Physically Based Voltage Prediction for Lithium-Ion Batteries Using Transmission Line Models

Abstract

The prediction of battery cell voltage is based on either (i) behavior models (i.e., equivalent circuit models) using a set of experimentally predetermined parameters and advantageous short computation times; or (ii) physical models (i.e., finite element method models) requiring long computation times and the knowledge of various physical parameters. In this study, we propose a hybrid solution. A semi-physical model calculates the load-dependent overvoltage in a two-step process. First, the complex impedance of the positive and the negative electrode is calculated separately by two individual transmission line models (TLM, Bisquert et al. [1]). In a second step, the frequency domain data are transformed to the time domain (Schmidt et. al. [2]), and the nonlinear and linear overvoltage contributions of electrodes and electrolyte are subtracted from the cell´s open-circuit voltage. Then, our semi-physical model approach is validated by measurements of a commercial high energy Kokam cell. Cell voltage curves are in good agreement up to moderate C-rates of C/2. Above C/2, deviations arise from additional nonlinear impedance contributions. These originate from a concentration gradient of Lithium ions in the liquid electrolyte, which is soaked in the pores of the electrodes along the entire thickness of the battery cell. After implementing this gradient into the TLM model, we report significant improvements.