(Keynote) Battery Archeology: Using Physics-Based Models to Unearth (Quantitative) Battery Aging Artifacts

Construction of simplified impedance model based on electrochemical mechanism and identification of mechanism parameters

Electrochemical impedance spectroscopy (EIS) is a powerful nondestructive tool that is widely used to identify physical parameters and health diagnostics in lithium-ion batteries.1 By applying a small perturbation of either current or voltage and subsequently analyzing the electrochemical responses over a range of frequencies, information can be revealed about the charge-transfer kinetics, transport phenomena, and thermodynamics of the cell.2 Small amplitude perturbations are used to ensure the battery operates in its linear-response regime. The frequency-dependent cell impedance Z(ω) is most commonly analyzed by fitting an equivalent circuit model and extracting parameters from these fits. However, equivalent circuit models limit the amount of physically insightful information that can be extracted from battery EIS data.3,4 Moreover, operating in the linear response regime also imposes a fundamental limitation on the total quantity of information contained in an impedance spectrum, since many of the physicochemical processes in a battery are inherently nonlinear in character. Nonlinear electrochemical impedance spectroscopy (NLEIS) is an adjunct to EIS where larger amplitude sinusoidal current or potential perturbations are applied, and the nonlinear response of the battery is measured by the presence of higher harmonics in the output. Through a fairly straightforward analysis, a purely frequency-dependent second harmonic “impedance” Z2(ω) can be defined. Higher harmonic, or nonlinear, electrochemical impedance spectra can provide deep insights into processes occurring in the electrochemical device under test, including insights into physicochemical processes that are invisible to standard (linearized) EIS approach.5 Here, Samsung 18650 LiNMC | C batteries (capacity = 1500 mAh) were cycled under various rates and conditions, with NLEIS data acquired throughout the duration of its cycle time, for different states of charge. For this particular battery capacity and chemistry, a typical “moderate” current perturbation was 300 to 500 mA. The experimentally measured nonlinear electrochemical impedance spectrum Z2(ω) can be compared to results derived from the psuedo-2D model of a Li-ion battery6. Our physics-based approach for computing the nonlinear electrochemical impedance is a natural extension of the linearized EIS analysis that has been done previously.4 We show that NLEIS experiments have all the information of EIS, plus additional information on the electrode thermodynamics (low frequencies) and charge transfer kinetics. We show that aggressive cycling increases the kinetic impedance of the positive electrode, with little impact on the negative electrode. NLEIS shows a correlated effect, but it is possible to use Z2(ω) to discern more about the nature of the interfacial degradation occurring on the positive electrode. In short, using nonlinear impedance in coordination with the linear impedance can provide further insight into more sensitive physicochemical phenomena that can be used to diagnose the state of health of Li-ion batteries during aging. [1] N. Lohmann, P. Weßkamp, P. Haußmann, J. Melbert, and T. Musch, J. Power Sources, 273, 613-623 (2015) [2] C. Chen and P.P. Mukherjee, Phys. Chem. Chem. Phys., 17, 9812-9827 (2015) [3] T. Osaka, D. Mukoyama, and H. Nara, J. Electrochem. Soc. 162, 2529-2537 (2015) [4] M. Doyle, J. P. Meyers, and J. Newman, J. Electrochem. Soc. 147, 99-110 (2000) [5] J.R. Wilson, D. T. Schwartz, and S. B. Adler, Electrochimica Acta, 51, 1389-1402 (2006) [6] T.F. Fuller, M. Doyle, and J. Newman, J. Electrochem. Soc. 141, 1-10 (1994)

Quantitative analysis of electrochemical impedance spectroscopy (EIS) and 2nd-harmonic nonlinear EIS (2nd-NLEIS) data from commercial Li-ion batteries is performed using the porous electrode half-cell models developed in Part I. Because EIS and 2nd-NLEIS signals have opposite parity, the full-cell EIS model relies on the sum of cathode and anode half-cells whereas the full-cell 2nd-NLEIS model requires subtraction of the anode half-cell from the cathode. The full-cell EIS model produces a low error fit to EIS measurements, but importing EIS best-fit parameters into the 2nd-NLEIS model fails to ensure robust model-data convergence. In contrast, simultaneously fitting opposite parity EIS and 2nd-NLEIS models to the corresponding magnitude-normalized experimental data provides a lower total error fit, more internally self-consistent parameters, and better assignment of parameters to individual electrodes than EIS analysis alone. Our results quantify the extent that mild aging of cells (<1% capacity loss) results in substantial increases in cathode charge transfer resistance, and for the first time, a breakdown in cathode charge transfer symmetry at 30% and lower state-of-charge (SoC). New avenues for model-based analysis are discussed for full-cell diagnostic and we identify several open questions.

