{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,21]],"date-time":"2026-03-21T02:44:48Z","timestamp":1774061088397,"version":"3.50.1"},"reference-count":34,"publisher":"Springer Science and Business Media LLC","issue":"11","license":[{"start":{"date-parts":[[2021,11,23]],"date-time":"2021-11-23T00:00:00Z","timestamp":1637625600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,11,23]],"date-time":"2021-11-23T00:00:00Z","timestamp":1637625600000},"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":["Soft Comput"],"published-print":{"date-parts":[[2022,6]]},"DOI":"10.1007\/s00500-021-06558-8","type":"journal-article","created":{"date-parts":[[2021,11,23]],"date-time":"2021-11-23T11:02:44Z","timestamp":1637665364000},"page":"5437-5455","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":18,"title":["Reinforced modified equilibrium optimization technique-based MS-PID frequency regulator for a hybrid power system with renewable energy sources"],"prefix":"10.1007","volume":"26","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0429-5542","authenticated-orcid":false,"given":"Amit","family":"Kumar","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Rajendra Kumar","family":"Khadanga","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sidhartha","family":"Panda","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2021,11,23]]},"reference":[{"key":"6558_CR1","doi-asserted-by":"publisher","first-page":"166","DOI":"10.1016\/j.ijepes.2015.11.029","volume":"77","author":"SM Abd-Elazim","year":"2016","unstructured":"Abd-Elazim SM, Ali ES (2016) Load frequency controller design via BAT algorithm for nonlinear interconnected power system. Int J Electr Power Energy Syst 77:166\u2013177","journal-title":"Int J Electr Power Energy Syst"},{"key":"6558_CR2","doi-asserted-by":"publisher","first-page":"607","DOI":"10.1007\/s00521-016-2668-y","volume":"30","author":"SM Abd-Elazim","year":"2018","unstructured":"Abd-Elazim SM, Ali ES (2018) Load frequency controller design of a two-area system composing of PV grid and thermal generator via firefly algorithm. Neural Comput Appl 30:607\u2013616","journal-title":"Neural Comput Appl"},{"key":"6558_CR3","doi-asserted-by":"publisher","first-page":"2497","DOI":"10.3390\/en11102497","volume":"11","author":"HH Alhelou","year":"2018","unstructured":"Alhelou HH, Hamedani-Golshan ME, Zamani R, Forushani EH, Siano P (2018) Challenges and Opportunities of Load Frequency Control in Conventional, Modern and Future Smart Power Systems: A Comprehensive Review. Energies 11:2497","journal-title":"Energies"},{"key":"6558_CR4","doi-asserted-by":"publisher","first-page":"682","DOI":"10.1016\/j.ijepes.2018.02.013","volume":"99","author":"HH Alhelouab","year":"2018","unstructured":"Alhelouab HH, Hamedani-Golshan ME, Askari-Marnania J (2018) Robust sensor fault detection and isolation scheme for interconnected smart power systems in presence of RER and EVs using unknown input observer. Int J Electr Power Energy Syst 99:682\u2013694","journal-title":"Int J Electr Power Energy Syst"},{"key":"6558_CR5","doi-asserted-by":"publisher","first-page":"224","DOI":"10.1016\/j.ijepes.2013.02.030","volume":"51","author":"ES Ali","year":"2013","unstructured":"Ali ES, Abd-Elazim SM (2013) BFOA based design of PID controller for two area load frequency control with nonlinearities\u2019. Int J Electr Power Energy Syst 51:224\u2013231","journal-title":"Int J Electr Power Energy Syst"},{"key":"6558_CR6","doi-asserted-by":"publisher","first-page":"90","DOI":"10.1080\/15325008.2015.1090502","volume":"44","author":"AY Almoataz","year":"2016","unstructured":"Almoataz AY, Ali ES (2016) Load frequency controller design via artificial cuckoo search algorithm. Electr Power Comp Syst 44:90\u201398","journal-title":"Electr Power Comp