{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,2]],"date-time":"2026-02-02T20:42:23Z","timestamp":1770064943183,"version":"3.49.0"},"reference-count":48,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2017,9,27]],"date-time":"2017-09-27T00:00:00Z","timestamp":1506470400000},"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>Although a well-organized power system is less subject to blackouts, the existence of a proper restoration plan is nevertheless still essential. The goal of a restoration plan is to bring the power system back to its normal operating conditions in the shortest time after a blackout occurs and to minimize the impact of the blackout on society. This paper presents a decentralized multi-agent system (MAS)-based restoration method for a low voltage (LV) microgrid (MG). In the proposed method, the MG local controllers are assigned to the specific agents who interact with each other to achieve a common decision in the restoration procedure. The evaluation of the proposed decentralized technique using a benchmark low-voltage MG network demonstrates the effectiveness of the proposed restoration plan.<\/jats:p>","DOI":"10.3390\/en10101491","type":"journal-article","created":{"date-parts":[[2017,9,27]],"date-time":"2017-09-27T10:52:25Z","timestamp":1506509545000},"page":"1491","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":19,"title":["A Decentralized Multi-Agent-Based Approach for Low Voltage Microgrid Restoration"],"prefix":"10.3390","volume":"10","author":[{"given":"Ebrahim","family":"Rokrok","sequence":"first","affiliation":[{"name":"Centre for Mechanical and Aerospace Science and Technologies (C-MAST), University of Beira Interior, R. Fonte do Lameiro, 6201-001 Covilh\u00e3, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1691-5355","authenticated-orcid":false,"given":"Miadreza","family":"Shafie-khah","sequence":"additional","affiliation":[{"name":"Centre for Mechanical and Aerospace Science and Technologies (C-MAST), University of Beira Interior, R. Fonte do Lameiro, 6201-001 Covilh\u00e3, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0975-0241","authenticated-orcid":false,"given":"Pierluigi","family":"Siano","sequence":"additional","affiliation":[{"name":"Department of Industrial Engineering, University of Salerno, 84084 Fisciano (SA), Italy"}]},{"given":"Jo\u00e3o","family":"Catal\u00e3o","sequence":"additional","affiliation":[{"name":"Centre for Mechanical and Aerospace Science and Technologies (C-MAST), University of Beira Interior, R. Fonte do Lameiro, 6201-001 Covilh\u00e3, Portugal"},{"name":"Institute for Systems and Computer Engineering, Technology and Science (INESC TEC), Faculty of Engineering, University of Porto, 4200-465 Porto, Portugal"},{"name":"Institute for Systems and Computer Engineering, Research and Development (INESC-ID), Instituto Superior T\u00e9cnico, University of Lisbon, Av. Rovisco Pais, 1049-001 Lisbon, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2017,9,27]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"24","DOI":"10.1109\/MPE.2013.2285591","article-title":"No Light in August: Power System Restoration Following the 2003 North American Blackout","volume":"12","author":"Allen","year":"2014","journal-title":"IEEE Power Energy Mag."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1007\/s40565-013-0014-2","article-title":"Generalized congestion of power systems: Insights from the massive blackouts in India","volume":"1","author":"Xue","year":"2013","journal-title":"J. Mod. Power Syst. Clean Energy"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1419","DOI":"10.1109\/59.207363","article-title":"Special considerations in power system restoration","volume":"7","author":"Andrews","year":"1992","journal-title":"IEEE Trans. Power Syst."},{"key":"ref_4","unstructured":"Adibi, M.M. (2000). A Framework for Power System Restoration Following a Major Power Failure. Power System Restoration: Methodologies amp, Implementation Strategies, Wiley-IEEE Press."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"22","DOI":"10.1109\/59.317561","article-title":"Power system restoration planning","volume":"9","author":"Adibi","year":"1994","journal-title":"IEEE Trans. Power Syst."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1109\/67.75871","article-title":"Power system restoration issues","volume":"4","author":"Adibi","year":"1991","journal-title":"IEEE Comput. Appl. Power"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1592","DOI":"10.1109\/59.336099","article-title":"Expert system requirements for power system restoration","volume":"9","author":"Adibi","year":"1994","journal-title":"IEEE Trans. Power Syst."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"395","DOI":"10.1109\/TPWRS.2006.888989","article-title":"Using Low Voltage MicroGrids for Service Restoration","volume":"22","author":"Moreira","year":"2007","journal-title":"IEEE Trans. Power Syst."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1074","DOI":"10.1109\/JPROC.2011.2114630","article-title":"Smart Distribution: Coupled Microgrids","volume":"99","author":"Lasseter","year":"2011","journal-title":"Proc. IEEE"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1110","DOI":"10.1109\/TPWRS.2010.2080327","article-title":"Improving Service Restoration of Power Distribution Systems Through Load Curtailment of In-Service Customers","volume":"26","author":"Kleinberg","year":"2011","journal-title":"IEEE Trans. Power Syst."