Electrochemical impedance spectroscopy (EIS) is a method to measure the performance of an electrochemical cell where linear responses are obtained when a small perturbation of current or voltage is applied to the cell. It is so often that different limiting steps of electrochemical processes give similar responses of the impedance spectrum. Therefore, the typical linear EIS measurements are not sufficient to understand the electrode reaction mechanism. On the other side, the frequency response analysis including nonlinearities can provide more information in addition to EIS, and is considered an advanced method to understand the reaction mechanism as reported by the research group of S. Adler [1,2]. In EIS, the small perturbation is applied to the cell so that the input and output can be regarded as a linear relationship. Meanwhile, in the non-linear electrochemical impedance spectroscopy (NLEIS) large perturbation is applied to the cell. In this way, NLEIS can visualize not only the fundamental waveform but also the changes in the harmonics, which is expected to enable more detailed analysis and reaction modeling. Using the above principles in potentiostatic mode, this study aims to elucidate the ORR process of La0.6Sr0.4CoO3- δ (LSC) porous electrode for SOFC cathode.A symmetrical cell was prepared by depositing LSC porous electrodes on both sides of a Gd0.1Ce0.9O1.95 electrolyte. The experiments were performed in I-V measurements and NLEIS as a function of temperature (873 – 1073 K) under various p(O2) (1 – 10-4 bar). An electrochemical workstation (Zahner Zennium, Zahner-Elektrik GmbH & Co. KG, Germany) was used for the measurement to obtain the non-linear response. The obtained harmonics are normalized by the amplitude of the fundamental wave after Fourier transformation, and data are output up to the fifth harmonic. NLEIS was performed at frequencies from 0.1 Hz to 1M Hz.The experimental results showed clear response at the second harmonic with the magnitude increasing and phase changing as the frequency decreased. Harmonic components tended to increase with decreasing p(O2) and increasing temperature. In addition to experiments, the simulation using an electric circuit simulator (LTspice, Analog Devices) was performed. As an equivalent circuit of a mixed-conducting porous electrode, a ladder circuit has been applied to analyze the nonlinear response. The currents related to ion diffusion were defined based on the Nernstian Einstein equation, and the currents related to surface reactions were defined based on an empirical model of oxygen adsorption and dissociation[3]. The result showed that the 1st harmonic and 2nd harmonic responses from the experimental result is in good agreement with the simulation results from LTspice at high p(O2) (1 – 10-2 bar) in the terms of the shape and phase of the response. At low p(O2) (10-3 – 10-4 bar), the effect of gas diffusion resistance could not be ignored.. The complete analysis on ORR process as a function of the p(O2) and temperature will be discussed after resolving technical issues related to computational convergence when gas diffusion resistance is included into the equivalent circuit.

Transmission line models (TLMs) are a powerful and adaptable modeling strategy for capturing complex electrochemical processes occurring in porous electrodes. [1,2] In practice, TLMs are less widely used than constant phase elements (CPEs) to model mid- to high-frequencies features in electrochemical impedance spectroscopy (EIS) data from porous electrodes; this can obscure the physical interpretation of interfacial processes. [3] We have recently shown how to convert physics-based models of the electrochemical double layer and charge transfer rates into well-established EIS and novel 2nd Harmonic Nonlinear EIS (2nd-NLEIS) circuit elements, extending a wide array of circuit structures into the weakly nonlinear regime. [4] The benefit of parameter estimation using both EIS and 2nd-NLEIS data is especially evident in two electrode cells, where simultaneous fitting of opposite parity of EIS and 2nd-NLEIS signals contributes to an internal self-consistency check on the uniqueness and assignment of parameters to each of the electrodes. [5] In this work, we will demonstrate a numerical framework that extends linear TLMs to second-harmonic nonlinear TLMs (2nd-nTLMs), enabling electrochemical analysts to benefit from the descriptive power of TLMs and the model discriminating power of combined EIS and 2nd-NLEIS analysis. Specifically, we will show that the overlapping time constant can be effectively separated by using EIS and 2nd-NLEIS with TLMs and 2nd-nTLMs in half-cells. We show how TLMs and 2nd-nTLMs can be combined to extract parameters from the complex electrochemical reactions in aging battery electrodes, allowing parameter estimation that includes the nonlinear charge transfer symmetry and curvature of thermodynamic open circuit voltage data at specific states of charge. Moreover, we will demonstrate the application of TLMs/2nd-nTLMs in obtaining current distribution within the porous electrode, which could guide the future design of high-performance battery electrodes.

