A Thermal Tanks-in-Series Model for Simulating over-Discharge Cycling in Lithium-Ion Batteries
Authors: Thiagarajan Raghav Sai , Concepcion Anthony , Tewari Deepti , Jeevarajan Judith , Subramanian Venkat R. 
Published: August 2024

Energy storage will play a crucial role in the transition to clean and renewable sources of energy production to meet future consumption demands.1 Lithium-ion (Li-ion) batteries are widely adopted due to their high energy density, low self-discharge rate and fast charging capabilities for applications like electric vehicles and grid storage.2

Li-ion batteries for high voltage operations, where several cells are connected in series, can experience inadvertent over-discharge due to differences between cells3,4. These differences can arise due to many reasons including changes in internal resistance and deviation in electrochemical degradation that can cause divergence of cell open circuit potentials. Over-discharge is a condition when the manufacturer recommended lower voltage limit is crossed while discharging4, which results in various side effects such as electrolyte decomposition, capacity degradation, cathode morphology change and possible internal short circuit3,5. Increase in anode potential during over-discharge leads to copper dissolution from the anode current collector and subsequent plating within cell components. The Solid Electrolyte Interface (SEI) can decompose during excessive deintercalation and reform during charging, reducing the lithium inventory. Excessive heat generation during cycle life testing after occurrences of over-discharges has been found in some cases to lead to temperatures >150 °C6,7.
Temperature plays a key role in the electrochemical performance of individual cells, affecting the diffusivities of ions, kinetics of reactions and rate of degradation of the battery. A physics-based modeling approach coupled with a thermal model can be employed to understand the effect of over-discharge on the electrochemical behavior of Li-ion batteries and provides insights into the interplay of various degradation mechanisms that cause capacity fade.
The Thermal Tank-In-Series9,10(TTiS) model is a systematically volume-averaged form of the standard pseudo-2-dimensional (p2D)11 model with energy balance equations for the current collectors, cathode, separator and anode. This reduces the number of equations in the model and improves computational speed while maintaining accuracy, as it is sensitive to changes in the battery’s state of charge (SOC) and cell temperature, which helps predict the overpotential changes to the cell electrodes and thermodynamics.
We use the TTiS model to identify the dominant fade mechanisms in 3 sets of experimental cycling and temperature data for the: i) normal operating window (2.5V – 4.2V), ii) 5 initial cycles of over-discharge (1.5V – 4.2V) followed by normal operation until 20% capacity fade and iii) 5 cycles of periodic over-discharge every 20 cycles, until 20% capacity fade. Analysis on the effect of C-rate, ambient temperature and voltage window of operation will facilitate understanding the temperature behavior and overpotentials in a cell sandwich. Key considerations required in extending a model to simulate over-discharge will also be examined.

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