Analysis of Li-Ion Battery Electrochemical Impedance Spectroscopy Data: An Easy-to-Implement Approach for Physics-Based Parameter Estimation Using an Open-Source Tool

Abstract

The quantitative analysis of electrochemical impedance spectroscopy (EIS) data is important for both characterization and prognostic applications in many electrochemical systems. Here we describe an open-source platform, the ImpedanceAnalyzer, for easy-to-use physics-based analysis of experimental EIS spectra. To demonstrate the use of the platform, we explore the basic capabilities of the pseudo two-dimensional (P2D) battery model to predict publicly available experimental EIS data from a 1500 mAh commercial lithium-ion (LiCoO 2 /graphite) cell. An a priori computed dataset of 38,800 P2D-based impedance spectra simulations, covering a wide range of frequencies (1 mHz to 100 kHz) and model parameters, enables a straightforward least squares matching approach for analyzing experimental spectra. We find an average error of 1.73% between the best-matching computed spectrum from the 38,800 member library and the experimental spectrum being analyzed. Our analysis shows there is significant opportunity to improve the fit between experimental data and physics-based impedance simulations by a combination of a larger computed dataset, local optimization, and further additions to the model physics. The approach and open source tools developed here can be easily extended to other electrochemical systems. Electrochemical impedance spectroscopy (EIS) is a powerful tool for investigating a wide variety of electrochemical systems. 1-3 EIS spectra separate individual electrochemical processes by their characteristic timescales, enabling both qualitative and quantitative analysis of electron transport, 4,5 reaction rates and mechanisms, 6,7 intercala-tion processes, 8 mass transport, 9,10 and electrode structure. 11,12 The noninvasive nature of EIS also makes impedance measurements useful in prognostic applications such as fuel cell health estimations 13,14 or prediction of remaining useful lifetime in batteries. 15,16 Qualitative analysis of EIS spectra generally involves assessing the shape of Nyquist plot features to determine the relative importance of different physicochemical processes. 17,18 In contrast, quantitative analysis relies on fitting a model to the data in order extract values for specific thermodynamic, transport, and/or kinetic parameters. Most experimental datasets are analyzed quantitatively using an equivalent circuit analog. Fitting an equivalent circuit to EIS data is straightforward using standard least squares regression techniques. 19,20 A good fit can often be found with a relatively simple equivalent circuit, particularly if non-ideal elements like the constant phase element are used. Moreover, many simple equivalent circuits, like the Randles' circuit, 21 have physically interpretable parameters based on linearized electro-chemical processes. However, as more complex equivalent circuits are derived and utilized, the lumped parameters can lose their direct physical interpretability and the structure of the equivalent circuit analogs themselves can be degenerate. 22 An alternative to equivalent circuits for quantitative analysis of EIS data is to directly fit the data with a physics-based mathematical model of the electrochemical system. Many years of electrochemical model-ing research have laid the groundwork for the physics-based analysis of impedance in a wide variety of fields including corrosion, 6 hy-drodynamic systems, 23,24 fuel cells, 25,26 and lithium-ion batteries. 27-29 Parameter estimation by fitting a physics-based model to experimental EIS data is complicated by the fact that electrochemical models often contain a combination of coupled differential equations, algebraic equations, and dozens of unknown parameters. For complex physics-based models, convergence to a global best fit is rarely assured , even with an excellent initial guess for the unknown parameters. As a result, parameter estimation methods often need to rely on many independent measurements to drastically narrow the number of fitted parameters. 30 In short, today there is gap between the desire to use physics-based models to estimate parameters in EIS, and the actual (routine) use of physics-based models for parameter estimation from data. Here we demonstrate an easily implemented and extendable approach for leveraging sophisticated physics-based models of EIS spectra to estimate parameters from experimental data. The parameter estimation approach used in this work relies on error minimization between experimental data and a large library of a priori simulated impedance spectra. One benefit of a dataset-based approach is that it always converges and the resulting parameter estimates are guaranteed to be reasonable if the original dataset was constructed from physically reasonable parameters. Another benefit of a dataset-based approach is that global sensitivity analysis can be used to understand the contribution of different parameters to the model variance. 31 On the other hand, a dataset-based approach will generally not provide the parameters with the lowest possible error between model and experiments. The work and software tool presented here is extendable to a wide range of electrochemical systems, though our first implementation is using the Doyle-Fuller-Newman pseudo two-dimensional (P2D) lithium-ion battery (LIB) model as the basis for analyzing EIS experiments. 32,33 The earliest uses of LIB physics-based impedance models have been to inform the analysis of experimental EIS data. For example, Doyle et al. 28 used physics-based EIS simulations to show that the low frequency portion of a LIB impedance spectrum appears (qualitatively) to be interpretable as a Warburg impedance, but using a Warburg plot can produce erroneous (quantitative) dif-fusivity estimates. Subsequently, additional physics has been added to the original P2D model to aid in the interpretation of EIS data. For example, a surface oxide model was added to the positive electrode particles by Dees et al. 30 to understand the increase in inter-facial impedance with aging of LiNi 0.8 Co 0.15 Al 0.05 O 2-based (NCA) positive electrodes. Abraham et al. 34 extended the model further to interpret the changing impedance response at different voltages in NCA electrodes. Despite the widespread use of the P2D model for simulating LIBs (2 of the top 4 most cited papers in the history of the Journal of the Electrochemical Society (as of November 1 st , 2017), 35 the model has seen limited use for quantitative analysis of experimental impedance data. In this work, we present the ImpedanceAnalyzer, an open-source,) unless CC License in place (see abstract). ecsdl.org/site/terms_use address. Redistribution subject to ECS terms of use (see 34.248.74.51 Downloaded on 2019-01-26 to IP