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

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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.