Diagnosing battery states such as health, state-of-charge, or temperature is crucial for ensuring the safety and reliability of electrochemical energy storage systems. While some states, such as temperature, may be measured using cheap sensors, accurate diagnosis of battery health metrics usually requires time-consuming performance measurements, making them infeasible for use in real-world operation. These health metrics can be measured during lab-testing and then estimated on-line using predictive life models or via state observer algorithms such as Kalman filters, but these predictive methods should be supplemented by actual measurement of battery health whenever possible to ensure reliability. Rapid measurement of battery health may be done by various types of fast diagnostic techniques such as electrochemical impedance spectroscopy (EIS), which can be performed in only a few minutes and require only a fraction of the energy and power needed for a full charge and discharge measurement. But there is a substantial challenge for estimating battery health using EIS data, as EIS is sensitive to cell temperature, state-of-charge, current, and resting time in addition to health. Thus, utilizing EIS data to predict battery capacity requires correcting for all these additional variables, a task that is extremely difficult to handle analytically.This talk utilizes machine-learning methods to estimate the effectiveness of battery capacity prediction from EIS data, leveraging a data set of hundreds of EIS measurements recorded at varying temperature and state-of-charge throughout a 500-day aging study of 32 commercial, large-format NMC-Graphite lithium-ion batteries. Using EIS as input to machine-learning models is complicated by the nonlinear response of impedance to battery health, temperature, and state-of-charge, as well as the collinearity between the impedance response at neighboring frequencies, which can easily lead to overfit models. To train robust models, features from EIS data need to be extracted from the data or some subset of critical frequencies selected. Many approaches for extracting and selecting features from EIS data from electrochemical analysis and machine-learning fields were identified for analysis: using the entire raw spectra; selection of one, two, or many frequencies from the entire spectra; selecting interesting points from the EIS measurement using domain knowledge; fitting EIS with an equivalent-circuit model; calculating statistics on the raw impedance values; and reducing the dimensionality of the data using unsupervised linear (principal component analysis) and non-linear (uniform manifold approximation and projection) methods. These approaches were rigorously compared using a machine-learning pipeline approach, training linear, Gaussian process, and random forest regression models and quantifying performance using cross-validation as well as a held-out test set. An artificial neural network model trained on the raw spectra was also tested. Promising pipelines were fine-tuned via Bayesian hyperparameter optimization using cross-validation loss and training with class-specific weights to counter data set imbalance.The most reliable method for utilizing impedance in this work was the selection of two optimal frequencies through an exhaustive search, resulting in about 2% mean absolute error on test data for both Gaussian process and random forest model architectures. Interrogation of a variety of models reveals critical frequencies of 100 Hz and 103 Hz for this data set, though the optimal set of frequencies is not necessarily intuitive, i.e., the best performing models are not simply those that use impedance at frequencies that have the highest correlation to the relative discharge capacity. The best performing model is an ensemble model, which is able to predict battery capacity with 1.9% mean absolute error for unseen cells using impedance recorded at a variety of temperatures and states-of-charge.

The incorporation of physics-based lithium-ion battery models in real-time optimization, control and estimation has the potential to substantially facilitate their efficient and safe operation.1,2 In addition to improved prediction of battery states, the access to predictions of variables internal to battery electrochemistry allows the formulation of more complete optimization and control problems than would be possible by simple circuit models.3 Various approaches have been employed to enable this integration by reducing the computational demands of electrochemical models, particularly for the macro-homogeneous ‘P2D’ models of Newman and co-workers.4 These may be broadly divided into two categories: simplifications of the full model subject to limiting assumptions,5–7 or reformulation techniques which exploit the underlying structure of model equations to achieve fast simulation.1,8,9 The single particle model (SPM) visualizes the electrodes in a lithium-ion battery as two spherical particles and considers the electrode reactions and lithium transport through the active particle. Importantly however, it neglects potential and concentration variations in the electrolyte phase, which limits its predictive ability to low-current scenarios. Reformulated P2D models offer the desired computational performance without sacrificing physical detail, but their utility is dependent on the precise estimation of a large number of parameters from experimental data.10 This talk focuses on the development of a lumped physics-based model for lithium-ion batteries. The governing equations of the P2D model are integrated over the volume of each region in a cathode-separator-anode representation. This results in a set of volume-averaged quantities and relations, with the temporal evolution of each averaged variable expressed as an overall balance containing internal source terms and interfacial fluxes, which need to be approximated. The averaged porous domains may thus be regarded as three ‘tanks-in-series’. The model equations are simulated, and the electrochemical variable predictions compared against both the full P2D model and SPM over a range of parameter combinations and operating conditions. Various approximations for the interfacial fluxes are also evaluated in terms of their impact on cell-level predictions. The model is also extended to incorporate thermal effects via volume-averaged energy balances. Model predictions for different galvanostatic discharge rates suggest that the lumped model is of intermediate sophistication between the SPM and the P2D models. This is most likely because it incorporates liquid phase transport in an average sense, in contrast to SPM, which ignores them entirely. The lumped model is conservative, and possesses the computational simplicity of SPM, while also incorporating elements from the P2D model, but with a smaller number of parameters, making it easier to parameterize and potentially facilitating use in real-time prediction and control. In addition, tank models have been extensively researched in control theory, enabling the extension of these concepts to battery systems through lumped models. The ‘tanks-in-series’ averaging procedure described herein may be generalized to any electrochemical battery model. Acknowledgements The authors are also thankful for financial support from the Battery500 Consortium and the Advanced Research Projects Agency (ARPA-E). The authors acknowledge financial support from the Department of Chemical Engineering and the Clean Energy Institute at the University of Washington. References A. M. Bizeray, S. Zhao, S. R. Duncan, and D. A. Howey, J. Power Sources, 296, 400 (2015).V. Ramadesigan, P. W. C. Northrop, S. De, S. Santhanagopalan, R. D. Braatz, and V. R. Subramanian, J. Electrochem. Soc., 159, R31 (2012).M. Pathak, D. Sonawane, S. Santhanagopalan, R. D. Braatz, and V. R. Subramanian, ECS Trans., 75, 51 (2017).M. Doyle, T. J. Fuller, and J. Newman, J. Electrochem. Soc., 140, 1526 (1993).S. Santhanagopalan and R. E. White, J. Power Sources, 161, 1346 (2006).B. S. Haran, B. N. Popov, and R. E. White, J. Power Sources, 75, 56 (1998).M. Guo, G. Sikha, and R. E. White, J. Electrochem. Soc., 158, A122 (2011).P. W. C. Northrop, V. Ramadesigan, S. De, and V. R. Subramanian, J. Electrochem. Soc., 158, A1461 (2011).P. W. C. Northrop, M. Pathak, D. Rife, S. De, S. Santhanagopalan, and V. R. Subramanian, J. Electrochem. Soc., 162, A940 (2015).V. Ramadesigan, K. Chen, N. A. Burns, V. Boovaragavan, R. D. Braatz, and V. R. Subramanian, J. Electrochem. Soc., 158, A1048 (2011).

