Coupled Tank-in-Series Electrochemical-Thermal Model for Lithium Sulfur Batteries
Authors: Parke Caitlin D. , Subramaniam Akshay , Kolluri Suryanarayana , Pathak Manan , Subramanian Venkat R. 
Published: May 2020

Lithium sulfur (LiS) batteries are a promising option for next-generation energy storage due to their high energy density. Applications where weight is especially important like electric flight and electric vehicles have driven the study of this chemistry because the current technology cannot meet the higher energy density requirements. A recent study (1) estimated specific energy requirements for short-range aircraft to start at 750 Wh/kg, about 3 times the specific energy of lithium ion battery packs. Lithium sulfur batteries have a high theoretical specific energy of 2600 Wh/kg, with some companies reporting values over 400 Wh/kg (2). For these applications, the demand for packing more energy into a battery can lead to batteries with higher resistance. For lithium sulfur batteries in particular, the resistance is seen to increase with higher capacities per cell (3). As the required energy and subsequent size of the battery packs increase, the importance of heat dissipation for safety and performance also grows, which requires an accurate thermal model for design and control.
A thermal study done by Stroe et al. (4) on lithium sulfur pouch cells detailed a lumped thermal model and experimental plan for determination of thermal parameters. However, the study assumed adiabatic conditions, meaning no external heat transfer was considered. For practical uses in a battery management system or battery pack sizing, adiabatic conditions no longer hold.
Physics-based models enable a look into the internal states of the battery, which correspond to physical phenomena that can contribute to decreased performance under certain conditions. The physics-based models for lithium sulfur have focused on transport, kinetics, or morphology under isothermal operation. The mathematical model for lithium sulfur batteries developed by Kumaresan et al. (5) was the first one-dimensional physics-based model for lithium sulfur batteries. This discharge model was developed on porous electrode theory and considers transport, kinetics, thermodynamics, and morphological changes. The corresponding physics-based model results in a numerically stiff set of equations with variables evolving across many orders of magnitude. To alleviate the computational footprint and still maintain 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. This model, with average quantities in each region, eliminates the spatial dependence for increased computational efficiency that expedites model use in estimation, control, and optimization.
In this work, the LiS tank-in-series model is coupled with a thermal model based on the work by Stroe (4). The thermal model 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 model allows further insight into battery performance.

Acknowledgments

The authors are thankful for financial support from the Battery500 Consortium, BAE Systems, and the Joint Center for Aerospace Technology Innovation.

References

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3. J. Offer and M. Wild, Lithium Sulfur Batteries, p. 149, John Wiley & Sons, New Jersey (2019).
4. I. Stroe, V. Knap, M. Swierczynski, and E. Schaltz, ECS Trans., 77, 467–476 (2017).
5. Kumaresan, Y. Mikhaylik, and R. E. White, J. Electrochem. Soc., 155, A576 (2008).