As lithium ion batteries are approaching their performance limits, research on alternative chemistries that can meet the energy demands for electric vehicles and grid applications has increased. Lithium sulfur is one chemistry with a high theoretical specific capacity of 2500 Wh/kg and practical values of 500-600 Wh/kg¹. Sulfur is also cheap, making lithium sulfur batteries very attractive. The current issues with these batteries include capacity fade, self-discharge, and high electrical resistance, which mostly stem from the shuttle effect of the polysulfide ions². During discharge, the solid sulfur at the cathode is dissolved into polysulfide ions; these ions are soluble in the electrolyte and can diffuse to the anode and react with the lithium metal; they form a film on the anode of Li₂S, which results in irreversible loss of capacity and active material¹.

Physics-based battery models can provide control and insight into better battery performance and design by modeling the internal states of a battery. The challenging aspects of modeling lithium sulfur batteries are due to the complicated reaction network, the number of species involved, and the multiple phase changes, from solid sulfur dissolution to Li₂S precipitation. Because of this, lithium sulfur battery models result in complex equations and require a stiff solver. Several groups have modeled different aspects of lithium sulfur cells. Mikhaylik and associates³ modeled lithium sulfur system through a zeroth order model. The first one-dimensional model that incorporates the electrochemical and chemical interactions of lithium sulfur batteries was developed by Kumaresan and associates⁴. Their model includes the kinetics of the electrochemical reactions and the precipitation and dissolution reactions and ionic transport described by the Nernst-Planck equation coupled with electroneutrality. For low currents, the qualitative nature of the lithium sulfur discharge curve is adequately captured. Ghaznavi and Chen performed an extensive sensitivity analysis of the Kumaresan model, including effects of current, reaction kinetics, sulfur loading, and cathode conductivity, which highlighted opportunities for further model development^5,6,7. Other groups have built on the original model through focusing on precipitation, charging, or simpler models with fewer fitted parameters^8-13.

In this work, we propose to do a comparison study of different numerical methods for solving the complicated and stiff equations that arise from the lithium sulfur chemistry (Kumaresan model). The study includes an attempt to reduce the simulation time to enable real-time control and integration into Battery Management Systems (BMS). To this end, the performance of multiple model reformulation techniques and solver algorithms will be evaluated in terms of accuracy, computational performance, and their ability to predict cell-level responses across practical operating conditions.

Acknowledgments

The authors are thankful for the financial support from the Battery 500 Consortium and the Clean Energy Institute (CEI) at the University of Washington.

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