Testing battery pack configurations for their performance under different dynamic load profiles for grid and electric vehicle applications is expensive. Lowering the cost to understand the response of packs and their control strategies is critical. Power hardware in the loop (PHIL) simulation is widely used in power engineering for system and component testing. A simulator computes the model output in real-time, and then controls a power source to generate a dynamic power output with the expected current and voltage response of the emulated battery pack. This emulated battery pack power output can be coupled to a physical load to perform testing.1 Small time steps are useful to observe the transient response of the emulated battery when there is a sudden change in the load. PHIL simulations can also be useful to study the transient response of controllers and inverters present in the battery management system by connecting these devices to the simulator. PHIL simulations can be used to test the model’s accuracy2, to conduct repeatability experiments and to test battery performance under extreme conditions without compromising on safety.3 It provides an efficient approach to designing and testing new configurations of batteries from data of a single cell without building their real prototypes. The computational speed required to solve the battery models chosen for PHIL simulations must be fast in order to achieve real-time implementation. Therefore, models chosen for these simulations tend to have less complexity. However, to provide a better understanding of a battery’s response under a specific load profile, it is necessary to use a model that that accurately represents the behavior of a real battery. Real-time simulations for physics-based battery models have been explored in the past.4 , 5 , 6 It is also essential to comprehend how different battery architectures and how aging affects the overall performance. In literature, equivalent circuit models that describe charge transfer and diffusion dynamics have been used as the main way to capture battery dynamics.7 , 8 We first show results generated using SIMULINK equivalent circuit models that are compiled to run fast on our Opal-RT real-time simulator. The Opal-RT simulator drives an AMETEK 40 kW power supply with feedback to the model, enabling an emulated battery pack response capable of 10ms dynamic control. We evaluate pack configurations with physical parameters that correspond to either LCO or NMC 18650 cells. Overall, this represents a 400V, 10kW pack. A programmable load is used to modulate the emulated battery pack and monitor its dynamic response. We further explore implementing single particle models with our PHIL simulations to help understand the internal dynamics of the cell captured by these models. Physics-based models have rarely been used for PHIL. Our results show that the PHIL emulation of the battery pack meets the expectations for the battery dynamics. However, we observe high frequency noise in the output signal of the emulated battery pack. Because this level of noise is not a trait present in real battery packs, we are exploring signal processing methods to filter and remove it, while retaining the essential dynamics of the emulated battery pack. References A. Viehweider, G. Lauss, and L. Felix, Simul. Model. Pract. Theory, 19, 1699–1708 (2011).Y. He, W. Liu, and B. J. Koch, J. Power Sources, 195, 2969–2974 (2010).H. Dai, X. Zhang, X. Wei, Z. Sun, J. Wang, and F. Hu, Electr. Power Energy Syst., 52, 174–184 (2013).P. W. C. Northrop, V. Ramadesigan, S. De, and V. R. Subramanian, J. Electrochem. Soc., 158, A1461 (2011).V. R. Subramanian, V. Boovaragavan, V. Ramadesigan, and M. Arabandi, J. Electrochem. Soc., 156, A260 (2009).P. W. C. Northrop, V. Suthar, Bharatkumar Ramadesigan, S. Santhanagopalan, R. D. Braatz, and V. R. Subramanian, J. Electrochem. Soc., 161, E3149 (2014).J. V. Barreras, C. Fleischer, A. E. Christensen, M. Swierczynski, E. Schaltz, S. J. Andreasen, and D. U. Sauer, IEEE Trans. Ind. Appl., 52, 5086–5099 (2016).H. Song, T. Kim, J. Jeong, B. Kim, D. Shin, B. Lee, and H. Heo, IET Power Electron., 6, 417–424 (2013).

