Design, analysis, and computation of mathematical models for lithium-ion batteries

锂离子电池（LIB）作为电能存储的手段在社会中占主导地位。它们经常用于移动的手机、医疗设备和其他电子产品，预计到2022年市场规模将超过850亿美元。气候变化等环境影响的经济和社会成本不断上升，政策制定者正在转向在未来30年内禁止燃烧车辆。锂离子动力汽车目前被预测为内燃机的替代选择，这将对目前价值超过3万亿美元的全球运输业产生巨大影响。 目前的工业挑战是到2030年将电池的能量密度从100-250 Wh/kg提高到450 Wh/kg。这需要在保持相对低的成本和生产安全电池的同时实现，由于移动的电话中的电池过热和爆炸，后者最近已经突出。为了充分实现这些成就，需要新的科学和工程进步。电池是电池的集合，其中每个电池由两个电极组成：阳极和阴极以及使它们分开的隔板。许多变量控制电池操作，包括电极材料、锂浓度和锂迁移率。然而，这些通常难以测量，并且通常仅电压和电流输出可用于监测电池性能。将内部电池操作变量与可测量的输出变量相关联的成功工具是数学建模。拟议研究的目标是通过指导数学建模来加速LIB的开发，该数学建模将设备性能与电池的基本化学过程联系起来。将采用两种数学建模方法：第一原理连续建模和简化建模。第一原理连续体建模涉及开发新模型，解决以前被忽视的电池过程。简化建模是将复杂模型简化为更快、更便宜的模拟形式的过程。在整个研究计划中，这些工具将用于解决LIB中的过热和爆炸，LIB的降解以及减少降解和提高能量密度的新型材料。还原将用于确定主要机制，例如生热速率，这些机制可以由工程师控制，用于下一代电池原型设计。我们还将设计可以在真实的时间内完成的模拟，并可以纳入未来电池管理系统的控制算法中。这项研究计划将提高电池的安全性、性能和寿命。这将导致新的原型开发，并通过更好的电池产生巨大的经济和社会影响，使加拿大处于锂离子电池行业的前沿，并解决联邦政府清洁能源和低碳经济的倡议。

Lithium-ion batteries (LIBs) dominate society as a means for electrical energy storage. They are frequently used in mobile phones, medical devices, and other electronics and are predicted to have a market size of over $85 billion by 2022. The rising economic and societal costs of environmental impacts such as climate change are shifting policy makers towards banning combustion vehicles within the next 30 years. LIB powered vehicles are currently predicted as a replacement option for the combustion engine which will have a massive impact on the global transportation industry currently valued at over $3 trillion. The current industrial challenge is to improve energy density in batteries from 100-250 Wh/kg to 450 Wh/kg by 2030. This needs to be achieved while maintaining relatively low costs and producing safe batteries, the latter of which has featured prominently recently due to overheating and exploding batteries in mobile phones. To be fully realised, these achievements will require new scientific and engineering advancements. A battery is a collection of cells where each cell is composed of two electrodes: an anode and a cathode as well as a separator which keeps them apart. Many variables control battery operation including electrode material, lithium concentration, and lithium mobility. However, these are often difficult to measure and typically only voltage and current outputs are available for monitoring battery performance. A successful tool for relating internal battery operation variables to measurable output variables is mathematical modelling. The goal of the proposed research is to accelerate LIB development through guided mathematical modelling that relates device performance to the underlying chemical processes of the battery. Two mathematical modelling approaches will be implemented: first principles continuum modelling and reduction modelling. First principles continuum modelling involves the development of new models addressing previously neglected battery processes. Reduction modelling is the process of simplifying complex models to forms which lead to faster and cheaper simulations. Throughout this research program these tools will be used to address overheating and explosions in LIBs, degradation of LIBs, and novel materials which reduce degradation and improve energy density. Reduction will be used to identify dominant mechanisms such as rate of heat generation which can be controlled by engineers for the next generation of battery prototyping. We will also design simulations that can be done in real time and can be incorporated into control algorithms in future battery management systems. This research program will improve battery safety, performance and longevity. This will lead to new prototype development and have immense economic and social impacts through better batteries, placing Canada at the forefront of the LIB industry and addressing the federal governments clean energy and low-carbon economy initiatives.