Electrothermal and Electrochemical Modeling of Lithium-ion Batteries: 3D Simulation with Experimental Validation

Mathematical modeling is an essential tool for the design, construction, and operation of battery cells and systems. There is a large number of battery models with various complexities and length scales of consideration. At the highest level there are system models which usually do not have a spatial dimension. The smallest component is typically a battery cell. Often they are real-time capable and can be used in HIL (hardware-in-the-loop) simulations. At the next level (length scales ~cm to ~mm) electrothermal models are used. They are capable of predicting the temperature distribution in battery cells, modules and packs and are typically based on empirical current/voltage relationships. For the length scales ~mm to ~mm electrochemical transport models are applied. In these models reaction layers are spatially resolved and basic physical transport mechanisms, e.g. the diffusion of lithium ions, are calculated. Finally, for the smallest scales (~mm to ~nm) molecular models exist which are used in material science.

This work focuses on the comparison of the electrothermal and electrochemical models implemented in the multiphysics software package FIRE ^®developed by AVL List GmbH [1]. Whereas electrothermal models often are three-dimensional, electrochemical models usually contain only one spatial direction (e.g. normal to the separator). In the present work, both models are used in three dimensions allowing for a detailed comparison of their results in temporal evolutions as well as spatial distributions. The most important characteristics of both models are listed in Table 1. The pros and cons are obvious: The electrochemical model provides a higher accuracy but also requires a higher calculation time. The electrothermal model needs a larger number of fitting parameters whereas the electrochemical model needs a larger number of material parameters but, hence, also allows for the investigation of different material properties of the reaction layers.

This work is divided into the following three main parts:

1. Theoretical background of both models
2. Model fitting to experimental data
3. Model application to a realistic case with experimental validation

For the second and third part a high energy lithium-ion battery of the pouch type, typically used in electric vehicles, is considered. In the second part, both the electrothermal and the electrochemical model are adjusted independently from each other to experimental discharge curves for different constant current loads and temperatures – see Figure 1 for the electrothermal model. After that, the calculation results obtained with both models are compared to each other: The temporal evolution of averaged quantities (e.g. cell voltage) as well as the spatial distribution of quantities (e.g. temperature or state of charge – see Figure 2) at fixed time steps are shown. Moreover, a deep insight into the battery is given with the electrochemical model via a visualization of results in the electrodes (e.g. lithium concentration). In the third part, finally, the models are tested for a case where the battery is loaded with a realistic current profile – see Figure 3. Voltage response and temperature evolution are being compared to experimental data. Moreover, the results of both models are being compared to each other once more.

With the results shown in this work the strengths and weaknesses of electrothermal and electrochemical models are pointed out clearly. Conclusions to adequate application fields for both models can be drawn from the results. Future work includes the application of the electrothermal and electrochemical model to battery modules and stacks as well as an investigation of degradation phenomena in batteries with the electrochemical model.

[1]   FIRE ^® v2013, Electrification / Hybridization Manual, AVL List GmbH, 2013.

[2]   M. Doyle and J. Newman, J. Electrochem. Soc. 143, 1890-1903, 1996.