Nonlinear electrochemical impedance spectroscopy (NLEIS) is a moderate-amplitude extension to linear EIS that provides a sensitive and complementary whole-battery diagnostic for charge transfer kinetics, mass transport, and thermodynamics. We present the first full-frequency, second harmonic NLEIS spectra for lithium-ion batteries using commercially available, 1.5 Ah LiNMC|C cells. The mathematical framework for NLEIS shows, and experiments confirm, that moderate-amplitude input modulations can generate a second harmonic output that does not intrinsically corrupt the linear EIS response. Experimental measurements at varied states-of-charge (SoC) and states-of-health (SoH) are used to illustrate and compare NLEIS and EIS data. At low frequencies, the second harmonic NLEIS spectrum is shown to produce a more distinct response to SoC dependent thermodynamic and diffusion processes than linear EIS. By combining NLEIS and EIS, we are able to characterize degradation in early cell cycling (where cells lost <1% of initial capacity). Second harmonic NLEIS is shown to be sensitive to degradation in charge transfer symmetry whereas linear EIS is mainly sensitive to changes in charge transfer rates. For example, NLEIS shows that fresh cells have highly symmetric charge transfer (αa = αc = 0.5) on both electrodes, whereas early in the cycling, there is a shift toward kinetics that favor oxidation on the positive electrode (αa, pos > 0.5, αc, pos < 0.5). Combined analysis of EIS and NLEIS spectra shows promise for improved parameter estimation and model validation. All experimental data and analysis code for this manuscript can be found on ECSarXiv.

Electrochemical impedance spectroscopy (EIS) is a powerful diagnostic tool used in a wide range of applications, including solid oxide fuel cells (SOFCs) and solid oxide electrolysis cells (SOECs). While EIS measurements on single cell level are commonplace, implementation of EIS on stack level remains limited, primarily due to the extremely low impedance of large-footprint cells, which imposes stringent demands on the impedance spectrometer and experimental setup (1). Furthermore, compared to single-cell EIS data, stack-level data reported in the literature are rarely subjected to the same degree of equivalent circuit modeling, making a detailed analysis of underlying electrochemical processes difficult.Here, we report a framework for analyzing stack-level impedance spectroscopy data. The quality of the acquired data is first verified using Kramers-Kronig transformations (2), followed by the application of distribution of relaxation times (DRT) and analysis of the difference of impedance spectra (ADIS) methods to experimental data collected under a set of pre-determined operating conditions (electrochemical test procedure) (3-4). DRT and ADIS results were incorporated into the complex non-linear least squares (CNLS) fitting procedure and the validity of the chosen equivalent circuit model was confirmed by reconstruction of Nyquist, Bode, the individual electrochemical contributions, and DRT plots of the fitted data.The developed framework was successfully implemented on a commercial 75-cell SOEC stack (TSP-1) developed by Haldor Topsoe (5). An electrochemical impedance spectrum is recorded simultaneously on all 13 cell groups in the stack using Zahner instrumentation. In this work, the electrochemical impedance data obtained from a state-of-the-art TSP-1 stack, containing three different types of Ni/YSZ based cells, is reported. The stack was initially investigated by EIS, using an electrochemical test procedure including CO2 electrolysis under constant conversion, H2O electrolysis under constant conversion, variations in the pO2 on the oxygen electrode, and finally temperature variations in CO2 electrolysis operation. This electrochemical test procedure was performed to develop an equivalent circuit model for the stack. Afterward, the stack was subjected to a degradation in steam electrolysis under 580 mA/cm2 (70% conversion), with an impedance spectrum being recorded every 24 hours. The operational point for this degradation test was chosen to match the real-life operation point of these stacks and hence to give a realistic image of any potential degradation. The developed framework and the equivalent circuit model developed for the stack was finally used to model the EIS data obtained during the degradation test. The modeling of these EIS data utilizes the full potential of electrochemical impedance spectroscopy and help identify any degradation mechanisms taking place in the stack, an analysis not previously reported on stack level.(1) R. R. Mosbæk, J. Hjelm, R. Barfod, and P. V. Hendriksen. ECS transactions, 35, 1 (2011).(2) B. Boukamp, J. Electrochem. Soc., 142, 1885 – 1894 (1995).(3) S. H. Jensen, A. Hauch, P.V. Hendriksen, M. Mogensen, N. Bonanos, and T. Jacobsen. Journal of the Electrochemical Society, 154(12), B1325-B1330, (2007)(4) H. Schichlein, and E. Ivers-Tiffee. Journal of Applied Electrochemistry, 32, 875-882, (2002).(5) J. Rass-Hansen, P. Blennow, T. Heiredal-Clausen, R. Küngas, T. Holt Nørby, and S. Primdahl, Proceedings of the 12th European SOFC & SOE Forum, 318-325 (2016). Figure 1

