenticated-orcid":false,"given":"Walter","family":"Gil-Gonz\u00e1lez","sequence":"first","affiliation":[{"name":"Laboratorio Inteligente de Energ\u00eda, Universidad Tecnol\u00f3gica de Bol\u00edvar, km 1 v\u00eda Turbaco, Cartagena 131001, Colombia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4467-7836","authenticated-orcid":false,"given":"Federico","family":"Martin Serra","sequence":"additional","affiliation":[{"name":"Laboratorio de Control Autom\u00e1tico (LCA), Universidad Nacional de San Luis, Villa Mercedes 5730, Argentina"}],"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":"Laboratorio Inteligente de Energ\u00eda, Universidad Tecnol\u00f3gica de Bol\u00edvar, km 1 v\u00eda Turbaco, Cartagena 131001, Colombia"},{"name":"Facultad de Ingenier\u00eda, Universidad Distrital Francisco Jos\u00e9 de Caldas, Carrera 7 No. 40B - 53, Bogot\u00e1 D.C 11021, Colombia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Carlos Alberto","family":"Ram\u00edrez","sequence":"additional","affiliation":[{"name":"Facultad de Ciencias B\u00e1sicas, Universidad Tecnol\u00f3gica de Pereira. AA: 97, Pereira 660003, Colombia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8184-6205","authenticated-orcid":false,"given":"C\u00e9sar","family":"Orozco-Henao","sequence":"additional","affiliation":[{"name":"Electrical and Electronic Engineering Department, Universidad del Norte, Barranquilla 080001, Colombia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,4,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Mensah-Darkwa, K., Zequine, C., Kahol, P.K., and Gupta, R.K. (2019). Supercapacitor energy storage device using biowastes: A sustainable approach to green energy. 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