  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.
