Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Fractional Calculus and Applied Analysis

Editor-in-Chief: Kiryakova, Virginia


IMPACT FACTOR 2018: 3.514
5-year IMPACT FACTOR: 3.524

CiteScore 2018: 3.44

SCImago Journal Rank (SJR) 2018: 1.891
Source Normalized Impact per Paper (SNIP) 2018: 1.808

Mathematical Citation Quotient (MCQ) 2018: 1.08

Online
ISSN
1314-2224
See all formats and pricing
More options …
Volume 22, Issue 6

Issues

State-of-art survey of fractional order modeling and estimation methods for lithium-ion batteries

YaNan Wang
  • Power Electronics and Mechatronics, Control Laboratory, Dept. of Automation, Beijing Institute of Technology, Beijing, 100081, China
  • Email
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ YangQuan Chen
  • Mechatronics, Embedded Systems and Automation Laboratory, Dept. of Engineering, University of California, Merced, CA 95343, USA
  • Email
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ XiaoZhong Liao
  • Power Electronics and Mechatronics, Control Laboratory, Dept. of Automation, Beijing Institute of Technology, Beijing, 100081, China
  • Email
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2019-12-31 | DOI: https://doi.org/10.1515/fca-2019-0076

Abstract

This paper presents a state-of-art survey of the research on fractional-order (FO) modeling with parameter identification, and FO estimation methods for state of charge (SOC), state of health (SOH), and remaining usage life (RUL) of lithium-ion batteries (LIBs) mainly in recent five years. FO electrochemical models and six different types of FO equivalent circuit models (ECMs) are introduced in detail. Then, the corresponding tuning algorithm for parameters of these FO models are also provided in brief. Moreover, FO estimation methods for SOC are listed and analyzed, mainly including FO observers, and FO Kalman filters (FO-KFs). SOH and RUL estimation is another vital aspect for LIBs ageing and degradation monitoring, thus FO estimation methods proposed in recent research within five years are all listed. Finally, some suggestions that may be helpful for further research are proposed in conclusion.

MSC 2010: Primary 26A33; Secondary 34A08; 60G22; 93A30; 93C95; 93E10; 93E12

Key Words and Phrases: fractional-order modeling; lithium-ion batteries; constant phase elements; state of charge; state of health; fractional-order Kalman filters

This paper is dedicated to the memory of late Professor Wen Chen

References

  • [1]

    T. Abuaisha, J. Kertzscher, Fractional-order modelling and parameter identification of electrical coils. Fract. Calc. Appl. Anal. 22, No 1 (2019), 193–216; ; https://www.degruyter.com/view/j/fca.2019.22.issue-1/issue-files/fca.2019.22.issue-1.xml.Crossref

  • [2]

    A. Adhikary, P. Sen, S. Sen, K. Biswas, Design and performance study of dynamic fractors in any of the four quadrants. Circuits Syst. Signal Process. 35, No 6 (2016), 1909–1932.CrossrefGoogle Scholar

  • [3]

    S. Alavi, C. Birkl, D. Howey, Time-domain fitting of battery electrochemical impedance models. J. Power Sources 288 (2015), 345–352.CrossrefGoogle Scholar

  • [4]

    A. Allagui, T.J. Freeborn, A.S. Elwakil, M.E. Fouda, B.J. Maundy, A.G. Radwan, Z. Said, M.A. Abdelkareem, Review of fractional-order electrical characterization of supercapacitors. J. Power Sources 400 (2018), 457–467.CrossrefGoogle Scholar

  • [5]

    A. Alsaedi, B. Ahmad, M. Kirane, A survey of useful inequalities in fractional calculus. Fract. Calc. Appl. Anal. 20, No 3 (2017), 574–594; ; https://www.degruyter.com/view/j/fca.2017.20.issue-3/issue-files/fca.2017.20.issue-3.xml.Crossref

  • [6]

