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Perspective modelling and measuring discharge voltage on truncated data of long-term stored Li-ion batteries based on functional state space model

Author

Listed:
  • Koláček, Jan
  • Vališ, David
  • Fuksová, Mária
  • Hlinka, Jiří
  • Procházka, Petr

Abstract

The subject of battery sources and electrical energy accumulators is currently very topical. Moreover, the possibilities of reusing already discarded sources are being explored as so-called “second-life batteries”. This article is concerned with studying and modelling the behaviour of a battery in an electric aircraft in operation — the voltage during discharge. Outcomes from extensive experiments on real long-term stored batteries have provided statistically robust sets of data on both long-term stored and new batteries; some of the data, however, are truncated. A modern approach that neglects the truncated issues and is based on functional data analysis and modified with a specific time series is used to model the process. This suggested model is much more accurate than the model used previously as it can effectively process truncated data. It also allows a certain degree of generalization. The aim is to determine the probability density of the time when the battery reaches the critical value, including the numerical statistics, for both stored and new batteries. The results are compared using the specific statistical Kullback–Leibler divergence approach to determine the degree of difference. The proposed model applies to similar issues where battery voltage is modelled in a time domain while the data form is truncated. It is proved, however, that further use of the stored batteries does not disrupt the safe and reliable operation of an electric airplane in terms of their functionality.

Suggested Citation

  • Koláček, Jan & Vališ, David & Fuksová, Mária & Hlinka, Jiří & Procházka, Petr, 2025. "Perspective modelling and measuring discharge voltage on truncated data of long-term stored Li-ion batteries based on functional state space model," Applied Energy, Elsevier, vol. 377(PB).
  • Handle: RePEc:eee:appene:v:377:y:2025:i:pb:s0306261924018798
    DOI: 10.1016/j.apenergy.2024.124496
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    References listed on IDEAS

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    1. Hyndman, Rob J. & Booth, Heather, 2008. "Stochastic population forecasts using functional data models for mortality, fertility and migration," International Journal of Forecasting, Elsevier, vol. 24(3), pages 323-342.
    2. Fang Liu & Rong Xu & Yecun Wu & David Thomas Boyle & Ankun Yang & Jinwei Xu & Yangying Zhu & Yusheng Ye & Zhiao Yu & Zewen Zhang & Xin Xiao & Wenxiao Huang & Hansen Wang & Hao Chen & Yi Cui, 2021. "Dynamic spatial progression of isolated lithium during battery operations," Nature, Nature, vol. 600(7890), pages 659-663, December.
    3. Hyndman, Rob J. & Shahid Ullah, Md., 2007. "Robust forecasting of mortality and fertility rates: A functional data approach," Computational Statistics & Data Analysis, Elsevier, vol. 51(10), pages 4942-4956, June.
    4. Seger, Pedro V.H. & Rigo-Mariani, Rémy & Thivel, Pierre-Xavier & Riu, Delphine, 2023. "A storage degradation model of Li-ion batteries to integrate ageing effects in the optimal management and design of an isolated microgrid," Applied Energy, Elsevier, vol. 333(C).
    5. Chuanlong Wang & Akila C. Thenuwara & Jianmin Luo & Pralav P. Shetty & Matthew T. McDowell & Haoyu Zhu & Sergio Posada-Pérez & Hui Xiong & Geoffroy Hautier & Weiyang Li, 2022. "Extending the low-temperature operation of sodium metal batteries combining linear and cyclic ether-based electrolyte solutions," Nature Communications, Nature, vol. 13(1), pages 1-11, December.
    6. Alexander Aue & Diogo Dubart Norinho & Siegfried Hörmann, 2015. "On the Prediction of Stationary Functional Time Series," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(509), pages 378-392, March.
    7. Wang, Shunli & Fan, Yongcun & Jin, Siyu & Takyi-Aninakwa, Paul & Fernandez, Carlos, 2023. "Improved anti-noise adaptive long short-term memory neural network modeling for the robust remaining useful life prediction of lithium-ion batteries," Reliability Engineering and System Safety, Elsevier, vol. 230(C).
    Full references (including those not matched with items on IDEAS)

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