Mathematical Modeling Of Lithium Batteries

Mathematical Modeling of Lithium Ion Batteries and Cells

Mathematical Modeling of Lithium Batteries

This book is unique to be the only one completely dedicated for battery modeling for all components of battery management system (BMS) applications. The contents of this book compliment the multitude of research publications in this domain by providing coherent fundamentals. An explosive market of Li ion batteries has led to aggressive demand for mathematical models for battery management systems (BMS). Researchers from multi-various backgrounds contribute from their respective background, leading to a lateral growth. Risk of this runaway situation is that researchers tend to use an existing method or algorithm without in depth knowledge of the cohesive fundamentals—often misinterpreting the outcome. It is worthy to note that the guiding principles are similar and the lack of clarity impedes a significant advancement. A repeat or even a synopsis of all the applications of battery modeling albeit redundant, would hence be a mammoth task, and cannot be done in a single offering. The authors believe that a pivotal contribution can be made by explaining the fundamentals in a coherent manner. Such an offering would enable researchers from multiple domains appreciate the bedrock principles and forward the frontier. Battery is an electrochemical system, and any level of understanding cannot ellipse this premise. The common thread that needs to run across—from detailed electrochemical models to algorithms used for real time estimation on a microchip—is that it be physics based. Build on this theme, this book has three parts. Each part starts with developing a framework—often invoking basic principles of thermodynamics or transport phenomena—and ends with certain verified real time applications. The first part deals with electrochemical modeling and the second with model order reduction. Objective of a BMS is estimation of state and health, and the third part is dedicated for that. Rules for state observers are derived from a generic Bayesian framework, and health estimation is pursued using machine learning (ML) tools. A distinct component of this book is thorough derivations of the learning rules for the novel ML algorithms. Given the large-scale application of ML in various domains, this segment can be relevant to researchers outside BMS domain as well. The authors hope this offering would satisfy a practicing engineer with a basic perspective, and a budding researcher with essential tools on a comprehensive understanding of BMS models.

Mathematical Modeling of Lithium-ion Intercalation Particles and Their Electrochemical Dynamics

Lithium-ion battery is a family of rechargeable batteries with increasing importance that is closely related to everyone's daily life. However, despite its enormously wide applications in numerous areas, the mechanism of lithium-ion transport within the battery is still unclear, especially for phase separable battery materials, such as lithium iron phosphate and graphite. Mathematical modeling of the battery dynamics during charging/discharging will be helpful to better understand its mechanism, and may lead to future improvement in the battery technology. In this thesis, a new theoretical framework, the Cahn-Hilliard reaction (CHR) model, is applied to model the bulk phase separation dynamics of the single intercalated particle in the lithium-ion battery. After a study of the efficient numerical algorithm for solving nonlinear diffusion equations, we numerically investigate the thermodynamics and electrokinetics of the 1D spherical CHR model with different possible material properties in detail. We also extend the CHR model to 2D and briefly study the effects of the surface electron-conducting coating layer. We also work on the Marcus theory, which is demonstrated to be a better theoretical framework for heterogeneous electron transfer at the surface of intercalated particles in the batteries. We provide simple closed-form approximations to both the symmetric Marcus-Hush-Chidsey (MHC) and the asymmetric-Marcus-Hush (AMH) models by asymptotic technique. By avoiding the numerical evaluations of the improper integral in the old formulae, computing the surface reaction rate with the new approximation is now more than 1000 times faster than before.