    E. Bazhlekova, Subordination in a class of generalized time-fractional diffusion-wave equations. Fract. Calc. Appl. Anal. 21, No 4 (2018), 869–900; ; https://www.degruyter.com/view/j/fca.2018.21.issue-4/issue-files/fca.2018.21.issue-4.xml.Crossref

  • [7]

    C.R. Birkl, M.R. Roberts, E. McTurk, P.G. Bruce, D.A. Howey, Degradation diagnostics for lithium ion cells. J. Power Sources 341 (2017), 373–386.CrossrefGoogle Scholar

  • [8]

    M. Cai, W. Chen, X. Tan, Battery state-of-charge estimation based on a dual unscented Kalman filter and fractional variable-order model. Energies 10, No 10 (2017), 1577.CrossrefGoogle Scholar

  • [9]

    H. Chaoui, A. El Mejdoubi, H. Gualous, Online parameter identification of lithium-ion batteries with surface temperature variations. IEEE Trans. Veh. Technol. 66, No 3 (2016), 2000–2009.Google Scholar

  • [10]

    H. Chaoui, H. Gualous, Adaptive state of charge estimation of lithium-ion batteries with parameter and thermal uncertainties. IEEE Trans. Cont. Sys. Technol. 25, No 2 (2016), 752–759.Google Scholar

  • [11]

    Y. Chen, D. Huang, Q. Zhu, W. Liu, C. Liu, N. Xiong, A new state of charge estimation algorithm for lithium-ion batteries based on the fractional unscented Kalman filter. Energies 10, No 9 (2017), 1313.CrossrefGoogle Scholar

  • [12]

    M. Cugnet, J. Sabatier, S. Laruelle, S. Grugeon, B. Sahut, A. Oustaloup, J.-M. Tarascon, On lead-acid-battery resistance and cranking-capability estimation. IEEE Trans. Ind. Electron. 57, No 3 (2009), 909–917.Google Scholar

  • [13]

    L. De Sutter, Y. Firouz, J. De Hoog, N. Omar, J. Van Mierlo, Battery ageing assessment and parametric study of lithium-ion batteries by means of a fractional differential model. Electrochim. Acta 305 (2019), 24–36.CrossrefGoogle Scholar

  • [14]

    A.N. Eddine, B. Huard, J.-D. Gabano, T. Poinot, Initialization of a fractional order identification algorithm applied for lithium-ion battery modeling in time domain. Commun. Nonlinear Sci. Numer. Simul. 59 (2018), 375–386.CrossrefGoogle Scholar

  • [15]

    C. Fleischer, W. Waag, H.-M. Heyn, D.U. Sauer, On-line adaptive battery impedance parameter and state estimation considering physical principles in reduced order equivalent circuit battery models part 2. parameter and state estimation. J. Power Sources 262 (2014), 457–482.CrossrefGoogle Scholar

  • [16]

    J. Francisco, J. Sabatier, L. Lavigne, F. Guillemard, M. Moze, M. Tari, M. Merveillaut, A. Noury, Lithium-ion battery state of charge estimation using a fractional battery model. In: ICFDA’14 - Intern. Conf. on Fractional Differentiation and Its Applications (2014), 1–6.Google Scholar

  • [17]

    T.F. Fuller, M. Doyle, J. Newman, Simulation and optimization of the dual lithium ion insertion cell. J. Electrochem. Soc. 141, No 1 (1994), 1–10.CrossrefGoogle Scholar

  • [18]

    J.-D. Gabano, T. Poinot, B. Huard, Bounded diffusion impedance characterization of battery electrodes using fractional modeling. Commun. Nonlinear Sci. Numer. Simul. 47 (2017), 164–177.CrossrefGoogle Scholar

  • [19]

    T. Goh, M. Park, G. Koo, M. Seo, S.W. Kim, State-of-health estimation algorithm of li-ion battery using impedance at low sampling rate. In: IEEE PES APPEEC (2016), 146–150.Google Scholar

