{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,30]],"date-time":"2026-01-30T04:39:34Z","timestamp":1769747974419,"version":"3.49.0"},"reference-count":45,"publisher":"MDPI AG","issue":"19","license":[{"start":{"date-parts":[[2021,9,29]],"date-time":"2021-09-29T00:00:00Z","timestamp":1632873600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100002322","name":"Coordena\u00e7\u00e3o de Aperfei\u00e7oamento de Pessoal de N\u00edvel Superior","doi-asserted-by":"publisher","award":["001"],"award-info":[{"award-number":["001"]}],"id":[{"id":"10.13039\/501100002322","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Energies"],"abstract":"<jats:p>Electric forklifts are extremely important for the world\u2019s logistics and industry. Lead acid batteries are the most common energy storage system for electric forklifts; however, to ensure more energy efficiency and less environmental pollution, they are starting to use lithium batteries. All lithium batteries need a battery management system (BMS) for safety, long life cycle and better efficiency. This system is capable to estimate the battery state of charge, state of health and state of function, but those cannot be measured directly and must be estimated indirectly using battery models. Consequently, accurate battery models are essential for implementation of advance BMS and enhance its accuracy. This work presents a comparison between four different models, four different types of optimizers algorithms and seven different experiment designs. The purpose is defining the best model, with the best optimizer, and the best experiment design for battery parameter estimation. This best model is intended for a state of charge estimation on a battery applied on an electric forklift. The nonlinear grey box model with the nonlinear least square method presented a better result for this purpose. This model was estimated with the best experiment design which was defined considering the fit to validation data, the parameter standard deviation and the output variance. With this approach, it was possible to reach more than 80% of fit in different validation data, a non-biased and little prediction error and a good one-step ahead result.<\/jats:p>","DOI":"10.3390\/en14196221","type":"journal-article","created":{"date-parts":[[2021,9,29]],"date-time":"2021-09-29T08:27:44Z","timestamp":1632904064000},"page":"6221","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["Battery Model Identification Approach for Electric Forklift Application"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0677-4870","authenticated-orcid":false,"given":"Cynthia Thamires","family":"da Silva","sequence":"first","affiliation":[{"name":"PEA\u2014Polytechnic School (POLI-USP), University of S\u00e3o Paulo, 05508-010 S\u00e3o Paulo, Brazil"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9037-4799","authenticated-orcid":false,"given":"Bruno Martin de Alc\u00e2ntara","family":"Dias","sequence":"additional","affiliation":[{"name":"PEA\u2014Polytechnic School (POLI-USP), University of S\u00e3o Paulo, 05508-010 S\u00e3o Paulo, Brazil"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7866-9068","authenticated-orcid":false,"given":"Rui Esteves","family":"Ara\u00fajo","sequence":"additional","affiliation":[{"name":"INESC TEC, Faculty of Engineering, University of Porto, 4200-465 Porto, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3780-0477","authenticated-orcid":false,"given":"Eduardo Lorenzetti","family":"Pellini","sequence":"additional","affiliation":[{"name":"PEA\u2014Polytechnic School (POLI-USP), University of S\u00e3o Paulo, 05508-010 S\u00e3o Paulo, Brazil"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0085-1927","authenticated-orcid":false,"given":"Armando Ant\u00f4nio Maria","family":"Lagan\u00e1","sequence":"additional","affiliation":[{"name":"PEA\u2014Polytechnic School (POLI-USP), University of S\u00e3o Paulo, 05508-010 S\u00e3o Paulo, Brazil"}]}],"member":"1968","published-online":{"date-parts":[[2021,9,29]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1057","DOI":"10.1016\/j.electacta.2018.11.134","article-title":"A Comparative Study of Global Optimization Methods for Parameter Identification of Different Equivalent Circuit Models for Li-Ion