Understanding Batteries via Simulations

This article aims to provide a good understanding of batteries and how various physical parameters affect the quantities of interest. For this, we would be utilizing PyBAMM [1], a Python-based battery simulation tool, as it offers holistic simulation capabilities with a relatively small learning curve.

What is a cell/battery?

Cells are devices that convert chemical to electrical energy. It consists of two electrodes, a cathode and an anode, which are immersed in a solution called an electrolyte.

Figure 1: Electrochemical Cell with its components (Source: Original Author: Barrie Lawson., CC BY-SA 3.0, via Wikimedia Commons)

Chemical reactions between them generate a flow of electrons and during discharge, electrons flow in the opposite direction. This flow of electrons between the two electrodes can be used to store and release energy.

“Battery” is a combination of cells, that could be connected to give the required voltage and current supply.

Simulations

Various 1D and 2D models are used to study the behaviour of electrochemical cells. A review of the commonly used models is provided in [2], which also includes a useful video abstract.

For this article, we will be using the 2D DFN model, which captures multi-dimensional effects but assumes the various components are homogenised and for a specific geometry.

Figure 2: Variation of terminal voltage with cathode thickness across time. Other parameters as defined in [3]

First, a typical Lithium-ion battery as described in [3] is considered. The cell is discharged at a “1C-rate”, meaning that the entire capacity can be discharged in 1 hour. And, for 2C-rate, it would mean twice the discharge rate, and that implies half an hour of operation.

The cathode (Li-side) thickness is varied between three values in Fig. 2 and it can be noted that the thicker electrodes have less drop in voltage over time. This is due to a larger surface area and less internal resistance even during operation.

Figure 3: Variation of terminal voltage with anode thickness across time. Other parameters as defined in [3]

Similarly, the anode (graphite) side thickness is varied between three values in Fig. 3. Here, the behaviour is non-monotonic due to several competing effects. A thicker anode can have less resistance but can create fewer pathways for ions to diffuse. Thus, it is difficult to predict such trends without carrying out simulations for particular load cycles.

Figure 4: Variation of terminal voltage with the initial concentration of electrolyte (in moles/litre or M) across time. Other parameters as defined in [3]

The next parameter that can be changed is the concentration of electrolyte. As seen in Fig. 4, a highly concentrated solution being used for electrolyte is leading to a situation where the terminal voltage registered is higher than the baseline. This is a trend that is maintained over time.

Figure 5: Variation of X-averaged reaction overpotential with initial concentration of electrolyte (in moles/litre or M) across time. Other parameters as defined in [3]

This can be more clearly observed when the battery reaction overpotential is plotted over time for various concentrations. Reaction overpotential, also known as polarization, is the additional potential or voltage required to drive an electrochemical reaction at a certain rate compared to the equilibrium. In Fig. 5, the large concentration leads to higher overpotential, which should lead to lesser terminal voltage. This shows the importance of other effects in determining the cell potential.

Figure 6: Variation of terminal voltage with discharge rate across time. Other parameters as defined in [3]

Faster discharge rates, as seen in Fig. 6, lead to quicker degradation of terminal voltage. However, it is interesting that 10C-rate discharge does provide high terminal voltage even beyond the 0.1-hour mark.

Figure 7: Variation of terminal voltage with battery chemistry across time. Cell parameters for lithium and LFP are defined in [3] and [4] respectively

Using a different battery chemistry leads to variation in the terminal voltage plot over time. The starting potential would be different due to the different standard potentials for the two electrodes being used. Higher standard electrode potential signifies ease of losing electrons. Fig. 7 shows that the Lithium cell indeed has a higher terminal voltage than its LFP (Lithium Iron Phosphate) counterpart.

Summary

This article discusses the contents of an electrochemical cell and how the variation of parameters of its contents affects its operation. First, an overview of the electrochemical cell is presented. Then, the effect of changing the cathode, anode and electrolyte is shown using Python-based simulations. The concept of discharge rate is discussed along with its effect on terminal voltage. In conclusion, the effect of electrode materials on its potential is presented. Due to various competing effects, the influence of parameters is not always straightforward and the need for detailed simulations is shown.

Code

The simulations used to generate the results in this article can be found in this link. All simulations were performed using default solver parameters of PyBAMM and converged according to those thresholds.

References

[1] Sulzer, V., Marquis, S. G., Timms, R., Robinson, M., & Chapman, S. J. (2021). “Python Battery Mathematical Modelling (PyBaMM)”. Journal of Open Research Software, 9 (1), 14.

[2] Brosa Planella, F., Ai, W., Boyce, A. M., Ghosh, A., Korotkin, I., Sahu, S., et al.(2022). A Continuum of Physics-Based Lithium-ion Battery Models Reviewed. Progress in Energy, 4(4), 042003.

[3] Chen, C. H., Planella, F. B., O’Regan, K., Gastol, D., Widanage, W. D., & Kendrick, E. (2020). Development of Experimental Techniques for Parameterization of Multi-Scale Lithium-ion Battery Models. Journal of The Electrochemical Society, 167(8), 080534.

[4] Prada, E., Di Domenico, D., Creff, Y., Bernard, J., Sauvant-Moynot, V., & Huet, F. (2013). A Simplified Electrochemical and Thermal Aging Model of LiFePO4-Graphite Li-ion Batteries: Power and Capacity Fade Simulations. Journal of The Electrochemical Society, 160(4), A616.