  • [20]

    A. Guha, A. Patra, Online estimation of the electrochemical impedance spectrum and remaining usage life of lithium-ion batteries. IEEE Trans. Instrum. Meas. 67, No 8 (2018), 1836–1849.CrossrefGoogle Scholar

  • [21]

    J. Hidalgo-Reyes, J.F. Gómez-Aguilar, R.F. Escobar-Jiménez, V.M. Alvarado-Marténez, M. López-López, Classical and fractional-order modeling of equivalent electrical circuits for supercapacitors and batteries, energy management strategies for hybrid systems and methods for the state of charge estimation: A state of the art review. Microelectron. J. 85 (2019), 109–128.CrossrefGoogle Scholar

  • [22]

    M. Hu, Y. Li, S. Li, C. Fu, D. Qin, Z. Li, Lithium-ion battery modeling and parameter identification based on fractional theory. Energy 165 (2018), 153–163.CrossrefGoogle Scholar

  • [23]

    X. Hu, H. Yuan, C. Zou, Z. Li, L. Zhang, Co-estimation of state of charge and state of health for lithium-ion batteries based on fractional-order calculus. IEEE Trans. Veh. Technol. 67, No 11 (2018), 10319–10329.CrossrefGoogle Scholar

  • [24]

    R. Huai, Z. Yu, H. Li, Historical data demand in window-based battery parameter identification algorithm. J. Power Sources 433 (2019), ID 126686.CrossrefGoogle Scholar

  • [25]

    P.E. Jacob, S.M.M. Alavi, A. Mahdi, S.J. Payne, D.A. Howey, Bayesian inference in non-Markovian state-space models with applications to battery fractional-order systems. IEEE Trans. Cont. Sys. Technol. 26, No 2 (2017), 497–506.Google Scholar

  • [26]

    Y. Jiang, B. Xia, X. Zhao, T. Nguyen, C. Mi, R.A. de Callafon, Data-based fractional differential models for non-linear dynamic modeling of a lithium-ion battery. Energy 135 (2017), 171–181.CrossrefGoogle Scholar

  • [27]

    Y. Jiang, B. Xia, X. Zhao, T. Nguyen, C. Mi, R.A. de Callafon, Identification of fractional differential models for lithium-ion polymer battery dynamics. IFAC-PapersOnLine 50, No 1 (2017), 405–410.CrossrefGoogle Scholar

  • [28]

    D.-K. Kang, H.-C. Shin, Investigation on cell impedance for high-power lithium-ion batteries. J. Solid State Electrochem. 11, No 10 (2007), 1405–1410.CrossrefGoogle Scholar

  • [29]

    C. Li, M. Cai, Theory and Numerical Approximations of Fractional Integrals and Derivatives. SIAM (2020); at https://epubs.siam.org/doi/pdf/10.1137/1.9781611975888.fm (2019).

  • [30]

    C. Li, Q. Yi, Modeling and computing of fractional convection equation. Commun. Appl. Math. Comput. (2019), 1–31.Google Scholar

  • [31]

    C. Li, Q. Yi, J. Kurths, Fractional convection. J. Comput. Nonlinear Dyn. 13, No 1 (2018), 011004.CrossrefGoogle Scholar

  • [32]

    C. Li, F. Zeng, Numerical Methods for Fractional Calculus. Chapman and Hall/CRC, (2015).Google Scholar

  • [33]

    S. Li, M. Hu, Y. Li, C. Gong, Fractional-order modeling and SOC estimation of lithium-ion battery considering capacity loss. Int. J. Energy Res. 43, No 1 (2019), 417–429.CrossrefGoogle Scholar

  • [34]

    X. Li, G. Fan, K. Pan, G. Wei, C. Zhu, G. Rizzoni, M. Canova, A physics-based fractional order model and state of energy estimation for lithium ion batteries. Part i: Model development and observability analysis. J. Power Sources 367 (2017), 187–201.CrossrefGoogle Scholar