Batteries","volume":"295","author":"Lai","year":"2019","journal-title":"J. Electrochim. Acta"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1298","DOI":"10.1109\/TIE.2017.2714118","article-title":"Dynamic Model of Li-Ion Batteries Incorporating Electrothermal and Ageing Aspects for Electric Vehicle Applications","volume":"65","author":"Mesbahi","year":"2018","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Tran, N., Khan, A.B., Nguyen, T., Kim, D., and Choi, W. (2018). SOC Estimation of Multiple Lithium-Ion Battery Cells in a Module Using a Nonlinear State Observer and Online Parameter Estimation. Energies, 11.","DOI":"10.3390\/en11071620"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1109\/TEC.2018.2861994","article-title":"State of Charge Estimation for Li-Ion Batteries: A More Accurate Hybrid Approach","volume":"34","author":"Misyris","year":"2019","journal-title":"IEEE Trans. Energy Convers."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Paul, T., Mesbahi, T., Durand, S., Flieller, D., and Uhring, W. (2020). Sizing of Lithium-Ion Battery\/Supercapacitor Hybrid Energy Storage System for Forklift Vehicle. Energies, 13.","DOI":"10.3390\/en13174518"},{"key":"ref_6","unstructured":"Alshaebi, A., Dauod, H., Weiss, J., and Yoon, S.W. (2017, January 20\u201323). Evaluation of Different Forklift Battery Systems Using Statistical Analysis and Discrete Event Simulation. Proceedings of the 2017 Industrial and Systems Engineering Conference, Pittsburgh, PA, USA."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"16","DOI":"10.1049\/iet-est.2018.5036","article-title":"Hybrid Battery-Supercapacitor System for Full Electric Forklifts","volume":"9","author":"Dezza","year":"2019","journal-title":"IET Electr. Syst. Transp."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"275","DOI":"10.1016\/j.autcon.2013.05.021","article-title":"Forklift with a Lithium-Titanate Battery during a Lifting\/Lowering Cycle: Analysis of the Recuperation Capability","volume":"35","author":"Minav","year":"2013","journal-title":"Autom. Constr."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Yu, Y.X., and Ahn, K.K. (2019, January 15\u201318). Energy Saving of an Electric Forklift with Hydraulic Accumulator. Proceedings of the 2019 19th International Conference on Control, Automation and Systems (ICCAS), Jeju, Korea.","DOI":"10.23919\/ICCAS47443.2019.8971761"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"523","DOI":"10.1007\/s10800-014-0669-z","article-title":"Hybrid Battery-Supercapacitor Storage for an Electric Forklift: A Life-Cycle Cost Assessment","volume":"44","author":"Conte","year":"2014","journal-title":"J. Appl. Electrochem."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"239","DOI":"10.1016\/j.jpowsour.2016.03.058","article-title":"Performance of Electric Forklift with Low-Temperature Polymer Exchange Membrane Fuel Cell Power Module and Metal Hydride Hydrogen Storage Extension Tank","volume":"316","author":"Lototskyy","year":"2016","journal-title":"J. Power Sources"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"10449","DOI":"10.20964\/2016.12.56","article-title":"Design and Performance Evaluation of a PEM Fuel Cell\u2014Lithium Battery\u2014Supercapacitor Hybrid Power Source for Electric Forklifts","volume":"11","author":"Hsieh","year":"2016","journal-title":"Int. J. Electrochem. Sci."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Jiao, M., Pan, F., Huang, X., and Yuan, X. (2021, January 28\u201330). Evaluation on Total Cost of Ownership of Electric Forklifts with Lithium-Ion Battery. Proceedings of the 2021 IEEE 4th International Electrical and Energy Conference (CIEEC), Wuhan, China.","DOI":"10.1109\/CIEEC50170.2021.9510828"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1825","DOI":"10.1109\/TCST.2016.2616380","article-title":"Data Driven Nonlinear Identification of Li-Ion Battery Based on a Frequency Domain Nonparametric Analysis","volume":"25","author":"Relan","year":"2017","journal-title":"IEEE Trans. Control Syst. Technol."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1008","DOI":"10.1016\/j.rser.2015.12.009","article-title":"A Review on Electric Vehicle Battery Modelling: From Lithium-ion toward Lithium-Sulphur","volume":"56","author":"Fotouhi","year":"2016","journal-title":"J. Renew. Sustain. Energy Rev."