In this work we present and discuss a modelling framework for the basic discharge process which occurs in simple electrochemical battery cells. The main purpose is to provide a setting for analyzing delivered capacity, battery life expectancy and other measures of performance. This includes a number of deterministic and stochastic variations of kinetic battery models. The primary tool is a novel phase plane analysis of the balance of nominal and theoretical capacity. In particular, we study spatial versions of such models which lead to a linear diffusion equation with Robin type boundary conditions under scaling. Explicit solutions are obtained by considering reflected Brownian motion.

Phase plane Theoretical Capacity Terminal Voltage Nominal Capacity Battery Model