  • [35]

    Y. Li, C. Wang, J. Gong, A wavelet transform-adaptive unscented Kalman filter approach for state of charge estimation of LiFePo4 battery. Int. J. Energy Res. 42, No 2 (2018), 587–600.CrossrefGoogle Scholar

  • [36]

    C. Liu, W. Liu, L. Wang, G. Hu, L. Ma, B. Ren, A new method of modeling and state of charge estimation of the battery. J. Power Sources 320 (2016), 1–12.CrossrefGoogle Scholar

  • [37]

    D. Liu, W. Xie, H. Liao, and Y. Peng, An integrated probabilistic approach to lithium-ion battery remaining usage life estimation. IEEE Trans. Instrum. Meas. 64, No 3 (2014), 660–670.Google Scholar

  • [38]

    D. Liu, J. Zhou, D. Pan, Y. Peng, X. Peng, Lithium-ion battery remaining usage life estimation with an optimized relevance vector machine algorithm with incremental learning. Measurement 63 (2015), 143–151.CrossrefGoogle Scholar

  • [39]

    K. Liu, K. Li, Q. Peng, and C. Zhang, A brief review on key technologies in the battery management system of electric vehicles. Front. Mech. Eng. 14, No 1 (2019), 47–64.CrossrefGoogle Scholar

  • [40]

    S. Liu, X. Dong, Y. Zhang, A new state of charge estimation method for lithium-ion battery based on the fractional order model. IEEE Access 7 (2019), 122949–122954.CrossrefGoogle Scholar

  • [41]

    X. Lu, H. Li, N. Chen, An indicator for the electrode ageing of lithium-ion batteries using a fractional variable order model. Electrochim. Acta 299 (2019), 378–387.CrossrefGoogle Scholar

  • [42]

    X. Lu, H. Li, J. Xu, S. Chen, N. Chen, Rapid estimation method for state of charge of lithium-ion battery based on fractional continual variable order model. Energies 11, No 4 (2018), 714.CrossrefGoogle Scholar

  • [43]

    J. Luo, J. Peng, H. He, Lithium-ion battery SOC estimation study based on cubature Kalman filter. Energy Procedia 158 (2019), 3421–3426.CrossrefGoogle Scholar

  • [44]

    Y. Ma, X. Zhou, B. Li, H. Chen, Fractional modeling and SOC estimation of lithium-ion battery. IEEE/CAA J. Automatica Sinica 3, No 3 (2016), 281–287.CrossrefGoogle Scholar

  • [45]

    J.T. Machado, V. Kiryakova, The chronicles of fractional calculus. Fract. Calc. Appl. Anal. 20, No 2 (2017), 307–336; ; https://www.degruyter.com/view/j/fca.2017.20.issue-2/issue-files/fca.2017.20.issue-2.xml.Crossref

  • [46]

    J.T. Machado, A.M. Lopes, Fractional state space analysis of temperature time series. Fract. Calc. Appl. Anal. 18, No 6 (2015), 1518–1536; ; https://www.degruyter.com/view/j/fca.2015.18.issue-6/issue-files/fca.2015.18.issue-6.xml.Crossref

  • [47]

    E. Martinez-Laserna, E. Sarasketa-Zabala, I.V. Sarria, D.-I. Stroe, M. Swierczynski, A. Warnecke, J.-M. Timmermans, S. Goutam, N. Omar, P. Rodriguez, Technical viability of battery second life: A study from the ageing perspective. IEEE Trans. Ind. Appl. 54, No 3 (2018), 2703–2713.CrossrefGoogle Scholar

  • [48]

    K.S. Mawonou, A. Eddahech, D. Dumur, D. Beauvois, E. Godoy, Improved state of charge estimation for li-ion batteries using fractional order extended Kalman filter. J. Power Sources 435 (2019), ID 226710.CrossrefGoogle Scholar

