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Advanced cell voltage modeling for lithium-ion-batteries using transmission line models
Cell characterization

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 (e.g. 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 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 discharge C-rates of 2 C. Above 2 C, 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 with the entire thickness of the battery cell. Therefore, the TLM has been extended by considering the location and time-dependent electrolyte concentration c(x,t) (see fig. 1). This makes it necessary to use location and time-dependent impedance elements since impedance elements e.g. describing the electrolyte resistance show a dependency on electrolyte concentration. Since location and time-dependent impedance elements cannot be used for electrode impedance calculation by Bisquert et al. [1], a novel method for calculating the electrode impedance was developed in this work. Finally, the results from the extended TLM show good consistency between the simulated and measured voltage curves for higher C-rates. Hereby it was shown that nonlinear processes due to electrolyte depletion can successfully be described with the extended model.

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M. Weiss, E. Ivers-Tiffée