A Fast Analytical Model for Predicting Battery Performance Under Mixed Kinetic Control

The prediction of battery rate performance traditionally relies on computation-intensive numerical simulations. While simplified analytical models have been developed to accelerate the calculation, they usually assume battery performance to be controlled by a single rate-limiting process, such as solid diffusion or electrolyte transport. Here, we propose an improved analytical model that could be applied to battery discharging under mixed control of mass transport in both solid and electrolyte phases. Compared to previous single-particle models extended to incorporate the electrolyte kinetics, our model is able to predict the effect of salt depletion on diminishing the discharge capacity, a phenomenon that becomes important in thick electrodes and/or at high rates. The model demonstrates good agreement with the full-order simulation over a wide range of cell parameters and offers a speedup of over 600 times at the same time. Furthermore, it could be combined with gradient-based optimization algorithms to very efficiently search for the optimal battery cell configurations while numerical simulation fails at the task due to its inability to accurately evaluate the derivatives of the objective function. The high efficiency and the analytical nature of the model render it a powerful tool for battery cell design and optimization.