Syst"},{"issue":"11","key":"6558_CR7","doi-asserted-by":"publisher","first-page":"4583","DOI":"10.1016\/j.jfranklin.2018.05.001","volume":"355","author":"Y Arya","year":"2018","unstructured":"Arya Y (2018) AGC of two-area electric power systems using optimized fuzzy PID with filter plus double integral controller. J Franklin Inst 355(11):4583\u20134617","journal-title":"J Franklin Inst"},{"key":"6558_CR8","doi-asserted-by":"publisher","first-page":"376","DOI":"10.1109\/TPAS.1982.317117","volume":"2","author":"NN Benjamin","year":"1982","unstructured":"Benjamin NN, Chan WC (1982) Variable structure control of electric power generation. IEEE Trans Power Apparatus Syst 2:376\u2013380","journal-title":"IEEE Trans Power Apparatus Syst"},{"key":"6558_CR9","first-page":"706","volume":"7","author":"H Bevrani","year":"2016","unstructured":"Bevrani H, Feizi MR, Ataee S (2016) Robust frequency control in an Islanded microgrid: H\u221e and \u03bc-synthesis approaches. IEEE Trans Smart Grid 7:706\u2013717","journal-title":"IEEE Trans Smart Grid"},{"key":"6558_CR10","first-page":"687","volume":"5","author":"H Bing","year":"2016","unstructured":"Bing H, Zhou L, Yang F, Xiang Z (2016) Individual pitch controller based on fuzzy logic control for wind turbine load mitigation. IET Renew Power Gener 5:687\u2013693","journal-title":"IET Renew Power Gener"},{"key":"6558_CR11","volume-title":"Electric energy systems theory","author":"OI Elgerd","year":"2006","unstructured":"Elgerd OI (2006) Electric energy systems theory. Tata McGraw Hill, New Delhi"},{"key":"6558_CR12","doi-asserted-by":"publisher","first-page":"105","DOI":"10.1016\/j.knosys.2019.105190","volume":"191","author":"A Faramarzi","year":"2020","unstructured":"Faramarzi A, Heidarinejad M, Stephens B, Mirjalili S (2020) Equilibrium optimizer: A novel optimization algorithm. Knowl-Based Syst 191:105\u2013190","journal-title":"Knowl-Based Syst"},{"key":"6558_CR13","doi-asserted-by":"publisher","first-page":"257","DOI":"10.1016\/j.ijepes.2012.04.024","volume":"42","author":"D Fatemeh","year":"2012","unstructured":"Fatemeh D, Bevrani H (2012) Multiobjective design of load frequency control using genetic algorithms. Int J Electr Power Energy Syst 42:257\u2013263","journal-title":"Int J Electr Power Energy Syst"},{"key":"6558_CR14","doi-asserted-by":"publisher","first-page":"282","DOI":"10.1016\/j.isatra.2018.11.035","volume":"87","author":"A Fathy","year":"2018","unstructured":"Fathy A, Kassem AM (2018) Antlion optimizer-ANFIS load frequency control for multi-interconnected plants comprising photovoltaic and wind turbine. ISA Trans 87:282\u2013296","journal-title":"ISA Trans"},{"key":"6558_CR15","first-page":"677","volume":"1","author":"TS Gorripotu","year":"2015","unstructured":"Gorripotu TS, Sahu RK, Panda S (2015) Application of firefly algorithm for AGC under deregulated power system. Comput Intell Data Mining 1:677\u2013687","journal-title":"Comput Intell Data Mining"},{"key":"6558_CR16","first-page":"212","volume":"2","author":"N Hasan","year":"2012","unstructured":"Hasan N (2012) Design and analysis of pole-placement controller for interconnected power systems. Int J Emerg Technol Adv Eng 2:212\u2013217","journal-title":"Int J Emerg Technol Adv Eng"},{"key":"6558_CR17","doi-asserted-by":"publisher","first-page":"254","DOI":"10.1016\/j.ijepes.2015.03.017","volume":"71","author":"KM Hassan","year":"2015","unstructured":"Hassan KM, Niknam T (2015) A new intelligent online fuzzy tuning approach for multi-area load frequency control Self-Adaptive Modified Bat Algorithm. Int J Electr Power Energy Syst 71:254\u2013261","journal-title":"Int J Electr Power Energy Syst"},{"key":"6558_CR18","first-page":"853","volume":"9","author":"KM Hassan","year":"2017","unstructured":"Hassan KM, Niknam T, Shasadeghi M, Dragicevic T, Blaabjerg F (2017) Load frequency control in microgrids based on a stochastic non-integer controller. IEEE Trans Sustain