Optimizing Experiments for Accurate Battery Circuit Parameters Estimation: Reduction and Adjustment of Frequency Set Used in Electrochemical Impedance Spectroscopy

TL;DR

This work addresses the challenge of long EIS measurement times by reducing the frequency set used to estimate Li-ion battery ECM parameters without sacrificing accuracy. It implements an $E$-optimal experimental design to adjust frequencies after deliberately lowering low-frequency measurements, leveraging the $FIM$-based $CRLB$ to guide updates. Case studies on real Li-ion cells show LF loss increases uncertainties for LF parameters, but gradient-guided frequency adjustments restore global parameter uncertainty, achieving comparable or better accuracy with reduced time. The approach offers practical time savings and improved design principles for battery diagnostics and ECM parameter estimation.

Abstract

In this paper, we study a suitable experimental design of electrochemical impedance spectroscopy (EIS) to reduce the number of frequency points while not significantly affecting the uncertainties of the estimated cell's equivalent circuit model (ECM) parameters. It is based on an E-optimal experimental design that aims to maximize the information about the ECM parameters collected by EIS measurements and, at the same time, minimize the overall uncertainty. In a numerical experiment, we first analyze to which extent reducing the number of measurement points at low frequencies affects the uncertainty of the estimated parameters. Secondly, we show that applying the frequency adjustments can lead to the same or even improved global uncertainty of ECM parameter estimates as with a higher number of measurements. This is numerically verified through a case study using the ECM parameters of a commercial battery cell.

Figures (8)

• Figure 1: ECM modelling the Li-ion cell impedance.
• Figure 2: An example of log-spaced frequency points from $f_{start} = 10^4$ Hz to $f_{end} = 0.01$ Hz with $\text{PPD} = 10$ for every decade, except for decades below the defined frequencies (a) $f = 0.1$ Hz and (b) $f = 1$ Hz, which have $\text{PPD} = 5$.
• Figure 3: Minimum theoretical variance (CRLB) for each of the ECM parameters for different numbers of PPD, i.e., $\text{PPD} \in \{5, 6, \ldots, 10\}$, for frequencies lower than 0.1 Hz.
• Figure 4: Minimum theoretical variance (CRLB) for each of the ECM parameters for different numbers of PPD, i.e., $\text{PPD} \in \{5, 6, \ldots, 10\}$, for frequencies lower than 1 Hz.
• Figure 5: Evolution of normalized ellipsoid volume over iterations of the algorithm for optimal frequency adjustments via E-optimal design, starting from a log-spaced frequency set with a reduced number of PPD at frequencies $f \leqslant 0.1$ Hz, for two different cell states.