Skip to main content

Advertisement

Log in

Estimation of battery capacity using the enhanced self-organization maps

  • Original Paper
  • Published:
Electrical Engineering Aims and scope Submit manuscript

Abstract

Accurate knowledge of capacity is crucial for battery management systems as it enables them to predict future failures, specifically through the state of health metric. The primary focus of this study is to estimate battery capacity using the enhanced self-organization maps (EASOM) algorithm. The EASOM is employed here to minimize uncertainties in state of charge estimation and measurements. It identifies the most suitable candidate using an objective function and incorporates a fading memory forgetting factor to improve battery capacity estimation. To validate the precision of the proposed algorithm, six tests were conducted for hybrid electric vehicle and electric vehicle applications. EASOM demonstrated excellent performance, with a maximum error of 1.25%. Additionally, all predictive performance metrics (the mean absolute percentage error, the root-mean-square error, and the mean squared error) were within 1% in all tests.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12

Similar content being viewed by others

Data availability

The datasets generated during and/or analyzed during the current study are available in the “Chapter 4: Algorithms for capacity estimation” repository, http://mocha-java.uccs.edu/BMS2/index.html.

Abbreviations

EASOM:

Enhanced self-organization maps

BMS:

Battery management system

SOH:

State of health

NiCd:

Nickel–cadmium

H∞:

H-infinity filters

ICA:

Incremental capacity analysis

AEKF:

Adaptive EKF

ECM:

Equivalent circuit models

FFRLS:

Forgetting factor recursive least squares

EV:

Electric vehicle

PHEV:

Plug-in hybrid electric vehicle

MKRVM:

Multiple kernel relevance vector machine

DNN:

Deep neural network

DCNN:

Deep convolution neural network

SOC:

State of charge

EKF:

Extended Kalman filter

RMSE:

Root-mean-square error

SRCKF:

Square root cubature Kalman filter

EK:

Extracting knowledge

TLS:

Total least squares

AWTLS:

Approximate weighted total least squares

WTLS:

Weighted total least squares

WLS:

Weighted least squares

DVA:

Differential voltage analysis

EIS:

Electrochemical impedance spectroscopy

LSSVM:

Least square support vector machine

RLU:

Remaining useful life

EM:

Electrochemical models

NN:

Neural network

DEKF:

Dual extended Kalman filter

EMD:

Empirical mode decomposition

PCoE:

Prognostics center of excellence

APE:

Absolute percentage error

MSE:

Mean squared error

MAPE:

Mean absolute percentage error

SOE:

State of energy

References

  1. Lipu MSH, Hannan MA, Hussain A et al (2018) A review of state of health and remaining useful life estimation methods for lithium-ion battery in electric vehicles: challenges and recommendations. J Clean Prod 205:115–133. https://doi.org/10.1016/J.JCLEPRO.2018.09.065

    Article  Google Scholar 

  2. E marghichi M, Mostafa B (2022) Battery total capacity estimation based on the sunflower algorithm. J Energy Storage 48:103900. https://doi.org/10.1016/J.EST.2021.103900

    Article  Google Scholar 

  3. Farmann A, Sauer DU (2016) A comprehensive review of on-board state-of-available-power prediction techniques for lithium-ion batteries in electric vehicles. J Power Sour 329:123–137. https://doi.org/10.1016/J.JPOWSOUR.2016.08.031

    Article  Google Scholar 

  4. Ma Z, Yang R, Wang Z (2019) A novel data-model fusion state-of-health estimation approach for lithium-ion batteries. Appl Energy 237:836–847. https://doi.org/10.1016/J.APENERGY.2018.12.071

    Article  Google Scholar 

  5. Ansean D, Garcia VM, Gonzalez M et al (2019) Lithium-ion battery degradation indicators via incremental capacity analysis. IEEE Trans Ind Appl 55:2992–3002. https://doi.org/10.1109/TIA.2019.2891213

