{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,8]],"date-time":"2026-04-08T08:46:33Z","timestamp":1775637993276,"version":"3.50.1"},"reference-count":24,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2020,9,10]],"date-time":"2020-09-10T00:00:00Z","timestamp":1599696000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2020,9,10]],"date-time":"2020-09-10T00:00:00Z","timestamp":1599696000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Neural Comput &amp; Applic"],"published-print":{"date-parts":[[2021,2]]},"DOI":"10.1007\/s00521-020-05315-6","type":"journal-article","created":{"date-parts":[[2020,9,10]],"date-time":"2020-09-10T19:34:47Z","timestamp":1599766487000},"page":"973-983","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Distributed cooperative control algorithm for optimal power sharing for AC microgrids using Cournot game theory"],"prefix":"10.1007","volume":"33","author":[{"given":"Hong","family":"Zhou","sequence":"first","affiliation":[]},{"given":"Chang","family":"Yu","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2020,9,10]]},"reference":[{"issue":"11","key":"5315_CR1","doi-asserted-by":"publisher","first-page":"5906","DOI":"10.1109\/TII.2019.2908666","volume":"15","author":"J Lai","year":"2019","unstructured":"Lai J, Lu X, Yu X, Monti A (2019) Cluster-oriented distributed cooperative control for multiple AC microgrids. IEEE Trans Ind Inform 15(11):5906\u20135918","journal-title":"IEEE Trans Ind Inform"},{"issue":"4","key":"5315_CR2","doi-asserted-by":"publisher","first-page":"1905","DOI":"10.1109\/TSG.2013.2295514","volume":"5","author":"DE Olivares","year":"2014","unstructured":"Olivares DE, Sani AM, Etemadi AH et al (2014) Trends in microgrid control. IEEE Trans Smart Grid 5(4):1905\u20131919","journal-title":"IEEE Trans Smart Grid"},{"issue":"4","key":"5315_CR3","doi-asserted-by":"publisher","first-page":"882","DOI":"10.1109\/TEC.2014.2358612","volume":"29","author":"D Wu","year":"2014","unstructured":"Wu D, Tang F, Dragicevic T, Vasquez JC, Guerrero JM (2014) Autonomous active power control for islanded AC microgrids with photovoltaic generation and energy storage system. IEEE Trans Energy Convers 29(4):882\u2013892","journal-title":"IEEE Trans Energy Convers"},{"issue":"3","key":"5315_CR4","doi-asserted-by":"publisher","first-page":"1605","DOI":"10.1109\/TPEL.2014.2314721","volume":"30","author":"H Mahmood","year":"2014","unstructured":"Mahmood H, Michaelson D, Jiang J (2014) Accurate reactive power sharing in an islanded microgrid using adaptive virtual impedances. IEEE Trans Power Electron 30(3):1605\u20131617","journal-title":"IEEE Trans Power Electron"},{"issue":"1","key":"5315_CR5","doi-asserted-by":"publisher","first-page":"100","DOI":"10.1109\/TSMC.2019.2924612","volume":"50","author":"J Lai","year":"2020","unstructured":"Lai J, Lu X, Yu X, Monti A et al (2020) Distributed voltage regulation for cyber-physical microgrids with coupling delays and slow switching topologies. IEEE Trans Syst Man Cybern Syst 50(1):100\u2013110","journal-title":"IEEE Trans Syst Man Cybern Syst"},{"key":"5315_CR6","doi-asserted-by":"publisher","DOI":"10.1109\/TSG.2020.3005595","author":"X Lu","year":"2020","unstructured":"Lu X, Lai J (2020) Distributed cluster cooperation for multiple DC MGs over two-layer switching topologies. IEEE Trans Smart Grid. https:\/\/doi.org\/10.1109\/TSG.2020.3005595 (to be published)","journal-title":"IEEE Trans Smart Grid"},{"issue":"3","key":"5315_CR7","doi-asserted-by":"publisher","first-page":"1037","DOI":"10.1109\/TEC.2016.2552497","volume":"31","author":"Y Han","year":"2016","unstructured":"Han Y, Shen P, Zhao X, Guerrero JM (2016) An enhanced power sharing scheme for voltage unbalance and harmonics compensation in an islanded AC microgrid. IEEE Trans Energy Convers 31(3):1037\u20131050","journal-title":"IEEE Trans