(Industrial Electrochemistry and Electrochemical Engineering Division H. H. Dow Memorial Student Achievement Award) Electrochemical Modeling and Simulation of Battery Systems: Approaches for Design, Control, and Multiscale Simulations
Authors: Subramaniam Akshay , Schwartz Daniel T. , Subramanian Venkat R. 
Published: July 2021

Current imperatives of electrification and decarbonization entail significant improvements in energy density, performance, and cost metrics for battery technology.1 This has motivated active research into new materials, cell designs, and external controls to ensure safe and efficient operation. Modeling and simulation approaches have a powerful complementary function in this regard, most notably exemplified by the models for Lithium-ion batteries by Newman and co-workers.2 The overarching theme of this talk is thus the development and application of electrochemical modeling approaches at multiple scales in problems relevant to the abovementioned contexts.
In the development of next-generation chemistries, continuum models can serve as a framework for the analysis and interpretation of experimental data, while providing design guidance and helping determine desirable operating regimes. Electrochemical phenomena at different length and time scales are manifested during operation through voltage and temperature signatures, cycle life, and coulombic efficiency. Optimization of cell-level metrics is thus predicated on their correlation with the internal electrochemistry.3,4 This entails the integration of electrochemical models at different levels of detail in a computationally efficient and robust manner. To this end, the first part of this talk describes our efforts to develop a unified, multiscale continuum simulation for framework Lithium-metal batteries. We first describe a robust computational framework to simulate Poisson Nernst Planck (PNP) models for Lithium symmetric cells characterized by thin double layers. This can be leveraged in applications where computational efficiency is of salience, such as cycling simulations and parameterization by coupling kinetic models of interest. This is demonstrated by a systems level method, enabling the quick evaluation of candidate mechanisms appropriately expressed as time-varying rate constants, making it useful for understanding the phenomena underpinning voltage transitions in Lithium symmetric cells.5 In a second study, we leverage these computational tools to propose an alternate mechanism for voltage signatures stemming from the interplay of transport and kinetic limitations, which is of relevance in transport-limited symmetric cells used in fundamental studies.6 We then describe the integration of electrochemical models of various levels of detail, evaluating computational approaches for numerical challenges associated with simulating moving interfaces and mechanical deformations.7 We expect this approach to advance fundamental understanding and design of Li-metal batteries, while creating accessible computational tools to complement experimental studies.
At the systems level, the development of more intelligent and powerful Battery Management Systems is enabled by fast electrochemical models, which must balance competing considerations of accuracy, computational efficiency, and ease of parameterization. To this end, we report a rigorous and generalized methodology for ‘upscaling’ electrochemical models.8 This approach, based on the visualization of a battery as Tanks-in-Series, has been demonstrated for both Lithium-ion and more complex Lithium-sulfur batteries.9 With respect to full models, voltage prediction errors below 20 mV are achieved for high-energy cells in most practical cases. <30 mV errors are achieved for aggressive conditions of high-rate operation at sub-zero ambient temperatures, illustrating their practical utility. This approach results in improved computational speed since each conservation law is replaced by a relatively simple volume-averaged differential or algebraic equation. For examples of large-scale problems, this leads to >10x savings in computation time over fast implementations of conventional models, illustrating competitiveness for real-time applications.
Taken together, these contributions are envisaged to advance the knowledge base for model-based design as well as Battery Management Systems, particularly in anticipation of the commercialization of emerging battery chemistries. Acknowledgments
The authors are thankful for financial support by the Assistant Secretary for Energy Efficiency and Renewable Energy, Office of Vehicle Technologies of the U.S. Department of Energy through the Advanced Battery Materials Research (BMR) Program (Battery500 Consortium). References

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