    Article  Google Scholar 

  6. Pastor-Fernández C, Uddin K, Chouchelamane GH et al (2017) A comparison between electrochemical impedance spectroscopy and incremental capacity-differential voltage as Li-ion diagnostic techniques to identify and quantify the effects of degradation modes within battery management systems. J Power Sour 360:301–318. https://doi.org/10.1016/J.JPOWSOUR.2017.03.042

    Article  Google Scholar 

  7. Li Y, Abdel-Monem M, Gopalakrishnan R et al (2018) A quick on-line state of health estimation method for Li-ion battery with incremental capacity curves processed by Gaussian filter. J Power Sour 373:40–53. https://doi.org/10.1016/J.JPOWSOUR.2017.10.092

    Article  Google Scholar 

  8. Dubarry M, Svoboda V, Hwu R, Liaw BY (2006) Incremental capacity analysis and close-to-equilibrium OCV measurements to quantify capacity fade in commercial rechargeable lithium batteries. Electrochem Solid-State Lett 9:A454. https://doi.org/10.1149/1.2221767/XML

    Article  Google Scholar 

  9. Dubarry M, Truchot C, Liaw BY (2012) Synthesize battery degradation modes via a diagnostic and prognostic model. J Power Sour 219:204–216. https://doi.org/10.1016/J.JPOWSOUR.2012.07.016

    Article  Google Scholar 

  10. Tian J, Xiong R, Yu Q (2019) Fractional-order model-based incremental capacity analysis for degradation state recognition of lithium-ion batteries. IEEE Trans Ind Electron 66:1576–1584. https://doi.org/10.1109/TIE.2018.2798606

    Article  Google Scholar 

  11. Honkura K, Takahashi K, Horiba T (2011) Capacity-fading prediction of lithium-ion batteries based on discharge curves analysis. J Power Sour 196:10141–10147. https://doi.org/10.1016/J.JPOWSOUR.2011.08.020

    Article  Google Scholar 

  12. Bloom I, Christophersen J, Gering K (2005) Differential voltage analyses of high-power lithium-ion cells: 2 Applications. J Power Sour 139:304–313. https://doi.org/10.1016/J.JPOWSOUR.2004.07.022

    Article  Google Scholar 

  13. Xiong R, Li L, Tian J (2018) Towards a smarter battery management system: a critical review on battery state of health monitoring methods. J Power Sour 405:18–29. https://doi.org/10.1016/J.JPOWSOUR.2018.10.019

    Article  Google Scholar 

  14. Honkura K, Honbo H, Koishikawa Y, Horiba T (2008) State analysis of lithium-ion batteries using discharge curves. ECS Trans 13:61–73. https://doi.org/10.1149/1.3018750/XML

    Article  Google Scholar 

  15. Bloom I, Jansen AN, Abraham DP et al (2005) Differential voltage analyses of high-power, lithium-ion cells: 1 technique and application. J Power Sourc 139:295–303. https://doi.org/10.1016/J.JPOWSOUR.2004.07.021

    Article  Google Scholar 

  16. Bloom I, Christophersen JP, Abraham DP, Gering KL (2006) Differential voltage analyses of high-power lithium-ion cells: 3 another anode phenomenon. J Power Sour 157:537–542. https://doi.org/10.1016/J.JPOWSOUR.2005.07.054

    Article  Google Scholar 

  17. Merla Y, Wu B, Yufit V et al (2016) Novel application of differential thermal voltammetry as an in-depth state-of-health diagnosis method for lithium-ion batteries. J Power Sour 307:308–319. https://doi.org/10.1016/J.JPOWSOUR.2015.12.122

    Article  Google Scholar 

  18. Abe Y, Hori N, Kumagai S (2019) Electrochemical impedance spectroscopy on the performance degradation of LiFePO4/graphite lithium-ion battery due to charge–discharge cycling under different C-rates. Energies 12:4507. https://doi.org/10.3390/EN12234507

    Article  Google Scholar 

  19. Andre D, Meiler M, Steiner K et al (2011) Characterization of high-power lithium-ion batteries by electrochemical impedance spectroscopy. I experimental investigation. J Power Sour 196:5334–5341. https://doi.org/10.1016/J.JPOWSOUR.2010.12.102