Energy Convers"},{"issue":"1","key":"5315_CR8","doi-asserted-by":"publisher","first-page":"158","DOI":"10.1109\/TIE.2010.2066534","volume":"58","author":"JM Guerrero","year":"2010","unstructured":"Guerrero JM, Vasquez JC, Matas J et al (2010) Hierarchical control of droop-controlled AC and DC microgrids\u2014a general approach toward standardization. IEEE Trans Ind Electron 58(1):158\u2013172","journal-title":"IEEE Trans Ind Electron"},{"issue":"3","key":"5315_CR9","doi-asserted-by":"publisher","first-page":"2427","DOI":"10.1109\/TPEL.2016.2569597","volume":"32","author":"Y Han","year":"2016","unstructured":"Han Y, Li H, Shen P et al (2016) Review of active and reactive power sharing strategies in hierarchical controlled microgrids. IEEE Trans Power Electron 32(3):2427\u20132451","journal-title":"IEEE Trans Power Electron"},{"issue":"1","key":"5315_CR10","doi-asserted-by":"publisher","first-page":"66","DOI":"10.1109\/MELE.2013.2297031","volume":"2","author":"L Che","year":"2014","unstructured":"Che L, Khodayar ME, Shahidehpour M (2014) Adaptive protection system for microgrids: protection practices of a functional microgrid system. IEEE Electrific Mag 2(1):66\u201380","journal-title":"IEEE Electrific Mag"},{"issue":"1","key":"5315_CR11","doi-asserted-by":"publisher","first-page":"40","DOI":"10.1109\/MELE.2013.2273994","volume":"1","author":"M Shahidehpour","year":"2013","unstructured":"Shahidehpour M, Khodayar M (2013) Cutting campus energy costs with hierarchical control: the economical and reliable operation of a microgrid. IEEE Electrific Mag 1(1):40\u201356","journal-title":"IEEE Electrific Mag"},{"issue":"4","key":"5315_CR12","doi-asserted-by":"publisher","first-page":"2746","DOI":"10.1109\/TSG.2020.2966691","volume":"11","author":"J Lai","year":"2020","unstructured":"Lai J, Lu X, Yu X, Monti A (2020) Stochastic distributed secondary control for AC microgrids via event-triggered communication. IEEE Trans Smart Grid 11(4):2746\u20132759","journal-title":"IEEE Trans Smart Grid"},{"issue":"4","key":"5315_CR13","doi-asserted-by":"publisher","first-page":"1761","DOI":"10.1109\/TPWRS.2012.2188912","volume":"27","author":"Z Zhang","year":"2012","unstructured":"Zhang Z, Chow MY (2012) Convergence analysis of the incremental cost consensus algorithm under different communication network topologies in a smart grid. IEEE Trans Power Syst 27(4):1761\u20131768","journal-title":"IEEE Trans Power Syst"},{"key":"5315_CR14","doi-asserted-by":"publisher","first-page":"126","DOI":"10.1016\/j.epsr.2013.11.023","volume":"114","author":"J Quesada","year":"2014","unstructured":"Quesada J, Sebastin R, Castro M et al (2014) Control of inverters in a low voltage microgrid with distributed battery energy storage. Part I: primary control. Electr Power Syst Res 114:126\u2013135","journal-title":"Electr Power Syst Res"},{"issue":"11","key":"5315_CR15","doi-asserted-by":"publisher","first-page":"7025","DOI":"10.1109\/TIE.2015.2436879","volume":"62","author":"JW Simpson-Porco","year":"2015","unstructured":"Simpson-Porco JW, Shafiee Q, D\u00f6rfler F et al (2015) Secondary frequency and voltage control of islanded microgrids via distributed averaging. IEEE Trans Ind Electron 62(11):7025\u20137038","journal-title":"IEEE Trans Ind Electron"},{"key":"5315_CR16","doi-asserted-by":"publisher","DOI":"10.1109\/TII.2020.2985905","author":"X Lu","year":"2020","unstructured":"Lu X, Lai J, Yu X (2020) A novel secondary power management strategy for multiple AC microgrids with cluster-oriented two-layer cooperative framework. IEEE Trans Ind Inform. https:\/\/doi.org\/10.1109\/TII.2020.2985905 (to be published)","journal-title":"IEEE Trans Ind Inform"},{"issue":"7","key":"5315_CR17","doi-asserted-by":"publisher","first-page":"4355","DOI":"10.1109\/TIE.2014.2379211","volume":"62","author":"F Guo","year":"2014","unstructured":"Guo