Macro-Scale Lithium-Ion Battery Simulation by Means of the Finite Element Method and Concentrated Solution Theory

Abstract

Lithium-ion batteries are the leading contender for high density energy storage for applications such as electric vehicles and personal electronic devices. While they promise well over 4 V of potential per cell, actually realizing such high voltages is quite difficult, given the many modes of energy loss during discharge. One dominant loss, especially at high currents (e.g., fast-charging) is losses due to ionic transport in the electrolyte. Mathematical models and their computational implementation have been used to simulate Lithium-ion battery discharge to better understand its complex physics and to optimize its design. Because of the complex and dynamic nature of Lithium-ion batteries, these models are transient and highly non-linear. A difficulty arises in that the scales on which key physics occurs varies over many orders of magnitude, meaning simulations often decouple scales to some degree to conserve computational resources. In this thesis, a transient and non-linear numerical model is developed for the lithium-ion battery macro-scale, that is, the scale on which heterogeneities due to microscopic components can be ignored. Additionally, the electrolyte is studied separately by isolating the separator contribution by modelling a symmetric Li-foil cell. The numerical model is supported by a rigorous set of mathematical derivations for the governing equations. This process utilizes concentrated solution theory and the finite element method. First the symmetric cell system is verified by reproducing the voltage response to a constant current step reported from experiments in the literature. A sensitivity analysis is performed for the electrolyte characteristics and discussed in terms of their influence on cell performance. After concluding that the electrolyte model accurately reproduces the real-world system, the model is applied to a novel electrolyte for which no previous numerical modelling has been performed. It is concluded that the experimental results do not match what is expected from the model, due to the non-reproducibility of the experimental data. The full macro-scale battery model is analyzed in terms of its voltage response and solution variable profiles during a constant current discharge. Following a study of the cell’s hysteresis, the battery’s capacity and efficiency are calculated. Another sensitivity analysis provides insight into the importance of the active material’s characteristics on cell performance. Finally, running the battery at different current densities confirms that increasing the rate of cell charge/discharge will negatively impact the efficiency of the system.