  • [49]

    S. Mohajer, J. Sabatier, P. Lanusse, O. Cois, A fractional-order electro-thermal ageing model for lifetime enhancement of lithium-ion batteries. IFAC-PapersOnLine 51, No 2 (2018), 220–225.CrossrefGoogle Scholar

  • [50]

    M. Montaru, S. Pelissier, Frequency and temporal identification of a li-ion polymer battery model using fractional impedance. Oil & Gas Scie. Tech.–Revue de l’Institut Français du Pétrole 65, No 1 (2010), 67–78.CrossrefGoogle Scholar

  • [51]

    H. Mu, R. Xiong, H. Zheng, Y. Chang, Z. Chen, A novel fractional order model based state-of-charge estimation method for lithium-ion battery. Appl. Energy 207 (2017), 384–393.CrossrefGoogle Scholar

  • [52]

    A. Mystkowski and A. Zolotas, PLC-based discrete fractional-order control design for an industrial-oriented water tank volume system with input delay. Fract. Calc. Appl. Anal. 21, No 4 (2018), 1005–1026; ; https://www.degruyter.com/view/j/fca.2018.21.issue-4/issue-files/fca.2018.21.issue-4.xml.Crossref

  • [53]

    A. Nasser-Eddine, B. Huard, J.-D. Gabano, T. Poinot, A two steps method for electrochemical impedance modeling using fractional order system in time and frequency domains. Control Eng. Practice 86 (2019), 96–104.CrossrefGoogle Scholar

  • [54]

    H. Perez, S. Dey, X. Hu, S. Moura, Optimal charging of li-ion batteries via a single particle model with electrolyte and thermal dynamics. J. Electrochem. Soc. 164, No 7 (2017), A1679–A1687.CrossrefGoogle Scholar

  • [55]

    H. Rafeiro, S. Samko, Fractional integrals and derivatives: mapping properties. Fract. Calc. Appl. Anal. 19, No 3 (2016), 580–607; ; https://www.degruyter.com/view/j/fca.2016.19.issue-3/issue-files/fca.2016.19.issue-3.xml.Crossref

  • [56]

    S.K. Rahimian, S. Rayman, R.E. White, Extension of physics-based single particle model for higher charge-discharge rates. J. Power Sources 224 (2013), 180–194.CrossrefGoogle Scholar

  • [57]

    J. Rifkin, The third industrial revolution: a radical new sharing Economy. https://www.singularityweblog.com/third-industrial-revolution/ (2018).

  • [58]

    J. Sabatier, M. Aoun, A. Oustaloup, G. Grégoire, F. Ragot, P. Roy, Fractional system identification for lead acid battery state of charge estimation. Signal Process. 86, No 10 (2006), 2645–2657.CrossrefGoogle Scholar

  • [59]

    J. Sabatier, M. Cugnet, S. Laruelle, S. Grugeon, B. Sahut, A. Oustaloup, J. Tarascon, A fractional order model for lead-acid battery crankability estimation. Commun. Nonlinear Sci. Numer. Simul. 15, No 5 (2010), 1308–1317.CrossrefGoogle Scholar

  • [60]

    J. Sabatier, J.M. Francisco, F. Guillemard, L. Lavigne, M. Moze, M. Merveillaut, Lithium-ion batteries modeling: A simple fractional differentiation based model and its associated parameters estimation method. Signal Process. 107 (2015), 290–301.CrossrefGoogle Scholar

  • [61]

    J. Sabatier, F. Guillemard, L. Lavigne, A. Noury, M. Merveillaut, J.M. Francico, Fractional models of lithium-ion batteries with application to state of charge and ageing estimation. In: Informatics in Control, Automation and Robotics, Springer (2018), 55–72.Google Scholar

  • [62]