    Article  Google Scholar 

  20. Teliz E, Zinola CF, Díaz V (2022) Identification and quantification of ageing mechanisms in Li-ion batteries by electrochemical impedance spectroscopy. Electrochim Acta 426:140801. https://doi.org/10.1016/J.ELECTACTA.2022.140801

    Article  Google Scholar 

  21. Li W, Sengupta N, Dechent P et al (2021) Online capacity estimation of lithium-ion batteries with deep long short-term memory networks. J Power Sour 482:228863. https://doi.org/10.1016/J.JPOWSOUR.2020.228863

    Article  Google Scholar 

  22. Li W, Cao D, Jöst D et al (2020) Parameter sensitivity analysis of electrochemical model-based battery management systems for lithium-ion batteries. Appl Energy 269:115104. https://doi.org/10.1016/J.APENERGY.2020.115104

    Article  Google Scholar 

  23. Bartlett A, Marcicki J, Onori S et al (2016) Electrochemical model-based state of charge and capacity estimation for a composite electrode lithium-ion battery. IEEE Trans Control Syst Technol 24:384–399. https://doi.org/10.1109/TCST.2015.2446947

    Article  Google Scholar 

  24. Li W, Fan Y, Ringbeck F et al (2020) Electrochemical model-based state estimation for lithium-ion batteries with adaptive unscented Kalman filter. J Power Sour 476:228534. https://doi.org/10.1016/J.JPOWSOUR.2020.228534

    Article  Google Scholar 

  25. Moura SJ, Chaturvedi NA, Krstić M (2014) Adaptive partial differential equation observer for battery state-of-charge/state-of-health estimation via an electrochemical model. J Dyn Syst Meas Control Asme. https://doi.org/10.1115/1.4024801

    Article  Google Scholar 

  26. Zheng L, Zhang L, Zhu J et al (2016) Co-estimation of state-of-charge, capacity and resistance for lithium-ion batteries based on a high-fidelity electrochemical model. Appl Energy 180:424–434. https://doi.org/10.1016/J.APENERGY.2016.08.016

    Article  Google Scholar 

  27. He H, Xiong R, Guo H (2012) Online estimation of model parameters and state-of-charge of LiFePO4 batteries in electric vehicles. Appl Energy 89:413–420. https://doi.org/10.1016/J.APENERGY.2011.08.005

    Article  Google Scholar 

  28. Zou Y, Hu X, Ma H, Li SE (2015) Combined state of charge and state of health estimation over lithium-ion battery cell cycle lifespan for electric vehicles. J Power Sour 273:793–803. https://doi.org/10.1016/J.JPOWSOUR.2014.09.146

    Article  Google Scholar 

  29. Li W, Rentemeister M, Badeda J et al (2020) Digital twin for battery systems: cloud battery management system with online state-of-charge and state-of-health estimation. J Energy Storage 30:101557. https://doi.org/10.1016/J.EST.2020.101557

    Article  Google Scholar 

  30. Wang S, Guo D, Han X et al (2020) Impact of battery degradation models on energy management of a grid-connected DC microgrid. Energy. https://doi.org/10.1016/J.ENERGY.2020.118228

    Article  Google Scholar 

  31. Wu J, Wei Z, Li W et al (2021) Battery thermal-and health-constrained energy management for hybrid electric bus based on soft actor-critic DRL algorithm. IEEE Trans Ind Inform 17:3751–3761. https://doi.org/10.1109/TII.2020.3014599

    Article  Google Scholar 

  32. Hu C, Jain G, Schmidt C et al (2015) Online estimation of lithium-ion battery capacity using sparse Bayesian learning. J Power Sour 289:105–113. https://doi.org/10.1016/J.JPOWSOUR.2015.04.166

    Article  Google Scholar 

  33. Richardson RR, Birkl CR, Osborne MA, Howey DA (2019) Gaussian process regression for in situ capacity estimation of lithium-ion batteries. IEEE Trans Ind Inform 15:127–138. https://doi.org/10.1109/TII.2018.2794997

