Measurement Uncertainty in Battery Electrochemical Impedance Spectroscopy

Abstract

Electrochemical impedance spectroscopy (EIS) is a widely used method for battery tests in manufacturing and automotive field applications. As such, accurate measurement of the impedance over a broad frequency spectrum is of high relevance, also requiring specific calibration methods and evaluation of error bounds. Here, we report for the first time a comprehensive uncertainty analysis of calibrated EIS for batteries. We aim to identify two uncertainty sources, the fixture repeatability and measurement noise, and evaluate their effect on the measured impedances. To this end, an error model assigned to each of them and the real and imaginary parts of the model parameters are characterized in the frequency range of 100 mHz-5 kHz by performing specific impedance measurements on a shunt resistor and a short standard. We demonstrate how different uncertainties are combined with the measured impedances, incorporating also the impedance calibration procedure. The errors are propagated through the calibration and correction functions by applying the linear error propagation method provided by the UncLib package from METAS. The error bounds are derived from uncertainty propagation in the shunt standard and the prismatic battery cell EIS and verified by conducting a series of measurements. Thereby, the uncertainty is shown as ellipsoids in every frequency point of the Nyquist plot. For instance, at 1 Hz, the 34-Ah prismatic cell shows a calibrated real-part impedance and two standard deviation error bounds of 1.07 m ± 26 μ.

Quantitative Cell Classification Based on Calibrated Impedance Spectroscopy and Metrological Uncertainty

“…A brief account is given in the following, with a detailed mathematical description available in the previous study. [16] First, various uncertainty sources are identified and characterized using multiple measurements on a short standard and a shunt standard. We characterized the effect of measurement repeatability uncer-tainty and measurement noise uncertainty as being the two primary random error sources.…”

“…Random errors and corresponding uncertainty analysis haven't been considered in EIS so far and have been introduced only recently. [16] Here we integrate full EIS calibration and metrological uncertainty analysis to show how error correction and uncertainty affect battery cell classification (see Figure 3). Also, the effect of using two fixtures on uncertainty evaluation and cell classification of different qualities is shown.…”

“…However, their effect can be shown by defining the uncertainty bounds of the calibrated measurements. [16] The consequence of testing methods having an error and an uncertainty is that there are false negatives, an unacceptable cell erroneously passing inspection, and false positives, an acceptable cell erroneously rejected. Therefore, an acceptance threshold must be chosen that balances between both errors.…”

“…[17] In all EIS studies presented so far, the impedance uncertainties were not fully characterized. Recent studies [3,16] show that systematic and random errors increase significantly with frequency, leading to considerable errors in impedance measurements. Unlike systematic errors, random errors and corresponding uncertainty can not be removed by calibration and need to be experimentally characterized.…”

“…Since random errors have random characteristics, they can not be removed from the result with calibration. However, their effect can be shown by defining the uncertainty bounds of the calibrated measurements [16] …”