    J. Sabatier, M. Merveillaut, J.M. Francisco, F. Guillemard, D. Porcelatto, Fractional models for lithium-ion batteries. In: Proc. of the European Control Conference (2013), 3458–3463.Google Scholar

  • [63]

    J. Sabatier, M. Merveillaut, J.M. Francisco, F. Guillemard, D. Porcelatto, Lithium-ion batteries modeling involving fractional differentiation. J. Power Sources 262 (2014), 36–43.CrossrefGoogle Scholar

  • [64]

    H. Sun, A. Chang, Y. Zhang, W. Chen, A review on variable-order fractional differential equations: mathematical foundations, physical models, numerical methods and applications. Fract. Calc. Appl. Anal. 22, No 1 (2019), 27–59; ; https://www.degruyter.com/view/j/fca.2019.22.issue-1/issue-files/fca.2019.22.issue-1.xml.Crossref

  • [65]

    Y. Sun, Y. Li, M. Yu, Z. Zhou, Q. Zhang, B. Duan, Y. Shang, C. Zhang, Variable fractional order-a comprehensive evaluation indicator of lithium-ion batteries. J. Power Sources (2019), .CrossrefGoogle Scholar

  • [66]

    P. Systems, Lithium-ion battery advantages. https://www.powertechsystems.eu/home/tech-corner/lithium-ion-battery-advantages/ (2019).

  • [67]

    T. Takamatsu, H. Ohmori, State and parameter estimation of lithium-ion battery by kreisselmeier-type adaptive observer for fractional calculus system. In: Proc. of the 54th Annual Conference SICE of Japan (2015), 86–90.Google Scholar

  • [68]

    T. Takamatsu, H. Ohmori, Online parameter estimation for lithium-ion battery by using adaptive observer for fractional-order system. Electr. Commun. Jpn. 101, No 3 (2018), 80–89.CrossrefGoogle Scholar

  • [69]

    X. Tang, Y. Wang, C. Zou, K. Yao, Y. Xia, F. Gao, A novel framework for lithium-ion battery modeling considering uncertainties of temperature and ageing. Energy Conv. Manag. 180 (2019), 162–170.CrossrefGoogle Scholar

  • [70]

    J. Tian, R. Xiong, Q. Yu, Fractional-order model-based incremental capacity analysis for degradation state recognition of lithium-ion batteries. IEEE Trans. Ind. Electron. 66, No 2 (2018), 1576–1584.Google Scholar

  • [71]

    B. Wang, S.E. Li, H. Peng, Z. Liu, Fractional-order modeling and parameter identification for lithium-ion batteries. J. Power Sources 293 (2015), 151–161.CrossrefGoogle Scholar

  • [72]

    B. Wang, Z. Liu, S.E. Li, S.J. Moura, H. Peng, State-of-charge estimation for lithium-ion batteries based on a nonlinear fractional model. IEEE Trans. Cont. Sys. Technol. 25, No 1 (2016), 3–11.Google Scholar

  • [73]

    C. Wang, Q. Huang, R. Ling, Battery SOC estimating using a fractional order unscented Kalman filter. In: Proc. of the Chinese Automation Congress (2015), 1268–1273.Google Scholar

  • [74]

    J. Wang, L. Zhang, D. Xu, P. Zhang, G. Zhang, A simplified fractional order equivalent circuit model and adaptive online parameter identification method for lithium-ion batteries. Math. Probl. Eng. 2019 (2019), ID 6019236.Google Scholar

  • [75]

    Y. Wang, Y. Chen, and X. Liao, Applied fractional calculus and second-life battery characterization. In: Proc. of the 1st Fractional Order Systems and Controls Conference (FOSCC) 2019 (2019), Accepted.Google Scholar

  • [76]

    Y. Wang, H. Fang, L. Zhou, T. Wada, Revisiting the state-of-charge estimation for lithium-ion batteries: A methodical investigation of the extended Kalman filter approach. IEEE Control Syst. Mag. 37, No 4 (2017), 73–96.CrossrefGoogle Scholar

