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Neural Ordinary Differential Equations for Grey-Box Modelling of Lithium-Ion Batteries on the Basis of an Equivalent Circuit Model

Author

Listed:
  • Jennifer Brucker

    (Institute of Sustainable Energy Systems, Offenburg University of Applied Sciences, Badstraße 24, 77652 Offenburg, Germany)

  • René Behmann

    (Institute of Sustainable Energy Systems, Offenburg University of Applied Sciences, Badstraße 24, 77652 Offenburg, Germany)

  • Wolfgang G. Bessler

    (Institute of Sustainable Energy Systems, Offenburg University of Applied Sciences, Badstraße 24, 77652 Offenburg, Germany)

  • Rainer Gasper

    (Institute of Sustainable Energy Systems, Offenburg University of Applied Sciences, Badstraße 24, 77652 Offenburg, Germany)

Abstract

Lithium-ion batteries exhibit a dynamic voltage behaviour depending nonlinearly on current and state of charge. The modelling of lithium-ion batteries is therefore complicated and model parametrisation is often time demanding. Grey-box models combine physical and data-driven modelling to benefit from their respective advantages. Neural ordinary differential equations (NODEs) offer new possibilities for grey-box modelling. Differential equations given by physical laws and NODEs can be combined in a single modelling framework. Here we demonstrate the use of NODEs for grey-box modelling of lithium-ion batteries. A simple equivalent circuit model serves as a basis and represents the physical part of the model. The voltage drop over the resistor–capacitor circuit, including its dependency on current and state of charge, is implemented as a NODE. After training, the grey-box model shows good agreement with experimental full-cycle data and pulse tests on a lithium iron phosphate cell. We test the model against two dynamic load profiles: one consisting of half cycles and one dynamic load profile representing a home-storage system. The dynamic response of the battery is well captured by the model.

Suggested Citation

  • Jennifer Brucker & René Behmann & Wolfgang G. Bessler & Rainer Gasper, 2022. "Neural Ordinary Differential Equations for Grey-Box Modelling of Lithium-Ion Batteries on the Basis of an Equivalent Circuit Model," Energies, MDPI, vol. 15(7), pages 1-20, April.
    • Handle: RePEc:gam:jeners:v:15:y:2022:i:7:p:2661-:d:787334
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    References listed on IDEAS

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    1. Franz Hamilton & Alun L Lloyd & Kevin B Flores, 2017. "Hybrid modeling and prediction of dynamical systems," PLOS Computational Biology, Public Library of Science, vol. 13(7), pages 1-20, July.
    2. Hongwen He & Rui Xiong & Jinxin Fan, 2011. "Evaluation of Lithium-Ion Battery Equivalent Circuit Models for State of Charge Estimation by an Experimental Approach," Energies, MDPI, vol. 4(4), pages 1-17, March.
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