{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,12]],"date-time":"2026-05-12T04:49:01Z","timestamp":1778561341903,"version":"3.51.4"},"reference-count":24,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2022,11,14]],"date-time":"2022-11-14T00:00:00Z","timestamp":1668384000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Jiangsu Engineering Technology Research Center for Energy Storage Conversion and Application","award":["NY80-22-002"],"award-info":[{"award-number":["NY80-22-002"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>A variable fractional-order equivalent circuit model is proposed to accurately describe the dynamic characteristics of lithium-ion batteries (LIBs). Firstly, a fractional impedance model (FIM) is established, such that the fractional-order (FO) is a polynomial function of the LIB state of charge (SOC). Then, a chaotic adaptive fractional particle swarm optimization (CAFPSO) method is derived to identify the parameters of the FIM. Experiments reveal the reliability of the novel approach through the root-mean-squared error (RMSE) and the mean absolute error (MAE) of the LIB terminals voltage, yielding the values 8.99 mV and 4.56 mV, respectively. This translates into accuracy improvements of 22.5% and 34.4% for the particle swarm optimization (PSO) algorithm and 57.9% and 72.8% for the adaptive fractional particle swarm optimization (AFPSO) algorithm, respectively.<\/jats:p>","DOI":"10.3390\/sym14112407","type":"journal-article","created":{"date-parts":[[2022,11,14]],"date-time":"2022-11-14T02:34:58Z","timestamp":1668393298000},"page":"2407","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Variable Fractional-Order Equivalent Circuit Model for Lithium-Ion Battery via Chaotic Adaptive Fractional Particle Swarm Optimization Method"],"prefix":"10.3390","volume":"14","author":[{"given":"Deshun","family":"Wang","sequence":"first","affiliation":[{"name":"School of Automation, Southeast University, Nanjing 210096, China"},{"name":"State Grid Shanghai Energy Interconnection Research Institute Co., Ltd., Shanghai 201203, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6667-3166","authenticated-orcid":false,"given":"Haikun","family":"Wei","sequence":"additional","affiliation":[{"name":"School of Automation, Southeast University, Nanjing 210096, China"}]},{"given":"Jinhua","family":"Xue","sequence":"additional","affiliation":[{"name":"State Grid Shanghai Energy Interconnection Research Institute Co., Ltd., Shanghai 201203, China"}]},{"given":"Fubao","family":"Wu","sequence":"additional","affiliation":[{"name":"Jiangsu Engineering Technology Research Center for Energy Storage Conversion and Application, China Electric Power Research Institute, Nanjing 210003, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7359-4370","authenticated-orcid":false,"given":"Ant\u00f3nio M.","family":"Lopes","sequence":"additional","affiliation":[{"name":"LAETA\/INEGI, Faculty of Engineering, University of Porto, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2022,11,14]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"274","DOI":"10.1016\/j.jpowsour.2018.07.116","article-title":"Recycling of lithium-ion batteries: Recent advances and perspectives","volume":"399","author":"Huang","year":"2018","journal-title":"J. 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