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Neural equivalent circuit models: Universal differential equations for battery modelling

Author

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  • Kuzhiyil, Jishnu Ayyangatu
  • Damoulas, Theodoros
  • Widanage, W. Dhammika

Abstract

Current battery modelling methodologies including equivalent circuital modelling and electrochemical modelling do not maintain accuracy over diverse operating conditions of current rates, depth-of-discharge and temperatures. To address this limitation, this article proposes the Universal Differential Equations (UDE) framework from scientific machine learning (SciML) as a methodology to generate battery models with improved generalisability. The effectiveness of UDE in enhancing generalisability is demonstrated through a specific battery modelling example. The approach starts with the Thermal Equivalent Circuital Model with Diffusion (TECMD), a state-of-the-art battery model, which is then enhanced through the integration of neural networks into its state equations, resulting in the Neural-TECMD; a UDE model. Additionally, a two-stage UDE parameterisation method is introduced, combining collocation-based pretraining with mini-batch training. The parameterisation method enables the neural networks in the Neural-TECMD to efficiently learn battery dynamics from multiple time series data sets, covering a wide operating spectrum. Consequently, the Neural-TECMD model offers accurate predictions over broader operating conditions, thus enhancing model generalisability. The Neural-TECMD model was validated using 20 data sets covering current rates of 0 to 2C and temperatures from 0 to 45 °C. This validation revealed substantial improvements in accuracy, with an average of 34.51% decrease in RMSE for voltage and a 24.94% decrease for temperature predictions compared to the standard TECMD model.

Suggested Citation

  • Kuzhiyil, Jishnu Ayyangatu & Damoulas, Theodoros & Widanage, W. Dhammika, 2024. "Neural equivalent circuit models: Universal differential equations for battery modelling," Applied Energy, Elsevier, vol. 371(C).
    • Handle: RePEc:eee:appene:v:371:y:2024:i:c:s0306261924010754
    DOI: 10.1016/j.apenergy.2024.123692
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    References listed on IDEAS

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    4. Fan, Chuanxin & O’Regan, Kieran & Li, Liuying & Higgins, Matthew D. & Kendrick, Emma & Widanage, Widanalage D., 2022. "Data-driven identification of lithium-ion batteries: A nonlinear equivalent circuit model with diffusion dynamics," Applied Energy, Elsevier, vol. 321(C).
    5. Paul Stapor & Leonard Schmiester & Christoph Wierling & Simon Merkt & Dilan Pathirana & Bodo M. H. Lange & Daniel Weindl & Jan Hasenauer, 2022. "Mini-batch optimization enables training of ODE models on large-scale datasets," Nature Communications, Nature, vol. 13(1), pages 1-17, December.
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