Extending the Single Particle Model using Method of Lines

In the past years, many reduced order electrochemical models for Lithium-ion batteries have been presented. One of the most popular being the Single Particle Model (SPM), that is derived from the full order Doyle-Fuller-Newman Model (DFN). Moreover, several different numerical solving approaches have been proposed, to enhance either the modelling accuracy or the numerical performance of these models. These approaches typically make use of mathematical solving strategies that are suited to implement specific electrochemical or thermal phenomena into the model. Hence, there is a lack of models, which provide an easy extensibility to simulate different operational conditions while considering varying aspects of interest like temperature behaviour or aging.

Our results present a solving strategy by applying the numerical Method of Lines (MOL) to the SPM. The high flexibility of the model was displayed by integrating dynamic diffusion coefficients for the solid phase diffusion and thermal effects for modelling the temperature behaviour of the cell. The comprehensive extension by using the Finite Difference Method (FDM) for the spatial discretization is explained. Furthermore, the MOL-SPM was verified in its function by comparing it to a full order DFN and experimental data. For validating the thermal model extension, potentiometric measurements were carried out to determine the entropy profile of the investigated cell. The model was compared against experiments of galvanostatic discharges and a dynamic photovoltaic current profile. The MOL-SPM reached a computational speedup of over 400 for the dynamic current profile. Along with that, it still delivered a similar small model error in comparison to the DFN with an RMSE difference of only 0.9 mV. Finally, also the thermal extension was verified by comparing it against experimental data.