Lithium ion battery is nowadays one of the most popular energy storage devices due to its high energy, power density and cycle life characteristics. It has been known that the overall performance of battery depends on not only electrolyte and electrode materials, but also operation condition and choice of physical parameters. Designers need to understand the thermodynamic and kinetic characteristics of battery, which is costly and time-consuming by experimental methods. However, lithium ion battery is a complicated electrochemical system with multi physicochemical processes including the mass, charge, and energy conservations as well as the electrochemical kinetics. It not only has a typical multiple level arrangement: across the electrode level, cell level, and extending to the battery module level, which is different from the basic active material particle level arrangement, but also confronts the challenges to meeting the requirements for sorting and consistency method for battery. These facts increase the difficulties in designing the battery and evaluating the overall performance. Owing to the rapid development of multi-scale numerical simulation technology, the multi-scale mathematical models for lithium ion battery are developed to help battery designer comprehensively and systematically gain the interaction mechanisms between different physicochemical fields in the battery working process and analyze the regulations of these interaction mechanisms, which is significant in providing theoretical supports for designing and optimizing the battery systems. At present, multi-type lithium ion battery models coupled with many physicochemical processes have been developed on different scales to study different issues, such as thermal behavior, inner polarization, micro structure, inner stress and capacitance fading, etc. In this paper, we review the research statuses and development trends of multi-scale mathematical models for lithium ion battery. The primary theoretical models for lithium ion battery are systemized and their features, application ranges and limitations are also summarized. Furthermore, the future research area and the difficulty in industry application are discussed. All of these are helpful for the theoretic research and engineering application of the multi-scale numerical models for lithium ion battery.
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