{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:51:57Z","timestamp":1760147517141,"version":"build-2065373602"},"reference-count":25,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2023,2,10]],"date-time":"2023-02-10T00:00:00Z","timestamp":1675987200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["No. 62173278","KJQN202100228"],"award-info":[{"award-number":["No. 62173278","KJQN202100228"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Science and Technology Research Program of Chongqing Municipal Education Commission","award":["No. 62173278","KJQN202100228"],"award-info":[{"award-number":["No. 62173278","KJQN202100228"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>This paper proposes a charging strategy for plug-in electric vehicles (PEVs) in a smart charging station (SCS) that considers load constraints and time anxieties. Due to the rapidly growing load demand of PEVs and the load capacity investments in infrastructure, PEV charging needs to be subject to overload limits, beyond which failures can occur. The time anxiety is presented to address some of the uncertainties that may arise while charging PEVs. Under an aggregative game framework, this paper constructs a price-driven charging model to minimize costs by choosing the optimal charging strategy. Meanwhile, since the driver information is an aggregated item in the PEV cost function, the drivers\u2019 privacy can be protected. Then, a distributed reflected forward\u2013backward (RFB) splitting method is developed to search for the generalized Nash equilibria (GNE) of the game. The convergence of the proposed algorithm and the effectiveness of the charging strategy are verified by the detailed simulation and results.<\/jats:p>","DOI":"10.3390\/axioms12020186","type":"journal-article","created":{"date-parts":[[2023,2,13]],"date-time":"2023-02-13T02:14:11Z","timestamp":1676254451000},"page":"186","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Aggregative Game for Distributed Charging Strategy of PEVs in a Smart Charging Station"],"prefix":"10.3390","volume":"12","author":[{"given":"Ti","family":"Kang","sequence":"first","affiliation":[{"name":"Chongqing Key Laboratory of Nonlinear Circuits and Intelligent Information Processing, College of Electronic and Information Engineering, Southwest University, Chongqing 400715, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Huaqing","family":"Li","sequence":"additional","affiliation":[{"name":"Chongqing Key Laboratory of Nonlinear Circuits and Intelligent Information Processing, College of Electronic and Information Engineering, Southwest University, Chongqing 400715, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lifeng","family":"Zheng","sequence":"additional","affiliation":[{"name":"Chongqing Key Laboratory of Nonlinear Circuits and Intelligent Information Processing, College of Electronic and Information Engineering, Southwest University, Chongqing 400715, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,2,10]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Poornesh, K., Nivya, K.P., and Sireesha, K. (2020, January 10\u201312). A comparative study on electric vehicle and internal combustion engine vehicles. Proceedings of the 2020 International Conference on Smart Electronics and Communication (ICOSEC), Trichy, India.","DOI":"10.1109\/ICOSEC49089.2020.9215386"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"802","DOI":"10.1109\/TPWRS.2010.2057456","article-title":"Modeling of load demand due to EV battery charging in distribution systems","volume":"26","author":"Qian","year":"2010","journal-title":"IEEE Trans. Power Syst."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"644","DOI":"10.1016\/j.apenergy.2018.10.010","article-title":"Electric vehicles\u2019 impacts on residential electric local profiles\u2014A stochastic modelling approach considering socio-economic, behavioural and spatial factors","volume":"233","author":"Fischer","year":"2019","journal-title":"Appl. Energy"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1787","DOI":"10.1109\/TSG.2016.2599819","article-title":"A novel online charging algorithm for electric vehicles under stochastic net-load","volume":"9","author":"Bilh","year":"2016","journal-title":"IEEE Trans. Smart Grid"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"2959","DOI":"10.1109\/TSG.2018.2815689","article-title":"Extended Range Electric Vehicle With Driving Behavior Estimation in Energy Management","volume":"10","author":"Vatanparvar","year":"2019","journal-title":"IEEE Trans. Smart Grid"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1806","DOI":"10.1109\/TSG.2015.2403411","article-title":"Robust-index method for household load scheduling considering uncertainties of customer behavior","volume":"6","author":"Wang","year":"2015","journal-title":"IEEE Trans. Smart Grid"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"2422","DOI":"10.1109\/TII.2020.3003669","article-title":"Distributed electric vehicles charging management considering time anxiety and customer behaviors","volume":"17","author":"Alsabbagh","year":"2020","journal-title":"IEEE Trans. Ind. Inform."