Measurement Uncertainty in Battery Electrochemical Impedance Spectroscopy

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 $\text{m}\Omega $ ± $26~ \mu \Omega $ .

I. Introduction

Over recent decades, rechargeable lithium-ion batteries (LiBs) gained significant interest due to demands for high energy and power density storage devices in consumer electronics and electric vehicles. For LiB characterization, electrochemical impedance spectroscopy (EIS) plays an important role, for instance, to determine the state-of-charge (SoC) [1], [2], [3] and the state-of-health (SoH) [4], [5], [6], [7], or to investigate the chemical–physical materials’ properties of LiBs [8], [9], [10], [11], [12]. For example, in [3], it is demonstrated how EIS and a simplified equivalent circuit model are used as a complementary technique to other methods such as open-circuit voltage (OCV) and Coulomb counting in predicting the SoC of LiBs. Studies in [5] show how EIS is used for SoH diagnosis and to detect lithium plating in graphitic anodes [11]. In EIS, the battery is typically excited by a low-amplitude sinusoidal current with a given frequency. The complex impedance is calculated by dividing the resulting voltage over the applied current in the frequency domain. EIS can be performed using the galvanostatic or potentiostatic approach. In the galvanostatic method, a sinusoidal current is applied, and the voltage response is recorded, while in the potentiostatic approach, a sinusoidal voltage is applied, and the current response is recorded. Typically, the galvanostatic method is used for low-impedance measurements. In commercial LiB cells, the internal impedance has dropped to very low values, and today the cell impedance variations that are of interest in EIS can be as low as a few micro-Ohms (). The frequency range of interest is typically very wide, ranging from 1 mHz to 10 kHz and beyond. Because of low impedance values and broad frequency range, it is essential to precisely understand the measurement error sources to characterize LiBs effectively. Also, adequate calibration workflows are required to maintain traceable LiB impedance measurements [13].