Lithium-ion battery has been widely used in many industrial applications. For better understanding of the performance of lithium-ion batteries, various numerical models have been developed. These models can be categorized into two groups: empirical models and the physics-based models. In empirical models, electrochemical physics is not resolved. Instead, correlations are established by curve-fitting experimental data of a battery. In physics-based models, the electrochemical kinetics and transport phenomena are considered and the models can produce more accurate prediction than empirical models. All these electrochemical models are proposed by electrochemical engineers and are used to predict a battery's electric performance such as charging/discharging characteristics. These models are usually zero dimensional (e.g., equivalent circuit models) or one dimensional (e.g., Newman's P2D model). In many battery applications such as electric vehicles, batteries are connected in parallel and/or in series to form large format of modules or packs. Thermal management becomes a critical issue in the design of such systems. To perform thermal analysis, electrochemical models developed by electrochemical engineers like the ones mentioned in the previous paragraph need to be coupled in the simulation since heat released during battery's operation relies on the prediction from these models. However, thermal analysis, even for a single battery cell, is three dimensional by nature. A multi-physics model has to be used to handle the complex interplay of different physics. A modeling methodology, called multi-scale multi-dimensional method (MSMD), has been proposed by Kim et al. for such applications. The method has been proven to be very effective in simulating single battery or battery packs. It has been implemented in a general computational fluid dynamics commercial code, Ansys FLUENT. In the MSMD method, different physics are resolved at different scales and in different domains. Then they are intimately coupled by exchanging information from one domain to another. One key idea in the MSMD method is that a battery's electric behavior can be represented by two co-located potential fields. The dual potential fields are solved on the same mesh as other flow variables like temperature. In this method every computational cell (control volume) in the active zone of a battery after discretization is treated as a mini-battery. The electrochemical model is applied to each mini-battery, which is at a subscale level. Since different physics is resolved in different domain and at different scale, in theory, any electrochemical submodel can be used in the MSMD method. Both empirical models and physics-based models have been used in the past under this methodology. Although the MSMD method is very effective, there are some challenges preventing the method from being used for large problems in a battery or pack simulation. One challenge is to couple a physics-based electrochemical submodel such as Newman's P2D model in a three dimensional thermal simulation. Several partial differential equations already need to be solved in the electrochemical submodel. If the submodel is called by every CFD computational cell, the high computational cost makes the method practically unfeasible even in a single battery simulation, let alone battery packs. Guo and White noticed that, under a battery's normal operation, electrochemical reactions progress pretty evenly within a battery and they proposed a linear approximation model. By using that assumption, the computational cost can be reduced by orders of magnitude, thus makes the physics-based model feasible in a real three dimensional electrochemical-thermal coupled simulation (ECT). The MSMD method needs two potential equations to be solved. Although the equations do not have transient terms, they need to be solved repeatedly at each time step in a transient fashion due to the time varying electric load condition and the change of state of charge of a battery. In this presentation, a linear scaling procedure is found to reconstruct the two potential fields from reference fields that can be calculated in advance. The procedure completely removes the need of solving two partial differential potential equations repeatedly. It can save the computational time significantly in an ECT simulation. The procedure is valid on the same basis as the linear approximation model. With this procedure, very large problems in battery application can be tackled. The cost of an ECT simulation is reduced to about the same as of a pure thermal simulation, which is the best as one can expect. In this presentation, the MSMD methodology is first reviewed. Then the scaling procedure, called the reduced order method (compared to solving two potential equations directly), is proposed in detail. The method is illustrated by simulating a single battery and a battery pack.

Electrochemical impedance spectroscopy (EIS) has been widely used to study the linear dynamics of many electrochemical systems, including Li-ion batteries.1-4 Most physical and chemical processes in an electrochemical system possess distinct characteristic time constants, enabling EIS to distinguish these processes by their frequency response. The dynamics of the porous electrodes used inside most commercially available Li-ion batteries are governed by the conduction and mass transfer in the solid and the electrolyte phase, and electro-chemical kinetics at the solid-electrolyte interface. Because EIS is able to separate processes by their time-scales, it is often possible to see changes in each battery electrode as well as the degradation that leads to capacity fade of the batteries.5-8 Equivalent circuits are the most commonly used models to study the impedance response of batteries; however, these models can suffer from a lack of physical interpretability and model degeneracy.9 Though much less used, physics-based models can provide more direct insight into the impedance response of a battery. Mathematically, physics-based impedance models are transformed from the time-domain to the frequency-domain by assuming a steady-periodic response, thereby eliminating time as an independent variable.10 Most rigorous physics-based models for the impedance of a Li-ion battery employ a numerical scheme to solve the resulting equations.10-12 The resulting equations are computationally expensive to solve, and this reduces their usefulness for multi-parameter optimization and analysis of different mechanisms from experimental impedance data. In this talk, we propose a hybrid analytical-collocation approach for simulating the impedance response of a Li-ion battery using the pseudo-two dimensional (P2D) model in real-time. The impedance response of the spherical diffusion equations is solved analytically and collocation is performed on the resulting boundary value problem across the electrode and separator thickness using an orthogonal collocation scheme based on Gauss-Legendre points. The profiles for a frequency range from 0.5 mHz to 10 kHz are compared with the numerical solution obtained by solving the original model in COMSOL Multiphysics. The internal variable profiles across a wide range of frequencies are compared between the two methods and the accuracy, robustness, and computational superiority of the proposed hybrid analytical-collocation approach is presented. The limitations of the proposed approach will also be discussed. Acknowledgments The authors would like to thank the Department of Energy (DOE) for providing partial financial support for this work, through the Advanced Research Projects Agency (ARPA-E) award number DE-AR0000275, along with the Assistant Secretary for Energy Efficiency and Renewable Energy, Office of Vehicle Technologies of the DOE through the Advanced Battery Material Research (BMR) Program (Battery500 consortium). References M. E. Orazem, and B. Tribollet, Electrochemical Impedance Spectroscopy, Wiley, New Jersey (2008).G. Barsoukov, and J.R. Macdonald, Impedance Spectroscopy: Theory, Experiment, and Applications, Wiley-Interscience, New Jersey (2005).M. G. S. R. Thomas, P.G. Bruce, and J.B. Goodenough, Journal of the Electrochemical Society, 132 (1985).P. Yu, B.N. Popov, J.A. Ritter, and R.E. White, Journal of the Electrochemical Society, 146 (1999).M. Dubarry, A. Devie, and B.Y. Liaw, Journal of Energy and Power Sources, 1, 242 (2014).M. Dubarry, C. Truchot, and B.Y. Liaw, Journal of Power Sources, 219, 204 (2012).C. Pastor-Fernandez, K. Uddin, G.H. Chouchelamane, W.D. Widanage, and J. Marco, Journal of Power Sources, 360, 301 (2017).U. Tröltzsch, O. Kanoun, and H.R. Tränkler, Electrochimica Acta, 51, 1664 (2006).S. Fletcher, Journal of the Electrochemical Society, 141, 1823 (1994).M. Doyle, J.P. Meyers, and J. Newman, Journal of the Electrochemical Society, 147, 99 (2000).M. D. Murbach, and D.T. Schwartz, Journal of the Electrochemical Society, 164, E3311 (2017).D. W. Dees, K.G. Gallagher, D.P. Abraham, and A.N. Jansen, Journal of the Electrochemical Society, 160, A478 (2013).