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"2096","DOI":"10.1109\/TSG.2017.2788440","article-title":"Optimized operational cost reduction for an EV charging station integrated with battery energy storage and PV generation","volume":"10","author":"Yan","year":"2018","journal-title":"IEEE Trans. Smart Grid"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"927","DOI":"10.1109\/TSTE.2014.2313765","article-title":"A multistage centralized control scheme for islanded microgrids with PEVs","volume":"5","author":"Abdelaziz","year":"2014","journal-title":"IEEE Trans. Sustain. Energy"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"52","DOI":"10.1109\/TSG.2016.2582749","article-title":"A Real-Time Charging Scheme for Demand Response in Electric Vehicle Parking Station","volume":"8","author":"Yao","year":"2017","journal-title":"IEEE Trans. Smart Grid"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"301","DOI":"10.1109\/TII.2016.2632761","article-title":"Noncooperative Game-Based Distributed Charging Control for Plug-In Electric Vehicles in Distribution Networks","volume":"14","author":"Li","year":"2018","journal-title":"IEEE Trans. Ind. Inform."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"940","DOI":"10.1109\/TPWRS.2012.2210288","article-title":"Optimal decentralized protocol for electric vehicle charging","volume":"28","author":"Gan","year":"2013","journal-title":"IEEE Trans. Power Syst."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1373","DOI":"10.1109\/TAC.2018.2849946","article-title":"Nash and wardrop equilibria in aggregative games with coupling constraints","volume":"64","author":"Paccagnan","year":"2018","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Savadkoohi, S.J.S., Kebriaei, H., and Aminifar, F. (2019, January 18\u201319). Aggregative Game for Charging Coordination of PEVs in a Network of Parking Lots. Proceedings of the 2019 Smart Grid Conference (SGC), Tehran, Iran.","DOI":"10.1109\/SGC49328.2019.9056619"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1386","DOI":"10.1109\/TCST.2017.2713321","article-title":"Data-Driven Charging Strategy of PEVs Under Transformer Aging Risk","volume":"26","author":"Li","year":"2018","journal-title":"IEEE Trans. Control. Syst. Technol."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"3483","DOI":"10.1109\/TII.2019.2950460","article-title":"Distributed Electric Vehicles Charging Management with Social Contribution Concept","volume":"16","author":"Alsabbagh","year":"2020","journal-title":"IEEE Trans. Ind. Inform."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Gadjov, D., and Pavel, L. (2019, January 11\u201313). Distributed GNE seeking over networks in aggregative games with coupled constraints via forward-backward operator splitting. Proceedings of the 2019 IEEE 58th Conference on Decision and Control (CDC), Nice, France.","DOI":"10.1109\/CDC40024.2019.9029369"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"163","DOI":"10.1007\/s11228-020-00542-4","article-title":"A reflected forward-backward splitting method for monotone inclusions involving Lipschitzian operators","volume":"29","author":"Cevher","year":"2021","journal-title":"Set-Valued Var. Anal."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Franci, B., Staudigl, M., and Grammatico, S. (2020, January 12\u201315). Distributed forward-backward (half) forward algorithms for generalized Nash equilibrium seeking. Proceedings of the 2020 European Control Conference (ECC), Saint Petersburg, Russia.","DOI":"10.23919\/ECC51009.2020.9143676"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"538","DOI":"10.1109\/TSG.2020.3020466","article-title":"Game theoretic-based distributed charging strategy for PEVs in a smart charging station","volume":"12","author":"Wan","year":"2020","journal-title":"IEEE Trans. Smart Grid"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Jasim, A.M., Jasim, B.H., Neagu, B.C., and Alhasnawi, B.N. (2023). Efficient Optimization Algorithm-Based Demand-Side Management Program for Smart Grid Residential Load. Axioms, 12.","DOI":"10.3390\/axioms12010033"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"969","DOI":"10.1109\/TII.2017.2781226","article-title":"A stochastic game approach for PEV charging station operation in smart grid","volume":"14","author":"Liu","year":"2017","journal-title":"IEEE Trans. Ind. Informatics"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"2044","DOI":"10.1109\/TCST.2015.2394319","article-title":"A distributed charging coordination for large-scale plug-in electric vehicles considering battery degradation cost","volume":"23","author":"Ma","year":"2015","journal-title":"IEEE Trans. Control. Syst. Technol."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"3527","DOI":"10.1109\/TAC.2016.2516240","article-title":"Decentralized Charging of Plug-in Electric Vehicles With Distribution Feeder Overload Control","volume":"61","author":"Ghavami","year":"2016","journal-title":"IEEE Trans. Autom. Control."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"283","DOI":"10.1016\/j.epsr.2017.05.042","article-title":"A demand power factor-based approach for finding the maximum loading point","volume":"151","author":"Contreras","year":"2017","journal-title":"Electr. Power Syst. Res."}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/12\/2\/186\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T18:30:49Z","timestamp":1760121049000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/12\/2\/186"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,2,10]]},"references-count":25,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2023,2]]}},"alternative-id":["axioms12020186"],"URL":"https:\/\/doi.org\/10.3390\/axioms12020186","relation":{},"ISSN":["2075-1680"],"issn-type":[{"type":"electronic","value":"2075-1680"}],"subject":[],"published":{"date-parts":[[2023,2,10]]}}}