  • [77]

    N. Wassiliadis, J. Adermann, A. Frericks, M. Pak, C. Reiter, B. Lohmann, M. Lienkamp, Revisiting the dual extended Kalman filter for battery state-of-charge and state-of-health estimation: A use-case life cycle analysis. J. Energy Storage 19 (2018), 73–87.CrossrefGoogle Scholar

  • [78]

    Z. Wei, B. Xiong, D. Ji, K. J. Tseng, Online state of charge and capacity dual estimation with a multi-timescale estimator for lithium-ion battery. Energy Procedia 105 (2017), 2953–2958.CrossrefGoogle Scholar

  • [79]

    R. Xiao, J. Shen, X. Li, W. Yan, E. Pan, Z. Chen, Comparisons of modeling and state of charge estimation for lithium-ion battery based on fractional order and integral order methods. Energies 9, No 3 (2016), 184.CrossrefGoogle Scholar

  • [80]

    R. Xiong, J. Cao, Q. Yu, H. He, F. Sun, Critical review on the battery state of charge estimation methods for electric vehicles. IEEE Access 6 (2017), 1832–1843.Google Scholar

  • [81]

    R. Xiong, J. Tian, H. Mu, C. Wang, A systematic model-based degradation behavior recognition and health monitoring method for lithium-ion batteries. Appl. Energy 207 (2017), 372–383.CrossrefGoogle Scholar

  • [82]

    R. Xiong, J. Tian, W. Shen, F. Sun, A novel fractional order model for state of charge estimation in lithium ion batteries. IEEE Trans. Veh. Technol. 68, No 5 (2019), 4130–4139.CrossrefGoogle Scholar

  • [83]

    R. Yamin, A. Rachid, Embedded state of charge and state of health estimator based on Kalman filter for electric scooter battery management system. In: Proc. of the IEEE ICCE-Berlin (2014), 440–444.Google Scholar

  • [84]

    Q. Yang, J. Xu, B. Cao, X. Li, A simplified fractional order impedance model and parameter identification method for lithium-ion batteries. PloS One 12, No 2 (2017), e0172424.CrossrefPubMedGoogle Scholar

  • [85]

    M. Ye, H. Guo, B. Cao, A model-based adaptive state of charge estimator for a lithium-ion battery using an improved adaptive particle filter. Appl. Energy 190 (2017), 740–748.CrossrefGoogle Scholar

  • [86]

    S. Yuan, H. Wu, X. Zhang, C. Yin, Online estimation of electrochemical impedance spectra for lithium-ion batteries via discrete fractional order model. In: Proc. of the IEEE Vehicle Power and Propulsion Conf. (VPPC) (2013), 1–6.Google Scholar

  • [87]

    C. Zhang, Y. Zhang, Y. Li, A novel battery state-of-health estimation method for hybrid electric vehicles. IEEE-ASME Trans. Mechatron. 20, No 5 (2015), 2604–2612.CrossrefGoogle Scholar

  • [88]

    L. Zhang, X. Hu, Z. Wang, F. Sun, D.G. Dorrell, A review of supercapacitor modeling, estimation, and applications: A control/management perspective. Sust. Energ. Rev. 81 (2018), 1868–1878.CrossrefGoogle Scholar

  • [89]

    Q. Zhang, N. Cui, Y. Shang, G. Xing, C. Zhang, Relevance between fractional-order hybrid model and unified equivalent circuit model of electric vehicle power battery. Science China Information Sciences 61, No 7 (2018), 70208–1.CrossrefGoogle Scholar

  • [90]

    Q. Zhang, Y. Li, Y. Shang, B. Duan, N. Cui, C. Zhang, A fractional-order kinetic battery model of lithium-ion batteries considering a nonlinear capacity. Electronics 8, No 4 (2019), 394.CrossrefGoogle Scholar

  • [91]

