{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,7]],"date-time":"2026-01-07T07:52:58Z","timestamp":1767772378656,"version":"build-2065373602"},"reference-count":29,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2021,6,22]],"date-time":"2021-06-22T00:00:00Z","timestamp":1624320000000},"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>This paper represents an adaptive continuous control set model predictive control (CCS-MPC) to solve the disturbance-caused instability problems in a DC microgrid consisting of symmetrical parallel buck converters, constant voltage loads (CVL), and constant power loads (CPL). The symmetric model of the system is founded at first to describe and analyze the disturbance-caused instability problem. To mitigate the instability by taking the disturbances into consideration, the proposed adaptive controller is made from a double loop feedback controller and a feedforward estimation algorithm. In the voltage loop of the double loop controller, a capacitor dynamic-based voltage controller is developed, while in the current loop, a CCS-MPC algorithm is modified and applied. Meanwhile, a feedforward algorithm is developed to estimate the disturbance information and send it to the double loop controller to improve its robustness, so the composite controller can maintain the bus voltage fixed at its reference and the symmetrical equal current sharing. Finally, comparative MATLAB simulations and OPAL-RT hardware-in-the-loop experiments are conducted to verify the effectiveness and dynamic performance of the proposed algorithm towards other previous nonlinear controllers.<\/jats:p>","DOI":"10.3390\/sym13071112","type":"journal-article","created":{"date-parts":[[2021,6,22]],"date-time":"2021-06-22T22:10:59Z","timestamp":1624399859000},"page":"1112","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Stabilization of Constant Power Loads in DC Microgrid Systems Using an Adaptive Continuous Control Set Model Predictive Control"],"prefix":"10.3390","volume":"13","author":[{"given":"Jiyao","family":"Zhou","sequence":"first","affiliation":[{"name":"State Key Laboratory of Reliability and Intelligence of Electrical Equipment, Hebei University of Technology, Tianjin 300130, China"},{"name":"Key Laboratory of Electromagnetic Field and Electrical Apparatus Reliability of Hebei Province, Hebei University of Technology, Tianjin 300130, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3232-8206","authenticated-orcid":false,"given":"Mustafa Alrayah","family":"Hassan","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering, National Kaohsiung University of Science and Technology, Kaohsiung 807618, Taiwan"},{"name":"Department of Electrical Engineering, University of Blue Nile, Damazeen 26613, Sudan"}]},{"given":"Jiaxuan","family":"Zhang","sequence":"additional","affiliation":[{"name":"State Grid International Development Co., Ltd., Beijing 100031, China"}]},{"given":"Mingxuan","family":"Hou","sequence":"additional","affiliation":[{"name":"Korqin District Power Supply Branch, East Inner Mongolia Electric Power Co., Ltd., States Grid, Tongliao 028000, China"}]},{"given":"Shang","family":"Wu","sequence":"additional","affiliation":[{"name":"State Grid Jibei Electric Power Co., Ltd., States Grid, Beijing 102488, China"}]},{"given":"Gaoqi","family":"Xing","sequence":"additional","affiliation":[{"name":"State Grid Zibo Power Supply Co., Zibo 255000, China"}]},{"given":"Song","family":"Chi","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Reliability and Intelligence of Electrical Equipment, Hebei University of Technology, Tianjin 300130, China"},{"name":"Key Laboratory of Electromagnetic Field and Electrical Apparatus Reliability of Hebei Province, Hebei University of Technology, Tianjin 300130, China"}]}],"member":"1968","published-online":{"date-parts":[[2021,6,22]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"54","DOI":"10.1109\/MPE.2008.918702","article-title":"Microgrids Management","volume":"6","author":"Katiraei","year":"2008","journal-title":"IEEE Power Energy Mag."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"925","DOI":"10.1109\/JESTPE.2017.2727578","article-title":"Guset Editorial Special Issue on Structured DC Microgrids","volume":"5","author":"Guerrero","year":"2017","journal-title":"IEEE J. Emerg. Sel. Top. Power Electron."},{"key":"ref_3","first-page":"4876","article-title":"DC Microgrids-Part I: A Review of Control Strategies and Stabilization Techniques","volume":"31","author":"Dragicevic","year":"2015","journal-title":"IEEE Trans. Power Electron."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"3528","DOI":"10.1109\/TPEL.2015.2464277","article-title":"DC Microgrids-Part II: A Review of Power Architectures, Applications, and Standardization Issues","volume":"31","author":"Dragicevic","year":"2015","journal-title":"IEEE Trans. Power Electron."},{"key":"ref_5","unstructured":"Donoso-Garcia, P.F., Cortizo, P.C., de Menezes, B.R., and Mendes, M.A.S. (1996, January 23\u201327). Sliding mode control for current distribution in DC-to-DC converters connected in parallel. Proceedings of the PESC Record. 27th Annual IEEE Power Electronics Specialists Conference, Baveno, Italy."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"407","DOI":"10.1016\/j.rser.2017.01.027","article-title":"Constant power loads and their effects in DC distributed power systems: A review","volume":"72","author":"Singh","year":"2017","journal-title":"Renew. Sustain. Energy Rev."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1112","DOI":"10.1109\/TVT.2006.877483","article-title":"Constant power loads and negative impedance instability in automotive systems: Definition, modeling, stability, and control of power electronic converters and motor drives","volume":"55","author":"Emadi","year":"2006","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"822","DOI":"10.1109\/TPEL.2010.2091285","article-title":"Dynamic behavior and stabilization of DC microgrids with instantaneous constant-power loads","volume":"26","author":"Kwasinski","year":"2011","journal-title":"IEEE Trans. Power Electron."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"3525","DOI":"10.1109\/TIA.2014.2309800","article-title":"Comprehensive review of stability criteria for DC power distribution systems","volume":"50","author":"Riccobono","year":"2014","journal-title":"IEEE Trans. Ind. Appl."