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"28","DOI":"10.1109\/MCS.2019.2938121","article-title":"Nonlinear System Identification\u2014A User Oriented Road Map","volume":"39","author":"Schoukens","year":"2019","journal-title":"IEEE Control Syst. Mag."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Ljung, L. (1999). System Identification. Theory for the User, Prentice Hall. [2nd ed.].","DOI":"10.1002\/047134608X.W1046"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"359","DOI":"10.1016\/j.jpowsour.2011.10.013","article-title":"A Comparative Study of Equivalent Circuit Models for Li-Ion Batteries","volume":"198","author":"Hu","year":"2012","journal-title":"J. Power Sources"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"5887","DOI":"10.1109\/TII.2020.3047687","article-title":"Signal-Disturbance Interfacing Elimination for Unbiased Model Parameter Identification of Lithium-Ion Battery","volume":"17","author":"Wei","year":"2020","journal-title":"IEEE Trans. Ind. Inform."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1007\/BF01211648","article-title":"Prediction Error Estimation Methods","volume":"21","author":"Ljung","year":"2002","journal-title":"Circuits Syst. Signal Process."},{"key":"ref_21","unstructured":"Bradley, S.P., Hax, A.C., and Thomas, L.M. (1977). Applied Mathematical Programming, Addison Wesley Publishing Company. [5st ed.]."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Rahimi-Eichi, H., Baronti, F., and Chow, M.Y. (2012, January 28\u201331). Modeling and Online Parameter Identification of Li-Polymer Battery Cells for SOC Estimation. Proceedings of the IEEE International Symposium on Industrial Electronics, Hangzhou, China.","DOI":"10.1109\/ISIE.2012.6237284"},{"key":"ref_23","first-page":"281","article-title":"Fractional Modeling and SOC Estimation of Lithium-ion Battery","volume":"3","author":"Ma","year":"2016","journal-title":"J. Autom. Sin."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Firouz, Y., Mierlo, V.J., and Bossche, P.V. (2019, January 16\u201318). Nonlinear Modeling of all Solid-State Battery Technology based on Hammerstein Wiener Systems. Proceedings of the IEEE Electrical Power and Energy Conference, Montreal, QC, Canada.","DOI":"10.1109\/EPEC47565.2019.9074779"},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Navid, Q., and Hassan, A. (2019). An Accurate and Precise Grey Box Model of a Low-Power Lithium-Ion Battery and Capacitor\/Supercapacitor for Accurate Estimation of State of Charge. Batteries, 5.","DOI":"10.3390\/batteries5030050"},{"key":"ref_26","unstructured":"Gavin, H. (2020). The Levenberg-Marquardt Algorithm for Nonlinear Least Squares Curve-Fitting Problems, Department of Civil and Environmental Engineering, Duke University. Available online: http:\/\/people.duke.edu\/~hpgavin\/ce281\/lm.pdf."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"217","DOI":"10.1007\/s10589-015-9734-8","article-title":"Parameter Identification for Nonlinear Elliptic-Parabolic Systems with Application in Lithium-Ion Battery Modeling","volume":"62","author":"Lass","year":"2015","journal-title":"Comput. Optim. Appl."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1620","DOI":"10.1002\/ente.201600154","article-title":"Analysis of a Lithium-Ion Battery Model Based on Electrochemical Impedance Spectroscopy","volume":"4","author":"Westerhoff","year":"2016","journal-title":"Energy Technol."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"417","DOI":"10.1016\/j.jpowsour.2007.12.083","article-title":"Optimal Battery\/Ultracapacitor Storage Combination","volume":"179","author":"Henson","year":"2008","journal-title":"J. Power Sources"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"2396","DOI":"10.1109\/TSG.2019.2953718","article-title":"Battery Model Parameterization Using Manufacturer Datasheet and Field Measurement for Real-Time HIL Applications","volume":"11","author":"Xie","year":"2020","journal-title":"IEEE Trans. Smart Grid."