EIS (electrochemical impedance spectroscopy) is well established as a work horse in the laboratory evaluation of organic coatings performance. This paper describes the first step in the development of a test protocol to apply a field-portable ECN (electrochemical noise) sensor / system to the assessment of in-service coatings. The correlation between EIS and ECN scans on long-term lab coating samples confirms that ECN has the ability to discriminate, clearly, between "Good", and "Poor" coatings performance. This may prove useful in extending laboratory EIS data on coatings to field evaluations of in-service coatings. EIS and a modified ECN technique were used to examine the protective properties of nine epoxy-paint coating samples. All coatings were on metallic substrates, and had been immersed in ASTM-D1141 synthetic seawater and had EIS data for periods ranging from two to ten years. Each tested-sample represented a different stage of coating aging and degradation, from “Good” to “Failed”, with the differences between all coatings discernable using EIS. The observed resolution in noise current measurements, by the modified ECN method, encourages its application to assessing in-service coating conditions, by comparing ECN readings on field samples to EIS values measured on laboratory data base samples of the service coatings.

Electrochemical impedance spectroscopy (EIS) is a powerful tool for the non-destructive diagnosis of lithium ion batteries (LIBs). Thanks to the measurement over a wide frequency range, electrochemical processes of different kinetics are reflected in EIS, which contains rich information on battery aging and degradation.Distribution of relaxation times (DRT) method has been increasingly utilised to interpret EIS data. Compared to conventional EIS presentations such as Nyquist plot and Bode plot, DRT isolates the processes with different time constants and gives an explicit showcase of timescales in the battery [1]. Another advantage of DRT is the possibility to separate contributions from cathode and anode without the meticulous work to make three-electrode cells, given that relaxation time peaks can be identified with half cells [2]. The information acquired through DRT can provide insight into battery degradation paths and help improve data-driven methods for battery diagnosis/prediction.This work looks into the DRT evolution of commercial NMC/graphite cylindrical cells (Sony US14500VR2 with a nominal capacity of 715mAh) under various cycling conditions. Before the experiment starts, the cells are in shipping status i.e. undergone pre-aging and kept at approximately 70% state of charge (SoC). All cells then go through one 0.1C/0.1C cycle and 99 continuous cycles under various C-rates and temperatures (see table 1). The lower C-rates under 25ºC and 35ºC are scaled against 45ºC by Arrhenius relation. All charges are constant-current constant-voltage and all discharges are constant-current, between 3V and 4.2V. Impedance spectra are measured over 10kHz~0.1Hz range after being fully charged and fully discharged in each cycle.The impedance spectra measured after every full charge of cells 1~5 are shown in Figure 1(a) ~ (e). The decrease of semicircle size as temperature increases can be seen. During continuous cycling, internal resistance and semicircle size grow monotonically as cycle number increases. While the semicircles in each EIS curve are overlapping, the impedance components with different relaxation times are clearly separated in the DRT plotted in Figure 2. In Figure 2(a) and (b), there are constantly four relaxation time peaks as cycle number increases in 25ºC. The feature time constant in lies tightly within 25ms~50ms range, corresponding to 20Hz~40Hz frequencies, regardless of C-rates. In Figure 2(c) and (d), relaxation time peaks differ with C-rates right after 35ºC cycling starts. With 0.5C/1C rate, the evolution trend of relaxation time is similar to 25ºC cases. With 1C/2C rate however, there are initially only three relaxation time peaks and the mid-frequency (between 0.1s and 1s) peak “splits” into two as cycle number approaches 100. This could be related to joule heating resulting from higher C-rate or kinetic factors, and is more similar to the 45ºC case as shown in Figure 2(e). In 45ºC with 1C/2C rate, the relaxation time peaks start with three and “split” into four around the 60th cycle.While the evolution of DRT needs further interpretation and more long-term experiments, we can see the effective of time scale separation for EIS under various cycling conditions. The time scale features can be incorporated into data-driven methods e.g. machine learning to aim at accurate battery diagnosis/prediction. Also, the fact that feature relaxation times (may be battery-type specific) are distributed in a relatively narrow range suggests the EIS measurement can be done with reduced frequency points to save on-board resources for future system-level application.This work is supported by Faraday Institution (EP/S003053/1) and North-East Centre of Energy Materials (EP/R021503/1) funded by EPSRC.[1] Ciucci, F., & Chen, C. (2015). Analysis of electrochemical impedance spectroscopy data using the distribution of relaxation times: A Bayesian and hierarchical Bayesian approach. Electrochimica Acta, 167, 439-454.[2] Sabet, P. S., Stahl, G., & Sauer, D. U. (2018). Non-invasive investigation of predominant processes in the impedance spectra of high energy lithium-ion batteries with Nickel-Cobalt-Aluminum cathodes. Journal of Power Sources, 406, 185-193. Figure 1

