The current flowing in the external circuit is directly linked to the rate at which lithium ions are (de)intercalated at the electrodes, which in turn depends on the speed of the charge transfer reactions. If the charge transfer reactions are slow, the battery cannot supply or accept electrons quickly, thus limiting the current and consequently the power. To drive the charge transfer reactions at a higher rate (to achieve higher currents), a larger overpotential (the difference between the electrode's equilibrium potential and its actual potential under current flow) is required. The relationship is described by the Butler-Volmer equation.
A significant overpotential, especially at high currents, leads to a larger voltage drop across the battery's internal resistances and kinetic barriers. This reduces the terminal voltage of the battery (V = OCV - Internal Losses - Kinetic Overpotential).
While increasing the overpotential can increase the current, excessive overpotential leads to a substantial drop in voltage, which can ultimately limit the maximum power output (P = V * I). A battery with slow kinetics will experience a more significant voltage drop at high currents, thus capping its power delivery.
Here's a Python implementation of a simulation that models the effect of fast charge transfer reactions on the power output of a lithium-ion battery. We'll use the Butler-Volmer equation to describe the charge transfer kinetics and simulate how variations in reaction rate constants influence the battery's power output.
https://gist.github.com/viadean/5bf592219ca31390ae5159d8c9d22968
exchange_current_density (i0) is a critical parameter that reflects how fast the charge transfer reactions can occur. A higher i0 implies faster charge transfer.current_density * overpotential.exchange_current_density.