F, Wen C, Mao J et al (2014) Distributed secondary voltage and frequency restoration control of droop-controlled inverter-based microgrids. IEEE Trans Ind Electron 62(7):4355\u20134364","journal-title":"IEEE Trans Ind Electron"},{"key":"5315_CR18","doi-asserted-by":"publisher","DOI":"10.1109\/TII.2020.2969458","author":"J Lai","year":"2020","unstructured":"Lai J, Lu X (2020) Nonlinear mean-square power sharing control for AC microgrids under distributed event detection. IEEE Trans Ind Inform. https:\/\/doi.org\/10.1109\/TII.2020.2969458 (to be published)","journal-title":"IEEE Trans Ind Inform"},{"key":"5315_CR19","doi-asserted-by":"crossref","unstructured":"Cheng M, Liu N (2017) Distributed energy management method for PV-assistant charging stations network: a non-cooperative game approach. In: 2017 12th IEEE conference on industrial electronics and applications (ICIEA). pp 439\u2013443","DOI":"10.1109\/ICIEA.2017.8282885"},{"issue":"2","key":"5315_CR20","doi-asserted-by":"publisher","first-page":"1510","DOI":"10.1109\/TSG.2019.2939586","volume":"11","author":"Y Fu","year":"2019","unstructured":"Fu Y, Zhang Z, Li Z et al (2019) Energy management for hybrid AC\/DC distribution system with microgrid clusters using non-cooperative game theory and robust optimization. IEEE Trans Smart Grid 11(2):1510\u20131525","journal-title":"IEEE Trans Smart Grid"},{"issue":"2","key":"5315_CR21","doi-asserted-by":"publisher","first-page":"748","DOI":"10.1109\/TSG.2014.2367494","volume":"6","author":"E Nekouei","year":"2014","unstructured":"Nekouei E, Alpcan T, Chattopadhyay D (2014) Game-theoretic frameworks for demand response in electricity markets. IEEE Trans Smart Grid 6(2):748\u2013758","journal-title":"IEEE Trans Smart Grid"},{"key":"5315_CR22","doi-asserted-by":"crossref","unstructured":"Sola M, Vitetta GM (2014) Demand-side management in a smart micro-grid: a distributed approach based on bayesian game theory. In: 2014 IEEE international conference on smart grid communications. pp 656\u2013661","DOI":"10.1109\/SmartGridComm.2014.7007722"},{"key":"5315_CR23","doi-asserted-by":"crossref","unstructured":"Brill E, Gonen A, Fligel E et al (2009) Empirical results about the nash-cournot equilibrium. In: 2009 IEEE international conference on industrial engineering and engineering management. pp 130\u2013134","DOI":"10.1109\/IEEM.2009.5373409"},{"key":"5315_CR24","doi-asserted-by":"crossref","unstructured":"D\u00f6rfler F, Bullo F (2012) Exploring synchronization in complex oscillator networks. In: 2012 IEEE 51st IEEE conference on decision and control. pp 7157\u20137170","DOI":"10.1109\/CDC.2012.6425823"}],"container-title":["Neural Computing and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00521-020-05315-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00521-020-05315-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00521-020-05315-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,9,10]],"date-time":"2021-09-10T00:35:30Z","timestamp":1631234130000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00521-020-05315-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,9,10]]},"references-count":24,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2021,2]]}},"alternative-id":["5315"],"URL":"https:\/\/doi.org\/10.1007\/s00521-020-05315-6","relation":{},"ISSN":["0941-0643","1433-3058"],"issn-type":[{"value":"0941-0643","type":"print"},{"value":"1433-3058","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,9,10]]},"assertion":[{"value":"26 May 2020","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"21 August 2020","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"10 September 2020","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Compliance with ethical standards"}},{"value":"The authors declare that they have no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}