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"70","DOI":"10.1109\/MPE.2013.2286317","article-title":"Only Connect: Microgrids for Distribution System Restoration","volume":"12","author":"Liang","year":"2014","journal-title":"IEEE Power Energy Mag."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1480","DOI":"10.1109\/59.466500","article-title":"A framework for power system restoration following a major power failure","volume":"10","author":"Ancona","year":"1995","journal-title":"IEEE Trans. Power Syst."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"347","DOI":"10.1007\/s10107-015-0887-0","article-title":"Transmission system repair and restoration","volume":"151","author":"Coffrin","year":"2015","journal-title":"Math. Program."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"He, X., Liao, Z., Guo, W., Wen, F., Liang, J., and Fu, J. (2008, January 6\u20139). A multi-objective model for transmission network restoration based on multi-agent and tabu search. Proceedings of the Third International Conference on Electric Utility Deregulation and Restructuring and Power Technologies, Nanjing, China.","DOI":"10.1109\/DRPT.2008.4523813"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"10","DOI":"10.1002\/eej.20752","article-title":"Service restoration problem in distribution power system using improved ga","volume":"166","author":"Iwasaki","year":"2009","journal-title":"Electr. Eng. Jpn."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"398","DOI":"10.1109\/TPWRS.2008.2009477","article-title":"New Challenges in Power System Restoration with Large Scale of Dispersed Generation Insertion","volume":"24","author":"Pham","year":"2009","journal-title":"IEEE Trans. Power Syst."},{"key":"ref_17","unstructured":"Gu, X. (2006, January 18\u201322). Others Reconfiguration of network skeleton based on discrete particle-swarm optimization for black-start restoration. Proceedings of the Power Engineering Society General Meeting, Montreal, QC, Canada."},{"key":"ref_18","unstructured":"Liu, Q., Shi, L., Zhou, M., Li, G., and Ni, Y. (2008, January 6\u20139). A new solution to generators start-up sequence during power system restoration. Proceedings of the Third International Conference on Electric Utility Deregulation and Restructuring and Power Technologies, Nanjing, China."},{"key":"ref_19","unstructured":"Adibi, S.W.M. (2000). An Approach to Standing Phase Angle Reduction A report by the Power System Restoration Working Group. Power Syst. Restor. Methodol. Implement. Strateg., 142\u2013150."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Mota, A.A., Mota, L.T.M., and Morelato, A. (2006, January 18\u201322). Restoration building blocks identification using a heuristic search approach. Proceedings of the Power Engineering Society General Meeting, Montreal, QC, Canada.","DOI":"10.1109\/PES.2006.1709560"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"923","DOI":"10.1109\/59.708813","article-title":"Decision aid function for restoration of transmission power systems: conceptual design and real time considerations","volume":"13","author":"Kostic","year":"1998","journal-title":"IEEE Trans. Power Syst."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1327","DOI":"10.1002\/etep.404","article-title":"Service restoration on distribution systems using Multi-MicroGrids","volume":"21","author":"Resende","year":"2011","journal-title":"Eur. Trans. Electr. Power."},{"key":"ref_23","unstructured":"Choo, Y.C., Lai, K.X., Kashem, M.A., and Negnevitsky, M. (2005, January 25\u201328). MicroGrid (MV Network) restoration using distributed resources after major emergencies. Proceedings of the Australasian Universities Power Engineering Conference (AUPEC), Hobart, Tasmania, Australia."},{"key":"ref_24","unstructured":"Wooldridge, M. (2009). An Introduction to Multiagent Systems, John Wiley & Sons."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"514","DOI":"10.1007\/s10955-014-1140-6","article-title":"An Algorithmic Approach to Collective Behavior","volume":"158","author":"Chazelle","year":"2015","journal-title":"J. Stat. Phys."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1867","DOI":"10.1109\/TAC.2005.858670","article-title":"Agreement over random networks","volume":"50","author":"Hatano","year":"2005","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"4479","DOI":"10.1109\/TSP.2016.2568168","article-title":"Sampled-Data Consensus over Random Networks","volume":"64","author":"Wu","year":"2015","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"203","DOI":"10.5028\/jatm.v8i2.608","article-title":"Formation Flight Control of Multi-UAV System with Communication Constraints","volume":"8","author":"Xue","year":"2016","journal-title":"J. Aerosp. Technol. Manag."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Zhang, H., and Gurfil, P. (2016, January 21\u201324). Cooperative control of multiple satellites via consensus. Proceedings of the 24th Mediterranean Conference on Control and Automation (MED), Athens, Greece.","DOI":"10.1109\/MED.2016.7536011"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1212","DOI":"10.1109\/TRO.2013.2271101","article-title":"Epipolar Visual Servoing for Multirobot Distributed Consensus","volume":"29","author":"Montijano","year":"2013","journal-title":"IEEE Trans. Robot."