    Q. Zhang, Y. Shang, Y. Li, N. Cui, B. Duan, C. Zhang, A novel fractional variable-order equivalent circuit model and parameter identification of electric vehicle li-ion batteries. ISA Trans. (2019), https://doi.org/10.1016/j.isatra.2019.08.004.PubMed

  • [92]

    R. Zhang, B. Xia, B. Li, L. Cao, Y. Lai, W. Zheng, H. Wang, W. Wang, State of the art of lithium-ion battery SOC estimation for electrical vehicles. Energies 11, No 7 (2018), 1820.CrossrefGoogle Scholar

  • [93]

    Y. Zhao, Y. Li, F. Zhou, Z. Zhou, Y. Chen, An iterative learning approach to identify fractional order KiBaM model. IEEE/CAA J. of Automatica Sinica 4, No 2 (2017), 322–331.CrossrefGoogle Scholar

  • [94]

    F. Zheng, Y. Xing, J. Jiang, B. Sun, J. Kim, M. Pecht, Influence of different open circuit voltage tests on state of charge online estimation for lithium-ion batteries. Appl. Energy 183 (2016), 513–525.CrossrefGoogle Scholar

  • [95]

    F. Zhong, H. Li, Q. Zhong, An approach for SOC estimation based on sliding mode observer and fractional order equivalent circuit model of lithium-ion batteries. In: Proc. of the IEEE Intern. Conf. Mechatronics and Automation (2014), 1497–1503.Google Scholar

  • [96]

    F. Zhong, H. Li, S. Zhong, Q. Zhong, C. Yin, An SOC estimation approach based on adaptive sliding mode observer and fractional order equivalent circuit model for lithium-ion batteries. Commun. Nonlinear Sci. Numer. Simul. 24, No 1-3 (2015), 127–144.CrossrefGoogle Scholar

  • [97]

    Q. Zhong, F. Zhong, J. Cheng, H. Li, S. Zhong, State of charge estimation of lithium-ion batteries using fractional order sliding mode observer. ISA Trans. 66 (2017), 448–459.PubMedCrossrefGoogle Scholar

  • [98]

    D. Zhou, K. Zhang, A. Ravey, F. Gao, A. Miraoui, Parameter sensitivity analysis for fractional-order modeling of lithium-ion batteries. Energies 9, No 3 (2016), 123.CrossrefGoogle Scholar

  • [99]

    Q. Zhu, M. Zheng, A state of charge estimation approach based on fractional order adaptive extended Kalman filter for lithium-ion batteries. In: Proc. of the IEEE 7th DDCLS (2018), 271–276.Google Scholar

  • [100]

    C. Zou, X. Hu, S. Dey, L. Zhang, X. Tang, Nonlinear fractional-order estimator with guaranteed robustness and stability for lithium-ion batteries. IEEE Trans. Ind. Electron. 65, No 7 (2017), 5951–5961.Google Scholar

  • [101]

    C. Zou, L. Zhang, X. Hu, Z. Wang, T. Wik, M. Pecht, A review of fractional-order techniques applied to lithium-ion batteries, lead-acid batteries, and supercapacitors. J. Power Sources 390 (2018), 286–296.CrossrefGoogle Scholar

  • [102]

    Y. Zou, S. E. Li, B. Shao, B. Wang, State-space model with non-integer order derivatives for lithium-ion battery. Appl. Energy 161 (2016), 330–336.CrossrefGoogle Scholar

About the article

Received: 2019-07-15

Published Online: 2019-12-31

Published in Print: 2019-12-18


Citation Information: Fractional Calculus and Applied Analysis, Volume 22, Issue 6, Pages 1449–1479, ISSN (Online) 1314-2224, ISSN (Print) 1311-0454, DOI: https://doi.org/10.1515/fca-2019-0076.

Export Citation

© 2019 Diogenes Co., Sofia.Get Permission

Comments (0)

Please log in or register to comment.
Log in