Energy 9:853\u2013861","journal-title":"IEEE Trans Sustain Energy"},{"key":"6558_CR19","doi-asserted-by":"publisher","first-page":"3257","DOI":"10.1049\/iet-gtd.2016.1542","volume":"11","author":"RK Khadanga","year":"2016","unstructured":"Khadanga RK, Kumar A (2016) Hybrid adaptive \u2018gbest\u2019-guided gravitational search and pattern search algorithm for automatic generation control of multi-area power system. IET Gener Trans Distrib 11:3257\u20133267","journal-title":"IET Gener Trans Distrib"},{"key":"6558_CR20","doi-asserted-by":"publisher","first-page":"262","DOI":"10.1016\/j.ijepes.2015.03.014","volume":"7","author":"RK Khadanga","year":"2015","unstructured":"Khadanga RK, Satapathy JK (2015) Time delay approach for PSS and SSSC based coordinated controller design using hybrid PSO\u2013GSA algorithm. Int J Electr Power Energy Syst 7:262\u2013273","journal-title":"Int J Electr Power Energy Syst"},{"key":"6558_CR21","doi-asserted-by":"publisher","first-page":"1060","DOI":"10.1016\/j.ijepes.2015.07.016","volume":"73","author":"RK Khadanga","year":"2015","unstructured":"Khadanga RK, Satapathy JK (2015) A new hybrid GA\u2013GSA algorithm for tuning damping controller parameters for a unified power flow controller. Int J Electr Power Energy Syst 73:1060\u20131069","journal-title":"Int J Electr Power Energy Syst"},{"key":"6558_CR22","doi-asserted-by":"publisher","first-page":"2349","DOI":"10.1002\/jnm.2349","volume":"31","author":"RK Khadanga","year":"2018","unstructured":"Khadanga RK, Padhy S, Panda S, Kumar A (2018a) Design and analysis of multi-stage PID controller for frequency control in an islanded microgrid using a novel hybrid whale optimization-pattern search algorithm. Int J Numer Model: Electron Netw Devices Fields 31:2349","journal-title":"Int J Numer Model: Electron Netw Devices Fields"},{"key":"6558_CR23","doi-asserted-by":"publisher","first-page":"3103","DOI":"10.1007\/s13369-018-3151-0","volume":"43","author":"RK Khadanga","year":"2018","unstructured":"Khadanga RK, Padhy S, Panda S, Kumar A (2018b) Design and analysis of tilt integral derivative controller for frequency control in an islanded microgrid: A novel hybrid dragonfly and pattern search algorithm approach. Arab J Sci Eng 43:3103\u20133114","journal-title":"Arab J Sci Eng"},{"key":"6558_CR24","first-page":"1","volume":"13","author":"RK Khadanga","year":"2019","unstructured":"Khadanga RK, Kumar A, Panda S (2019) A novel modified whale optimization algorithm for load frequency controller design of a two-area power system composing of PV grid and thermal generator. Neural Comput Appl 13:1\u201312","journal-title":"Neural Comput Appl"},{"issue":"15","key":"6558_CR25","doi-asserted-by":"publisher","first-page":"3764","DOI":"10.1049\/iet-gtd.2016.0106","volume":"10","author":"PK Mohanty","year":"2016","unstructured":"Mohanty PK, Sahu BK, Pati TK, Panda S, Kar SK (2016) Design and analysis of fuzzy PID controller with derivative filter for AGC in multi area interconnected power system. IET Gener Trans Distrib 10(15):3764\u20133776","journal-title":"IET Gener Trans Distrib"},{"key":"6558_CR26","doi-asserted-by":"publisher","first-page":"2656","DOI":"10.1016\/j.enconman.2004.12.010","volume":"46","author":"Y Oysal","year":"2005","unstructured":"Oysal Y (2005) A comparative study of adaptive load frequency controller designs in a power system with dynamic neural network models. Energy Convers Manage 46:2656\u20132668","journal-title":"Energy Convers Manage"},{"key":"6558_CR27","doi-asserted-by":"publisher","first-page":"19","DOI":"10.1016\/j.isatra.2015.03.003","volume":"62","author":"I Pan","year":"2016","unstructured":"Pan I, Das S (2016) Fractional order fuzzy control of hybrid power system with renewable generation using chaotic PSO. ISA Trans 62:19\u201329","journal-title":"ISA