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Grandi, R., Falconi, R., and Melchiorri, C. (2013, January 12\u201314). Coordination and control of autonomous mobile robot groups using a hybrid technique based on Particle Swarm Optimization and Consensus. Proceedings of the International Conference on Robotics and Biomimetics (ROBIO), Shenzhen, China.","DOI":"10.1109\/ROBIO.2013.6739681"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"562","DOI":"10.1049\/iet-gtd.2009.0146","article-title":"Adaptive voltage droop scheme for voltage source converters in an islanded multibus microgrid","volume":"4","author":"Rokrok","year":"2010","journal-title":"IET Gener. Transm. Distrib."},{"key":"ref_33","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_34","doi-asserted-by":"crossref","first-page":"1963","DOI":"10.1109\/TSG.2012.2197425","article-title":"Hierarchical Structure of Microgrids Control System","volume":"3","author":"Bidram","year":"2012","journal-title":"IEEE Trans. Smart Grid."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"916","DOI":"10.1109\/TPWRS.2006.873018","article-title":"Defining control strategies for microgrids islanded operation","volume":"21","author":"Lopes","year":"2006","journal-title":"IEEE Trans. Power Syst."},{"key":"ref_36","unstructured":"Nagpal, M., Moshref, A., Morison, G.K., and Kundur, P. (February, January 28). Experience with testing and modeling of gas turbines. Proceedings of the Power Engineering Society Winter Meeting, Columbus, OH, USA."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"405","DOI":"10.1016\/j.solener.2006.04.005","article-title":"Robust maximum power point tracker using sliding mode controller for the three-phase grid-connected photovoltaic system","volume":"81","author":"Kim","year":"2007","journal-title":"Sol. Energy."},{"key":"ref_38","unstructured":"Gonz\u00e1lez-Longatt, F., Amaya, O., Cooz, M., and Duran, L. (2007, January 2\u20134). Dynamic behavior of constant speed wt based on induction generator directly connected to grid. Proceedings of the 6th World Wind Energy Conference and Exhibition (WWEC), Buenos Aires, Argentina."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/S0378-7796(02)00033-0","article-title":"Development of models for analyzing the load-following performance of microturbines and fuel cells","volume":"62","author":"Zhu","year":"2002","journal-title":"Electr. Power Syst. Res."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"495","DOI":"10.1016\/S0378-7753(99)00430-9","article-title":"An integrated SOFC plant dynamic model for power systems simulation","volume":"86","author":"Padulles","year":"2000","journal-title":"J. Power Sources"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"797","DOI":"10.1016\/j.rser.2015.01.008","article-title":"Hierarchical control structure in microgrids with distributed generation: Island and grid-connected mode","volume":"44","author":"Palizban","year":"2015","journal-title":"Renew. Sustain. Energy Rev."},{"key":"ref_42","doi-asserted-by":"crossref","unstructured":"Wang, Y., Dong, X., Wang, B., Liu, J., and Guo, A.X. (April, January 31). Black start studies for micro-grids with distributed generators. Proceedings of the 12th IET International Conference on Developments in Power System Protection (DPSP 2014), Copenhagen, Denmark.","DOI":"10.1049\/cp.2014.0142"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"4734","DOI":"10.1109\/TPEL.2012.2199334","article-title":"Control of Power Converters in AC Microgrids","volume":"27","author":"Rocabert","year":"2012","journal-title":"IEEE Trans. Power Electron."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1016\/j.sysconle.2004.02.022","article-title":"Fast linear iterations for distributed averaging","volume":"53","author":"Xiao","year":"2004","journal-title":"Syst. Control Lett."},{"key":"ref_45","doi-asserted-by":"crossref","unstructured":"Marshall, A.W., Olkin, I., and Arnold, B.C. (2010). Doubly Stochastic Matrices. Inequalities: Theory of Majorization and Its Applications. Springer Series in Statistics, Springer.","DOI":"10.1007\/978-0-387-68276-1"},{"key":"ref_46","doi-asserted-by":"crossref","unstructured":"Horn, R.A., and Johnson, C.R. (2012). Matrix Analysis, Cambridge University Press. [2nd ed.].","DOI":"10.1017\/CBO9781139020411"},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1016\/j.jpdc.2006.08.010","article-title":"Distributed average consensus with least-mean-square deviation","volume":"67","author":"Xiao","year":"2007","journal-title":"J. Parallel Distrib. Comput."},{"key":"ref_48","unstructured":"Papathanassiou, S., Hatziargyriou, N., and Strunz, K. (2005, January 16\u201320). Others A benchmark low voltage microgrid network. Proceedings of the CIGRE Symposium: Power Systems with Dispersed Generation, Athens, Greece."}],"container-title":["Energies"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1996-1073\/10\/10\/1491\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T18:46:05Z","timestamp":1760208365000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1996-1073\/10\/10\/1491"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,9,27]]},"references-count":48,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2017,10]]}},"alternative-id":["en10101491"],"URL":"https:\/\/doi.org\/10.3390\/en10101491","relation":{},"ISSN":["1996-1073"],"issn-type":[{"value":"1996-1073","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,9,27]]}}}