A Simplified Single-Layer Pseudo-4D Electrochemical/Thermal Model for Large-Format Li-Ion Pouch Cells
Authors: Lin Jie , Chu Howie N. , Howey David Alastair , Monroe Charles W. 
Published: May 2020

Ever since the first commercial Li-ion battery launched in 1991, Li-ion batteries have been the best available energy storage systems for consumer electronics [1]. With recent advances in cell capacity, cycle time and battery management systems, they have become even more popular as an ideal candidate for grid-scale energy storage and electric vehicles [2].
When a battery is being charged or discharged, there is inevitable heat generation due to electrochemical reactions, ohmic resistance and entropy changes [3]. If the amount of heat generated is not sufficiently dissipated from the battery, it could substantially increase the cell temperature which leads to severe cell degradation and even catastrophic thermal runaway. Furthermore, large temperature inhomogeneity is commonly observed in large-format pouch cells due to the non-uniform local current density and reaction rate. Therefore, in order to maintain stable and durable performance, it is vital to understand the irregular heat generation and temperature distribution associated with cell geometry and properties, and design appropriate cooling techniques accordingly.
Battery modeling is a useful tool to investigate the electrochemical reactions and consequent heat generation during charging and discharging. An experimentally validated battery model has the ability to accurately predict the cell response under different test conditions, eliminating the need for repeated lengthy experiments. Among all the existing Li-ion battery models, the pseudo-2D (P2D) model, originally proposed by John Newman and his students [4-6], is the most widely accepted electrochemical model for Li-ion batteries. Based on this, a few battery thermal models have been established by coupling a P2D electrochemical model with a 3D heat transfer model [7-9]. The electric and concentration fields are solved in a 1D unit-cell and are extracted to calculate the heat generation rates in a 3D battery geometry. However, such a method would introduce large errors in large-format pouch cells as the assumption of uniform current density and reaction rate is not valid.
Therefore, in this study, we would like to propose a pseudo-4D (P4D) battery model, which extends the original P2D model from 1D to 3D battery geometry. The charge balance, mass balance and reaction kinetics, as well as energy balance, are spatially resolved for the entire battery geometry, considering the inhomogeneity of battery state properties. Furthermore, a scaling analysis is carried out via non-dimensionalization of the model equations to demonstrate that a single-layer cell would be sufficient to simulate the overall electrical and thermal performance of the battery which actually contains multiple cell layers. The complexity of the model can thereby be reduced to make the model more time-efficient.

References

[1] B.A. Johnson, R.E. White, J Power Sources, 70 (1998) 48-54.
[2] J. Li, Y. Cheng, M. Jia, Y. Tang, Y. Lin, Z. Zhang, Y. Liu, J Power Sources, 255 (2014) 130-143.
[3] G.L. Plett, Battery Management Systems: Battery Modeling, Artech House, 2015.
[4] J.S. Newman, C.W.J.J.o.T.E.S. Tobias, 109 (1962) 1183-1191.
[5] T.F. Fuller, M. Doyle, J.J.J.o.t.E.S. Newman, 141 (1994) 1-10.
[6] M. Doyle, T.F. Fuller, J.J.J.o.t.E.S. Newman, 140 (1993) 1526-1533.
[7] S. Basu, K.S. Hariharan, S.M. Kolake, T. Song, D.K. Sohn, T. Yeo, Appl Energ, 181 (2016) 1-13.
[8] M. Farag, H. Sweity, M. Fleckenstein, S. Habibi, J Power Sources, 360 (2017) 618-633.
[9] X. Zhang, X. Chang, Y. Shen, Y. Xiang, Journal of Energy Storage, 11 (2017) 249-257.