Simple Analytical Method for Determining Parameters of Discharging Batteries

This paper derives simple and explicit formulas for computing the parameters of Thevenin's equivalent circuit model for a discharging battery. The general Thevenin's equivalent circuit model has n pairs of parallel resistors and capacitors (nth-order model). The main idea behind the new method is to transform the problem of solving a system of high-order polynomial equations into one of solving several linear equations and a single-variable nth-order polynomial equation, via some change of variables. The computation can be implemented with a simple MATLAB code less than half-page long. Experimental and computational results are obtained for three types of batteries: Li-polymer, lead-acid, and nickel metal hydride. For all the tested batteries, the first-order models are not able to generate voltage responses that closely match the measured responses, while second-order models can generate well-matched responses. For some of the batteries, a third-order model can do a better job matching the voltage responses.