Trans"},{"key":"6558_CR28","doi-asserted-by":"publisher","first-page":"4198","DOI":"10.35940\/ijitee.J1058.0881019","volume":"8","author":"BK Sahu","year":"2019","unstructured":"Sahu BK, Mohanty PK (2019) Design and implementation of fuzzy-PID controller with derivative filter for AGC of two-area interconnected hybrid power system. Int J Innov Technol Explor Eng 8:4198\u20134212","journal-title":"Int J Innov Technol Explor Eng"},{"key":"6558_CR29","doi-asserted-by":"publisher","first-page":"721","DOI":"10.1016\/j.asej.2014.02.004","volume":"5","author":"RK Sahu","year":"2014","unstructured":"Sahu RK, Panda S, Padhan S (2014) Optimal gravitational search algorithm for automatic generation control of interconnected power systems. Ain Shams Eng J 5:721\u2013733","journal-title":"Ain Shams Eng J"},{"key":"6558_CR30","doi-asserted-by":"publisher","first-page":"195","DOI":"10.1016\/j.ijepes.2015.07.025","volume":"74","author":"GC Sekhar","year":"2016","unstructured":"Sekhar GC, Sahu RK, Baliarsingh AK, Panda S (2016) Load frequency control of power system under deregulated environment using optimal firefly algorithm. Int J Electr Power Energy Syst 74:195\u2013211","journal-title":"Int J Electr Power Energy Syst"},{"key":"6558_CR31","doi-asserted-by":"publisher","first-page":"846","DOI":"10.1016\/j.epsr.2008.11.005","volume":"5","author":"W Tan","year":"2009","unstructured":"Tan W, Xu Z (2009) Robust analysis and design of load frequency controller for power systems. Electr Power Syst Res 5:846\u2013853","journal-title":"Electr Power Syst Res"},{"key":"6558_CR32","doi-asserted-by":"publisher","first-page":"996","DOI":"10.1016\/j.ijepes.2012.05.063","volume":"43","author":"W Tan","year":"2012","unstructured":"Tan W, Zhou H (2012) Robust analysis of decentralized load frequency control for multi-area power systems. Int J Electr Power Energy Syst 43:996\u20131005","journal-title":"Int J Electr Power Energy Syst"},{"key":"6558_CR33","doi-asserted-by":"publisher","first-page":"157","DOI":"10.1016\/j.apenergy.2016.12.080","volume":"189","author":"X Zhang","year":"2017","unstructured":"Zhang X, Chen Y, Yu T, Yang B, Qu K, Mao S (2017) Equilibrium-inspired multiagent optimizer with extreme transfer learning for decentralized optimal carbon-energy combined-flow of large-scale power systems. Appl Energy 189:157\u2013176","journal-title":"Appl Energy"},{"key":"6558_CR34","doi-asserted-by":"publisher","first-page":"3534","DOI":"10.1109\/TPWRS.2013.2259641","volume":"28","author":"B Zhou","year":"2013","unstructured":"Zhou B, Chan KW, Yu T, Chung CY (2013) Equilibrium-inspired multiple group search optimization with synergistic learning for multiobjective electric power dispatch. IEEE Trans Power Syst 28:3534\u20133545","journal-title":"IEEE Trans Power Syst"}],"container-title":["Soft Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00500-021-06558-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00500-021-06558-8\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00500-021-06558-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,5,13]],"date-time":"2022-05-13T11:13:08Z","timestamp":1652440388000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00500-021-06558-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,11,23]]},"references-count":34,"journal-issue":{"issue":"11","published-print":{"date-parts":[[2022,6]]}},"alternative-id":["6558"],"URL":"https:\/\/doi.org\/10.1007\/s00500-021-06558-8","relation":{},"ISSN":["1432-7643","1433-7479"],"issn-type":[{"value":"1432-7643","type":"print"},{"value":"1433-7479","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,11,23]]},"assertion":[{"value":"11 November 2021","order":1,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"23 November 2021","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors have no conflicts of interest with any person.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}