@article{BruckerBehmannBessleretal.2022,
  author    = {Brucker, Jennifer and Behmann, Ren{\´e} and Bessler, Wolfgang G. and Gasper, Rainer},
  title     = {Neural Ordinary Differential Equations for Grey-Box Modelling of Lithium-Ion Batteries on the Basis of an Equivalent Circuit Model},
  journal   = {Energies},
  volume    = {15},
  number    = {7},
  issn      = {1996-1073},
  doi       = {10.3390/en15072661},
  institution = {Fakult{\"a}t Maschinenbau und Verfahrenstechnik (M+V)},
  pages     = {2661},
  year      = {2022},
  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.},
  language  = {en}
}