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Two-Outputs Nonlinear Grey Box Model for Lithium-Ion Batteries

Author

Listed:
  • Cynthia Thamires da Silva

    (PEA—Polytechnic School (POLI-USP), University of São Paulo, São Paulo 05508-010, Brazil)

  • Bruno Martin de Alcântara Dias

    (PEA—Polytechnic School (POLI-USP), University of São Paulo, São Paulo 05508-010, Brazil)

  • Rui Esteves Araújo

    (INESC TEC and Faculty of Engineering, University of Porto, 4200-465 Porto, Portugal)

  • Eduardo Lorenzetti Pellini

    (PEA—Polytechnic School (POLI-USP), University of São Paulo, São Paulo 05508-010, Brazil)

  • Armando Antônio Maria Laganá

    (PEA—Polytechnic School (POLI-USP), University of São Paulo, São Paulo 05508-010, Brazil)

Abstract

Storing energy efficiently is one of the main factors of a more sustainable world. The battey management system in energy storage plays an extremely important role in ensuring these systems’ efficiency, safety, and performance. This battery management system is capable of estimating the battery states, which are used to give better efficiency, a long life cycle, and safety. However, these states cannot be measured directly and must be estimated indirectly using battery models. Therefore, accurate battery models are essential for battery management systems implementation. One of these models is the nonlinear grey box model, which is easy to implement in embedded systems and has good accuracy when used with a good parameter identification method. Regarding the parameter identification methods, the nonlinear least square optimization is the most used method. However, to have accurate results, it is necessary to define the system’s initial states, which is not an easy task. This paper presents a two-outputs nonlinear grey box battery model. The first output is the battery voltage, and the second output is the battery state of charge. The second output was added to improve the system’s initial states identification and consequently improve the identified parameter accuracy. The model was estimated with the best experiment design, which was defined considering a comparison between seven different experiment designs regarding the fit to validation data, the parameter standard deviation, and the output variance. This paper also presents a method for defining a weight between the outputs, considering a greater weight in the output with greater model confidence. With this approach, it was possible to reach a value 1000 times smaller in the parameter standard deviation with a non-biased and little model prediction error when compared to the commonly used one-output nonlinear grey box model.

Suggested Citation

  • Cynthia Thamires da Silva & Bruno Martin de Alcântara Dias & Rui Esteves Araújo & Eduardo Lorenzetti Pellini & Armando Antônio Maria Laganá, 2023. "Two-Outputs Nonlinear Grey Box Model for Lithium-Ion Batteries," Energies, MDPI, vol. 16(5), pages 1-15, February.
    • Handle: RePEc:gam:jeners:v:16:y:2023:i:5:p:2218-:d:1079966
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    References listed on IDEAS

    as
    1. Peng, Jiankun & Luo, Jiayi & He, Hongwen & Lu, Bing, 2019. "An improved state of charge estimation method based on cubature Kalman filter for lithium-ion batteries," Applied Energy, Elsevier, vol. 253(C), pages 1-1.
    2. Cynthia Thamires da Silva & Bruno Martin de Alcântara Dias & Rui Esteves Araújo & Eduardo Lorenzetti Pellini & Armando Antônio Maria Laganá, 2021. "Battery Model Identification Approach for Electric Forklift Application," Energies, MDPI, vol. 14(19), pages 1-26, September.
    3. Xiangdong Sun & Jingrun Ji & Biying Ren & Chenxue Xie & Dan Yan, 2019. "Adaptive Forgetting Factor Recursive Least Square Algorithm for Online Identification of Equivalent Circuit Model Parameters of a Lithium-Ion Battery," Energies, MDPI, vol. 12(12), pages 1-15, June.
    4. Chao-Yang Wang & Teng Liu & Xiao-Guang Yang & Shanhai Ge & Nathaniel V. Stanley & Eric S. Rountree & Yongjun Leng & Brian D. McCarthy, 2022. "Fast charging of energy-dense lithium-ion batteries," Nature, Nature, vol. 611(7936), pages 485-490, November.
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