    Article  Google Scholar 

  34. Zhang C, He Y, Yuan L, Xiang S (2017) Capacity prognostics of lithium-ion batteries using EMD denoising and multiple kernel RVM. IEEE Access 5:12061–12070. https://doi.org/10.1109/ACCESS.2017.2716353

    Article  Google Scholar 

  35. Shen S, Sadoughi M, Li M et al (2020) Deep convolutional neural networks with ensemble learning and transfer learning for capacity estimation of lithium-ion batteries. Appl Energy 260:114296. https://doi.org/10.1016/J.APENERGY.2019.114296

    Article  Google Scholar 

  36. Qian C, Xu B, Chang L et al (2021) Convolutional neural network based capacity estimation using random segments of the charging curves for lithium-ion batteries. Energy 227:120333. https://doi.org/10.1016/J.ENERGY.2021.120333

    Article  Google Scholar 

  37. Shen S, Sadoughi M, Chen X et al (2019) A deep learning method for online capacity estimation of lithium-ion batteries. J Energy Storage 25:100817. https://doi.org/10.1016/J.EST.2019.100817

    Article  Google Scholar 

  38. You won G, Park S, Oh D (2016) Real-time state-of-health estimation for electric vehicle batteries: a data-driven approach. Appl Energy 176:92–103. https://doi.org/10.1016/J.APENERGY.2016.05.051

    Article  Google Scholar 

  39. Deng Z, Xu L, Liu H et al (2023) Prognostics of battery capacity based on charging data and data-driven methods for on-road vehicles. Appl Energy 339:120954. https://doi.org/10.1016/J.APENERGY.2023.120954

    Article  Google Scholar 

  40. Deng Z, Lin X, Cai J, Hu X (2022) Battery health estimation with degradation pattern recognition and transfer learning. J Power Sour 525:231027. https://doi.org/10.1016/J.JPOWSOUR.2022.231027

    Article  Google Scholar 

  41. Greenbank S, Howey D (2022) automated feature extraction and selection for data-driven models of rapid battery capacity fade and end of life. IEEE Trans Ind Inform 18:2965–2973. https://doi.org/10.1109/TII.2021.3106593

    Article  Google Scholar 

  42. Khaleghi S, Hosen MS, Karimi D et al (2022) Developing an online data-driven approach for prognostics and health management of lithium-ion batteries. Appl Energy 308:118348. https://doi.org/10.1016/J.APENERGY.2021.118348

    Article  Google Scholar 

  43. Guo P, Cheng Z, Yang L (2019) A data-driven remaining capacity estimation approach for lithium-ion batteries based on charging health feature extraction. J Power Sour 412:442–450. https://doi.org/10.1016/J.JPOWSOUR.2018.11.072

    Article  Google Scholar 

  44. Xiong R, Wang J, Shen W et al (2021) Co-estimation of state of charge and capacity for lithium-ion batteries with multi-stage model fusion method. Engineering 7:1469–1482. https://doi.org/10.1016/J.ENG.2020.10.022

    Article  Google Scholar 

  45. Chen C, Xiong R, Shen W (2018) A lithium-ion battery-in-the-loop approach to test and validate multiscale dual H infinity filters for state-of-charge and capacity estimation. IEEE Trans Power Electron 33:332–342. https://doi.org/10.1109/TPEL.2017.2670081

    Article  Google Scholar 

  46. Nian P, Shuzhi Z, Xiongwen Z (2021) Co-estimation for capacity and state of charge for lithium-ion batteries using improved adaptive extended Kalman filter. J Energy Storage 40:102559. https://doi.org/10.1016/J.EST.2021.102559

    Article  Google Scholar 

  47. Shuzhi Z, Xu G, Xiongwen Z (2021) A novel one-way transmitted co-estimation framework for capacity and state-of-charge of lithium-ion battery based on double adaptive extended Kalman filters. J Energy Storage 33:102093. https://doi.org/10.1016/J.EST.2020.102093

