A Reduced-Order Model of the Coupled Venting-Thermal-Electrochemical Behavior to Predict First Venting Under External Short Circuit Conditions
Authors: Tran Vivian , Siegel Jason , Stefanopoulou Anna 
Published: August 2024

Modeling abusive battery operation before thermal runaway (TR) can reduce the testing requirements and facilitate the development of effective and reliable early failure detection and fast discharge strategies [1] which require multiple types of sensor signals, including current, voltage, temperature, and pressure. We present a multi-physics model that can predict the rapidly evolving discharge behavior of cells undergoing an external short circuit, including hazards like first venting. First venting models account for gas generation due to SEI decomposition and electrolyte vaporization at high temperatures to calculate the build-up of internal cell pressure under constant-displacement conditions [2]. Modeling gas generation requires accurate temperature prediction, which subsequently requires accurate Joule heating calculated from current and voltage predictions. From the cascading chain of model input dependencies, the first challenge is managing error propagation through the submodels with appropriate parameterization. Previous modeling work parameterized a venting model for a cell undergoing an external short circuit (ESC) but did not include a thermal or electrical model [2]. The second challenge is modeling the diffusion-limited discharge behavior with currents approaching 50-80 C with a fast and accurate model that is feasible for detection and control applications. Diffusion-limited behavior occurs when the local Li concentration saturates, suddenly causing large concentration overpotentials that are observable in the terminal voltage and current (see Fig. 1) as well as numerical instability when solving the Butler-Volmer (BV) equation. Previous ESC modeling works either used the Doyle-Fuller-Newman (DFN) model with a limiting current density in the BV equation [3] or an equivalent circuit model (Eq-CM) [1]. However, solving the DFN is computationally intensive for a control application, while Eq-CMs cannot predict the diffusion-limited electrical behavior beyond the data they were parameterized on, requiring apriori experiments to be accurate. To balance the trade-offs, we instead look towards reduced-order modeling.
In this work, we present a control-oriented, reduced-order, multi-physics model that captures the electrochemical, thermal, and venting behavior of four 4.6 Ah NMC pouch cells undergoing an external short circuit with different initial state-of-charge (SOC). The multi-physics model couples a first venting model with a lumped thermal model driven by Joule heating calculated through the overpotentials from the Single-Particle Model with electrolyte (SPMe). The combined model was parameterized through four experiments by fitting five key parameters in the submodels related to the SEI decomposition rate, cell thermal behavior, and solid electrode diffusion to capture the first venting timing, peak temperature, and diffusion-limited current-voltage drops. Additionally, two resistances were tuned to match the initial current and voltage with all other parameters were taken from the literature. Applying the same parameter set consisting of the average of the fitted values on all four cells, the combined multi-physics model correctly predicted that the fully-charged cells would vent and conservatively predicted the cell venting timing up to about 40 s before it occurred in the experiment. For high initial SOC cells, the SPMe also accurately predicted the current and voltage drops associated with diffusion limitations and SOC up until the cell vented. This is the first work that systematically parameterizes and couples a reduced-order, physics-based model to capture the electrical, thermal, and venting behavior under battery abuse conditions. Future work will explore applications for the model in early detection and response to critical safety events.
REFERENCES
[1] Tran, Vivian, Jason Siegel, and Anna Stefanopoulou. "Emergency Li-ion Battery Discharge using Nonlinear Model Predictive Control with Temperature and Venting Pressure Constraints." 2023 American Control Conference (ACC). IEEE, 2023.
[2] Cai, Ting, et al. "Modeling li-ion battery first venting events before thermal runaway." IFAC-PapersOnLine 54.20 (2021): 528-533.
[3] Rheinfeld, Alexander, et al. "Quasi-isothermal external short circuit tests applied to lithium-ion cells: Part ii. modeling and simulation." Journal of The Electrochemical Society 166.2 (2019): A151.

Fig. 1: 15-min simulation of an external short circuit for cells at different initial SOC. Model results and experimental measurements are shown for four cells that were externally shorted. The measured current, voltage, temperature, and expansion force were measured at 10 Hz and plotted versus log time to highlight the dynamic current-voltage behavior in the first few minutes. The diffusion-limited current and voltage behavior are captured by the model. The two cells at 100% SOC, experienced venting and higher peak temperatures, which are well captured by the model. The cell venting timing was predicted to be 43 s and 7 s early for Cell 100A and 100B, respectively. The cells that were shorted at lower SOC did not vent.

Figure 1