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Liao, C., Li, H., and Wang, L. (2009, January 7\u201310). A Dynamic Equivalent Circuit Model of LiFePO4 Cathod Material for Lithium-Ion Batteries on Hybrid Electric Vehicles. Proceedings of the IEEE Vehicle Power and Propulsion Conference, Dearborn, MI, USA.","DOI":"10.1109\/VPPC.2009.5289681"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"266","DOI":"10.1016\/j.jpowsour.2003.12.001","article-title":"Rapid Test and Non-Linear Model Characterization of Solid-State Lithium-Ion Batteries","volume":"130","author":"Doerffel","year":"2004","journal-title":"J. Power Sources"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"504","DOI":"10.1109\/TEC.2006.874229","article-title":"Accurate Electrical Battery Model Capable of Predicting Runtime and IV Performance","volume":"21","author":"Chen","year":"2006","journal-title":"IEEE Trans. Energy Convers."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"582","DOI":"10.3390\/en4040582","article-title":"Evaluation of Lithium-Ion Battery Equivalent Circuit Models for State of Charge Estimation by an Experimental Approach","volume":"4","author":"He","year":"2011","journal-title":"Energies"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"413","DOI":"10.1016\/j.apenergy.2011.08.005","article-title":"Online Estimation of Model Parameters and State of Charge of LiFePO4 Batteries in Electric Vehicles","volume":"89","author":"He","year":"2012","journal-title":"Appl. Energy"},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Huria, T., Ceraolo, M., Gazzarri, J., and Jackey, R. (2012, January 4\u20138). High Fidelity Electrical Model with Thermal Dependence for Characterization and Simulation of High-Power Lithium Battery Cells. Proceedings of the IEEE International Electric Vehicle Conference, Greenville, SC, USA.","DOI":"10.1109\/IEVC.2012.6183271"},{"key":"ref_37","unstructured":"Rahmoun, A., and Biechl, H. (2012, January 16\u201321). Parameters Identification of Equivalent Circuit Diagrams for Li-Ion Batteries. Proceedings of the 2012 11th International Symposium, P\u00e4rnu, Estonia."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"4572","DOI":"10.3390\/en6094572","article-title":"Optimization of Experimental Model Parameter Identification for Energy Storage Systems","volume":"6","author":"Gallo","year":"2013","journal-title":"Energies"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"2053","DOI":"10.1109\/TIE.2013.2263774","article-title":"Online Adaptive Parameter Identification and State of Charge Coestimation for Lithium-Polymer Battery Cells","volume":"61","author":"Baronti","year":"2014","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_40","unstructured":"Santos, S.R., Marques, F.L.R., Nascimento, T.C., and Beck, R. (, January October). A Brief Overview of Battery Management Systems for Lithium-Ion Batteries: Modeling, Estimation and Control. Proceedings of the 10th Seminar on Power Electronics and Control, Santa Maria, Brazil."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"312","DOI":"10.1109\/TIE.2019.2962429","article-title":"Noise-Immune Model Identification and State-of-Charge Estimation for Lithium-Ion Battery Using Bilinear Parameterization","volume":"68","author":"Wei","year":"2021","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_42","unstructured":"Matos, M.R.S. (2010). Study and Parameter Estimation of an Electric Battery Model. [Master\u2019s Thesis, Department of Electrical and Computer Engineering, University of Porto]."},{"key":"ref_43","unstructured":"Rice, J.A. (2007). Mathematical Statistics and Data Analysis, Thomson Higher Education. [3rd ed.]."},{"key":"ref_44","unstructured":"Johnson, R.A., and Wichern, D.W. (2007). Applied Multivariate Statistical Analysis, Prentice Hall. [6th ed.]."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"106","DOI":"10.1137\/050624935","article-title":"Approximate Gauss-Newton Methods for Nonlinear Least Squares Problems","volume":"18","author":"Gratton","year":"2007","journal-title":"SIAM J. Optim."}],"container-title":["Energies"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1996-1073\/14\/19\/6221\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T07:07:13Z","timestamp":1760166433000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1996-1073\/14\/19\/6221"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,9,29]]},"references-count":45,"journal-issue":{"issue":"19","published-online":{"date-parts":[[2021,10]]}},"alternative-id":["en14196221"],"URL":"https:\/\/doi.org\/10.3390\/en14196221","relation":{},"ISSN":["1996-1073"],"issn-type":[{"value":"1996-1073","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,9,29]]}}}