    Article  Google Scholar 

  48. Plett GL (2011) Recursive approximate weighted total least squares estimation of battery cell total capacity. J Power Sour 196:2319–2331. https://doi.org/10.1016/J.JPOWSOUR.2010.09.048

    Article  Google Scholar 

  49. Gregory L, Plett (2016) Battery management systems: equivalent-circuit methods. ARTECH HOUSE, BOSTON, LONDON 329 Link for AWTLS method, EV and HEV scenarios: http://mocha-java.uccs.edu/BMS2/index.html

  50. Cuevas E, Galvez J (2019) An optimization algorithm guided by a machine learning approach. Int J Mach Learn Cybern 10:2963–2991. https://doi.org/10.1007/S13042-018-00915-0/TABLES/21

    Article  Google Scholar 

  51. Hannan MA, Lipu MSH, Hussain A, Mohamed A (2017) A review of lithium-ion battery state of charge estimation and management system in electric vehicle applications: challenges and recommendations. Renew Sustain Energy Rev 78:834–854. https://doi.org/10.1016/J.RSER.2017.05.001

    Article  Google Scholar 

  52. Elmarghichi M, Bouzi M, Ettalabi N, Derri M (2021) Comparison of state of charge estimation algorithms for lithium battery. Lect Notes Electr Eng 681:293–300. https://doi.org/10.1007/978-981-15-6259-4_30/COVER

    Article  Google Scholar 

  53. Zheng Y, Ouyang M, Han X et al (2018) Investigating the error sources of the online state of charge estimation methods for lithium-ion batteries in electric vehicles. J Power Sour 377:161–188. https://doi.org/10.1016/J.JPOWSOUR.2017.11.094

    Article  Google Scholar 

  54. Xiong R, Cao J, Yu Q et al (2017) Critical review on the battery state of charge estimation methods for electric vehicles. IEEE Access 6:1832–1843. https://doi.org/10.1109/ACCESS.2017.2780258

    Article  Google Scholar 

  55. Shrivastava P, Soon TK, Bin IMYI, Mekhilef S (2019) Overview of model-based online state-of-charge estimation using Kalman filter family for lithium-ion batteries. Renew Sustain Energy Rev 113:109233. https://doi.org/10.1016/J.RSER.2019.06.040

    Article  Google Scholar 

  56. Mouncef E, Mostafa B, Naoufl E (2020) Online parameter estimation of an electric vehicle lithium-ion battery using AFFRLS. 2020 IEEE 2nd International Conference on Electronics, Control, Optimization and Computer Science ICECOCS 2020. https://doi.org/10.1109/ICECOCS50124.2020.9314577

  57. Elmarghichi M, Bouzi M, Ettalabi N (2020) Robust parameter estimation of an electric vehicle lithium-ion battery using adaptive forgetting factor recursive least squares. Int J Intell Eng Syst 13:74–84

    Google Scholar 

  58. El MM, Loulijat A, El HI (2023) Variable recursive least square algorithm for lithium-ion battery equivalent circuit model parameters identification. Period Polytech Electr Eng Comput Sci. https://doi.org/10.3311/PPEE.21339

    Article  Google Scholar 

  59. Metaheuristic algorithm and machine learning—File Exchange—MATLAB Central. https://www.mathworks.com/matlabcentral/fileexchange/70481-metaheuristic-algorithm-and-machine-learning?s_tid=ta_fx_results. Accessed 1 Jul 2023

Download references

Funding

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

Author information

Authors and Affiliations

Authors

Contributions

The paper conceptualization, methodology, software, validation, formal analysis, investigation, resources, data curation, writing—original draft preparation, writing—review and editing, visualization, the supervision, and project administration have been done by the corresponding author (MEM).

Corresponding author

Correspondence to Mouncef El marghichi.

Ethics declarations

Conflict of interest

The author declares no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

El marghichi, M. Estimation of battery capacity using the enhanced self-organization maps. Electr Eng 106, 1549–1567 (2024). https://doi.org/10.1007/s00202-023-01966-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00202-023-01966-5

Keywords

Navigation