A Coupled Tank-in-Series Electrochemical-Thermal Model for Lithium Sulfur Batteries
Authors: Parke Caitlin D. , Subramaniam Akshay , Kolluri Suryanarayana , Schwartz Daniel T , Subramanian Venkat R. 
Published: December 2020

Lithium sulfur batteries are a promising option for next-generation energy storage in electric transportation, and some companies have reported values over 400 Wh/kg (1). The push for more energy density within batteries can result in higher resistive batteries. For lithium sulfur batteries in particular, a study has shown that the cell resistance increases with increased capacity (2). As the energy stored within battery packs increase, the importance of thermal management for safety and performance also grows, which requires an accurate thermal model for design and control. A joint understanding of the thermal and electrochemical behavior is especially important in a system as nonlinear and complex as lithium sulfur batteries. However, the majority of lithium sulfur physics-based models are isothermal and do not consider thermal effects. To that end, we propose coupling a thermal and electrochemical model for lithium sulfur batteries.
To describe the electrochemical behavior, our work utilizes physics-based models that give insight into the internal states of a battery, which describe phenomena that can contribute to decreased performance under certain conditions. The lithium sulfur model in this study is the one-dimensional physics-based model developed by Kumaresan et al. (3) that considers transport, kinetics, thermodynamics, and morphological changes within the lithium sulfur cell under isothermal conditions. The corresponding set of equations results in a numerically stiff system with variables evolving across many orders of magnitude. To alleviate the computational footprint while maintaining a high degree of accuracy, we have previously developed a mass-conserving lumped model through volume-averaging, called the Lithium Sulfur Tank-in-Series Model. The tank-in-series method was developed for lithium ion batteries (4) and adapted to the lithium sulfur system. The Lithium Sulfur Tank-in-Series model, with average quantities in each region, eliminates the spatial dependence for increased computational efficiency that expedites model use in estimation, control, and optimization.
Mathematical thermal models have been developed for lithium sulfur batteries, including both 2D (5) and lumped models (6). These models are based on the general energy balance for batteries by Bernardi et al. (7) and include heat generation terms that are functions of thermodynamics, overpotentials, and material conductivities. The work by Stroe et al. (6) also detailed an experimental plan for determination of parameters, as well as their experimentally derived values. The results from the 2D model study (5) found that the temperature gradients within the cell were negligible, which indicates that a lumped model may capture the thermal behavior well.
In this work, we extend mathematical modeling of lithium sulfur batteries by coupling the Tank-in-Series model with a thermal model based on the work by Stroe (6), which includes heat generation due to internal resistance and entropic contributions. Suitable approximations are made to estimate the various source terms within the thermal model. Coupling the thermal model with a more accurate predictive electrochemical model allows further insight into battery performance and future use in estimation and control.

Acknowledgments

The authors are thankful for financial support from the Advanced Battery Material Research (BMR) Program (Battery 500 Consortium).

References

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