A Linear Method to Fit Equivalent Circuit Model Parameter Values to HPPC Relaxation Data From Lithium-Ion Cells1

Abstract

Battery management systems require mathematical models of the battery cells that they monitor and control. Commonly, equivalent circuit models are used. We would like to be able to determine the parameter values of their equations using simple tests and straightforward optimizations. Historically, it has appeared that nonlinear optimization is required to find the state-equation time constants. However, this article shows that the relaxation interval following a current or power pulse provides data that can be used to find these time constants using linear methods. After finding the time constants, the remaining parameter values can also be found via linear regression. Overall, only linear algebra is used to find all of the parameter values of the equivalent circuit model. This yields fast, robust, and simple implementations, and even enables application in an embedded system, such as a battery management system, desiring to retune its model parameter values as its cell ages.