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1832","DOI":"10.1109\/TPEL.2011.2151880","article-title":"Constant-power load system stabilization by passive damping","volume":"26","author":"Cespedes","year":"2011","journal-title":"IEEE Trans. Power Electron."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1843","DOI":"10.1109\/TPEL.2012.2211619","article-title":"Stability criterion for cascaded system with constant power load","volume":"28","author":"Du","year":"2013","journal-title":"IEEE Trans. Power Electron."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"2018","DOI":"10.1109\/TPEL.2010.2045658","article-title":"Analysis of boundary control for buck converters with instantaneous constant-power loads","volume":"25","author":"Onwuchekwa","year":"2010","journal-title":"IEEE Trans. Power Electron."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1448","DOI":"10.1109\/TIA.2013.2273751","article-title":"A sliding-mode duty-ratio controller for DC\/DC buck converters with constant power loads","volume":"50","author":"Zhao","year":"2013","journal-title":"IEEE Trans. Ind. Appl."},{"key":"ref_14","unstructured":"Kondratiev, I., Santi, E., Dougal, R., and Dougal, G. (2004, January 20\u201325). Synergetic control for DC-DC buck converters with constant power load. Proceedings of the IEEE 35th Annual Power Electronics Specialists Conference, Aachen, Germany."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"2029","DOI":"10.1109\/JESTPE.2018.2874449","article-title":"Adaptive passivity-based control of DC\u2013DC buck power converter with constant power load in DC microgrid systems","volume":"7","author":"Hassan","year":"2018","journal-title":"IEEE J. Emerg. Sel. Top. Power Electron."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"14","DOI":"10.1109\/MIE.2013.2290138","article-title":"Model predictive control: A review of its applications in power electronics","volume":"8","author":"Vazquez","year":"2014","journal-title":"IEEE Ind. Electron. Mag."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"935","DOI":"10.1109\/TIE.2016.2625238","article-title":"Model predictive control for power converters and drives: Advances and trends","volume":"64","author":"Vazquez","year":"2017","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1706","DOI":"10.1049\/iet-pel.2017.0835","article-title":"Composite adaptive model predictive control for DC\u2013DC boost converters","volume":"11","author":"Li","year":"2018","journal-title":"IET Power Electron."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"9064","DOI":"10.1109\/TPEL.2017.2785255","article-title":"Model predictive control for DC\u2013DC boost converters with reduced-prediction horizon and constant switching frequency","volume":"33","author":"Cheng","year":"2017","journal-title":"IEEE Trans. Power Electron."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"5331","DOI":"10.1109\/TPEL.2019.2941714","article-title":"An Offset-Free Composite Model Predictive Control Strategy for DC\/DC Buck Converter Feeding Constant Power Loads","volume":"35","author":"Xu","year":"2019","journal-title":"IEEE Trans. Power Electron."},{"key":"ref_21","first-page":"822","article-title":"Nonlinear Model Predictive Stabilization of DC\u2013DC Boost Converters with Constant Power Loads","volume":"9","author":"Tlacuahuac","year":"2020","journal-title":"IEEE J. Emerg. Sel. Top. Power Electron."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"451","DOI":"10.1109\/JESTPE.2019.2957231","article-title":"Decentralized Model Predictive Control of DC Microgrids with Constant Power Load","volume":"9","author":"Karami","year":"2019","journal-title":"IEEE J. Emerg. Sel. Top. Power Electron."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"901","DOI":"10.1109\/JESTPE.2018.2889971","article-title":"EKF-based predictive stabilization of shipboard DC microgrids with uncertain time-varying load","volume":"7","author":"Yousefizadeh","year":"2018","journal-title":"IEEE J. Emerg. Sel. Top. Power Electron."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"3128","DOI":"10.1109\/TPEL.2011.2179672","article-title":"Model predictive control of an AFE rectifier with dynamic references","volume":"27","author":"Quevedo","year":"2011","journal-title":"IEEE Trans. Power Electron."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"9122","DOI":"10.1109\/TPEL.2018.2822314","article-title":"A model predictive control for renewable energy based AC microgrids without any PID regulators","volume":"33","author":"Shan","year":"2018","journal-title":"IEEE Trans. Power Electron."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1823","DOI":"10.1109\/TSTE.2018.2873390","article-title":"Model predictive control of bidirectional DC-DC converters and AC\/DC interlinking converters-A new control method for PV-wind-battery microgrids","volume":"10","author":"Shan","year":"2018","journal-title":"IEEE Trans. Sustain. Energy"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"132","DOI":"10.1109\/TSTE.2014.2360628","article-title":"Adaptive droop control strategy for load sharing and circulating current minimization in low-voltage standalone DC microgrid","volume":"6","author":"Augustine","year":"2015","journal-title":"IEEE Trans. Sustain. Energy"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"4362","DOI":"10.1109\/TPEL.2017.2714342","article-title":"A decentralized current-sharing controller endows fast transient response to parallel DC-DC converters","volume":"33","author":"Wang","year":"2018","journal-title":"IEEE Trans. Power Electron."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"92393","DOI":"10.1109\/ACCESS.2020.2992780","article-title":"Constant power load stabilization in DC microgrid systems using passivity-based control with nonlinear disturbance observer","volume":"8","author":"Hassan","year":"2020","journal-title":"IEEE Access"}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/13\/7\/1112\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T06:21:20Z","timestamp":1760163680000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/13\/7\/1112"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,6,22]]},"references-count":29,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2021,7]]}},"alternative-id":["sym13071112"],"URL":"https:\/\/doi.org\/10.3390\/sym13071112","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2021,6,22]]}}}