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Modeling the impedance spectra of lithium-ion battery cells

Electrochemical impedance spectroscopy seems best suited for determining the aging condition of a lithium-ion battery (LIB), where the battery cell is excited by a sinusoidal electrical current and the voltage response is measured (or vice-versa). Since different frequencies are used for exciting the battery cell, an impedance spectrum can be generated that images the influence of physico-chemical processes with different time constants, if correctly interpreted. Measurements of cells of different ages show significant changes in the spectrum. These age-induced changes are revealed by means of a reference procedure developed at PTB. To be able to attribute physico-chemical processes to the changes in the spectrum, a model was developed within the scope of the project that simulates the impedance measurement on the basis of charge and mass transportation equations. The model provides the possibility to vary all parameters and to simulate thus the age-induced changes measured. This approach aims at identifying parameters that quantify the aging condition of a battery.

This pseudo-2-dimensional battery model is based on the work of Doyle, Fuller and Newman [1], who were the first to use a model of this kind for the simulation of charge-discharge cycles of an LIB in 1993. Models of this type balance charge and mass transport and substance decomposition at the battery interfaces and couple the balance equations by means of equations that describe reaction kinetics. The transportation processes in the electrodes and in the electrolyte are described on the basis of the laws of Fick and Ohm. Porous electrodes and a concentrated electrolyte solution are assumed. The model can be extended by approaches which represent the properties of surface layers on the electrodes. The solid electrolyte interface (SEI) is such a layer; it forms on the anode through reactions of the electrolyte and its additives and has widely varying properties. The formation of the SEI is one of the prime reasons for the degradation of LIBs, because SEI formation leads to a stronger internal resistance of the cell, binds active lithium and passivates the active electrode surface. Thus, impedance spectra which were calculated by means of a model extended by an SEI feature different properties enabling conclusions as to the aging condition. Variations of the internal resistance of the battery in the high-frequency range of the impedance spectrum can, for example, be read at the intercept point of the spectrum and the real part axis (see Fig. 1). Within the framework of parameter studies, the simulation results can be fitted to the measurements. This approach clearly shows which parameters are influenced by the degradation of the battery.

 

Figure 1: Impact of the electrolytic conductivity on the impedance spectrum