{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,1]],"date-time":"2025-11-01T02:42:55Z","timestamp":1761964975614,"version":"build-2065373602"},"reference-count":34,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2018,5,6]],"date-time":"2018-05-06T00:00:00Z","timestamp":1525564800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Energies"],"abstract":"<jats:p>In this paper, the local control structure of a microgrid is partially modified by a Lyapunov-based controller. This controller is derived based on direct Lyapunov stability theory (DLST) in order to calculate proper switching functions for the stable operation of the local controller as well as proper local performance of each inverter-based distributed generation (DG) unit. The main contribution is the use of DLST-based controller in a hierarchical primary control structure along with a DC-side voltage regulator. A current-based droop controller is also introduced along with a voltage harmonic compensation technique. The control limits of droop equations are calculated based on steady-state and dynamic capability curve as well as voltage-frequency ellipse curve. The effect of the variations of voltages and circuit parameters on the capability curves are also investigated and the microgrid (MG) steady-state operation area is obtained. In the proposed method, the DC-voltage variations are regulated by an additional voltage control loop based on a current reference correction signal. The above-mentioned approaches are derived thoroughly with mathematical equations. The effectiveness of the designed controllers is verified by a MATLAB\/SIMULINK simulation platform (Matlab\/Simulink R2014a, Mathworks, Inc.) with harmonically distorted intermittent loads. The results show the appropriate performance of the proposed controllers during both steady-state and transient dynamic conditions.<\/jats:p>","DOI":"10.3390\/en11051161","type":"journal-article","created":{"date-parts":[[2018,5,7]],"date-time":"2018-05-07T03:12:21Z","timestamp":1525662741000},"page":"1161","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Direct-Lyapunov-Based Control Scheme for Voltage Regulation in a Three-Phase Islanded Microgrid with Renewable Energy Sources"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4121-7399","authenticated-orcid":false,"given":"Hadi Hosseini","family":"Kordkheili","sequence":"first","affiliation":[{"name":"Faculty of Electrical and Robotic Engineering, Shahrood University of Technology, Shahrood 3619995161, Iran"}]},{"given":"Mahdi","family":"Banejad","sequence":"additional","affiliation":[{"name":"Faculty of Electrical and Robotic Engineering, Shahrood University of Technology, Shahrood 3619995161, Iran"}]},{"given":"Ali Akbarzadeh","family":"Kalat","sequence":"additional","affiliation":[{"name":"Faculty of Electrical and Robotic Engineering, Shahrood University of Technology, Shahrood 3619995161, Iran"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2217-5293","authenticated-orcid":false,"given":"Edris","family":"Pouresmaeil","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering and Automation, Aalto University, 02150 Espoo, Finland"}]},{"given":"Jo\u00e3o P. S.","family":"Catal\u00e3o","sequence":"additional","affiliation":[{"name":"INESC TEC, Faculty of Engineering, University of Porto, Porto 4200-465, Portugal"},{"name":"C-MAST, University of Beira Interior, Covilh\u00e3 6201-001, Portugal"},{"name":"INESC-ID, Instituto Superior T\u00e9cnico, University of Lisbon, Lisbon 1049-001, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2018,5,6]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"724","DOI":"10.1016\/j.rser.2009.10.025","article-title":"Distributed energy resources and benefits to the environment","volume":"14","author":"Akorede","year":"2010","journal-title":"Renew. Sustain. Energy Rev."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"10","DOI":"10.1016\/j.epsr.2015.07.004","article-title":"A control plan for the stable operation of microgrids during grid-connected and islanded modes","volume":"129","author":"Mehrasa","year":"2015","journal-title":"Electr. Power Syst. 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