Non-equilibrium thermal models of lithium batteries

Temperature fluctuations impact battery performance, safety, and health. Industry-standard cell-level models of these phenomena ignore thermal gradients within the electrodes' active material, i.e., assume the latter to be in "thermal equilibrium". We present a "non-equilibrium"thermal model that explicitly accounts for spatial variability of temperature with the active material (and the carbon-binder domain). We investigate the conditions, expressed in terms of the heat-generation rate and the thermal properties of a cell's liquid (electrolyte) and solid (active material and CBD) phases, under which the thermal equilibrium assumption breaks down and our model should be used instead. The differences between these two thermal models are investigated further by coupling them with an industry-standard electrochemical model. The resulting thermal-electrochemical model demonstrates the importance of thermal gradients within the active material at high C-rates (discharge current densities) and for large grain sizes. Under these conditions, the equilibrium assumption underestimates internal temperature by as much as 50%. These two thermal models are then applied to a commercial NMC battery with multiple units. Our non-equilibrium model predicts the battery surface temperature that is in good agreement with measurements, while the equilibrium model underestimates the observed temperature.