A New Multiphysics Modeling Framework to Simulate Large Battery Packs
Authors: Jordan Skylar , Schreiber Owen , Kolluri Suryanarayana , Shah Krishna , Parhizi Mohammad 
Published: November 2022

Li-ion batteries are used in a wide variety of applications, ranging from consumer electronics to electric vehicles (EVs) and large-scale energy storage. There are also ongoing efforts to electrify air transportation. The system level issues such as safety, thermal effects, and cell balancing need to be addressed as use of batteries become widespread in the transportation sector. These issues can be studied experimentally, however, extensive experimental testing at system level involving large battery packs is impractical. Additionally, experimental testing alone cannot provide insights into these issues. This makes experimental characterization studies necessary as well, which are not feasible beyond the lab scale. Appropriate use of modeling and simulation can provide an attractive alternative to gain insights into the system level issues. Presently, simplified equivalent circuit and empirical models are typically used at pack level. Since these models do not capture various physical phenomena and electrochemical processes, they cannot provide necessary insights into these issues. There are many simulation studies on thermal management of battery packs, but these studies are limited to studying heat transfer and fluid flow without capturing their effect on the life and performance of batteries. At the scale of a single li-ion cell, there are physics-based models incorporating various processes, including transport processes, reaction kinetics, thermal effect, and degradation mechanisms. However, these models are typically not used to study battery packs. One such attempt reported in literature involved the use of thermal single-particle battery model at the pack level, but this study considered simplified thermal boundary conditions representing natural convection type heat transfer, a rather simplistic treatment for the heat leaving the batteries1. There have been other similar studies as well2-4. Since thermal management systems presently used in EVs and new designs developed by researchers involve far more complex heat transfer processes, a model capturing heat transfer processes in these thermal management systems in an accurate manner is necessary. Using an accurate physics-based electrochemical-thermal model at the battery pack level and combing it with a heat transfer model for battery thermal management system can enable studying battery performance, aging, and safety characteristics at the pack level. However, this type of simulation would be computationally prohibitively expensive, especially for large battery packs, like the ones used in EVs.
In the present work, we first develop volume averaged heat transfer models for two different battery pack designs, one involving prismatic/pouch cells, and other involving cylindrical cells, like the Tesla EV battery pack. These volume averaged models are informed by full-order steady-state computational fluid dynamics (CFD) simulations, and later validated against full-order transient CFD simulations for a wide variety of operating conditions. The simulations conducted using volume averaged heat transfer models are at least two orders of magnitude faster than conventional simulations while maintaining the same level of accuracy. Next, the volume averaged heat transfer model for one of these battery pack designs and the recently reported volume averaged thermal tank-in-series battery model are used to develop a modeling framework for multiple cells connected in series to form a module, and multiple such modules connected in parallel forming a battery pack. This modeling framework enables fast simulation of large battery packs while considering complex battery physics in each individual battery and heat transfer in the thermal management system. This proposed approach can be used for any battery pack design and configuration. Using this modeling framework, we perform detailed analysis on the battery pack, including studying electrochemical and thermal behavior of individual batteries in the pack as well as pack level characteristics under different operating conditions. Finally, we also study effect of cell-cell to variations due to possible manufacturing variations and variations in the state of charge (SOC) of batteries across the battery pack.
References:

Guo, M.; White, R. E., Thermal Model for Lithium Ion Battery Pack with Mixed Parallel and Series Configuration. J Electrochem Soc
2011,
158 (10), A1166-A1176.

Huang, H. H.; Chen, H. Y.; Liao, K. C.; Young, H. T.; Lee, C. F.; Tien, J. Y., Thermal-electrochemical coupled simulations for cell-to-cell imbalances in lithium-iron-phosphate based battery packs. Appl Therm Eng
2017,
123, 584-591.

Schindler, M.; Durdel, A.; Sturm, J.; Jocher, P.; Jossen, A., On the Impact of Internal Cross-Linking and Connection Properties on the Current Distribution in Lithium-Ion Battery Modules. J Electrochem Soc
2020,
167 (12).

Wang, B.; Ji, C. W.; Wang, S. F.; Sun, J. J.; Pan, S.; Wang, D.; Liang, C., Study of non-uniform temperature and discharging distribution for lithium ion battery modules in series and parallel connection. Appl Therm Eng
2020,
168.