The growth of the barrier oxide layer on aluminum during low-current anodic polarization in aqueous solutions occurs in accordance with the high-field Cabrera-Mott growth law,1 as recently confirmed for pure aluminum by use of simultaneous ellipsometry and chronoamperometry to measure the transient film growth following a potential step.2 Electrochemical impedance spectroscopy (EIS) was used to determine the steady-state barrier layer thickness between each potential step as in situ calibration for the measurement of the film growth rate by the other two methods. Complementarity of the three techniques was demonstrated for studying the kinetics of growth and dissolution of thin passivating oxides in aqueous solution. The purpose of the present study is to investigate whether the same approach can be used for studying the modification of the interface by contamination by the common trace element Pb as a result of heat treatment. Pb is known to activate the surface by destabilizing the passivating barrier layer.3 The microstructure and composition of the contaminated interface has been characterized by ex-situ STEM and various surface analytical techniques for samples heat treated at high (600°C) temperatures, resulting in detectable Pb segregation in the form of both nanosize (up to 10 nm) Pb particles and a few nm thick Pb-rich film along the metal-oxide interface. Pb segregation by heat treatment at lower temperatures was not possible by these techniques. Supplementary data were necessary for samples heat treated at lower temperatures, especially for modification of the electrochemical properties of the interface. The samples investigated were model AlPb alloys prepared from pure components in the laboratory and cold rolled into 2.2 mm thick plates, followed by polishing metallographically through 1 µm surface finish. They were subsequently heat treated in an air-circulation furnace in the temperature range 300 - 500°C. The amorphous oxide is reported to thicken moderately in the range 10 - 20 nm as a result of 1 h heat treatment at this temperature range.4 Experiments were conducted in a conventional three electrode electrochemical cell in the manner described above. Ellipsometry could not be used because of slow measurement relative to the rate of barrier-layer growth and unexpected loss of specularity of the sample surface during heat treatment. The EIS data were evaluated by use of the equivalent-circuit model derived rigorously by Armstrong and Edmondson,5 which was shown to be applicable to the present electrochemical interface in the case of pure Al.2 Oxide growth was calculated from the current-time data by use of Faraday's law corrected for current leakage (passive current). The growth data were analyzed by use of the integrated form of the Cabrera-Mott law, according to Ghez,6 giving the well-known inverse logarithmic growth law. The changes in the barrier layer thickness appeared to fit the Ghez equation, but not as successfully as pure Al. The EIS data showed that the film thickened with increasing applied potential at the rate of 1.2 nm/V for all heat treatment temperatures except for 600°C, as expected for pure Al. The passive current density increased and the film resistance decreased at a given applied potential, with increasing annealing temperature, indicating reduced passivity. However, the film capacitance, measured by EIS at a given applied potential, increased with annealing temperature, giving an apparent decrease in the film thickness with increasing annealing temperature, in contrast to the expected trend to the opposite.4 The changes in the barrier film properties, measured by EIS, are attributed to the segregation of metallic Pb at the metal-film interface, in the film, and possibly at the film surface, contributing to the increased capacitance of the electrochemical interface. The model used for correlation of the EIS data has to be modified to incorporate the effect of segregated Pb in the form of particles and continuous film for more reliable measurement of the barrier film thickness in future work. References J. W. Diggle, T. C. Downie, and C. W. Goulding, Chem. Rev., 69 (3), 365 (1969). N. H. Giskeødegård, O. Hunderi and K. Nisancioglu, J. Solid State Electrochem. 19, 3473 (2015). Anawati, B. Graver, H. Nordmark, Z. Zhao, G. S. Frankel, J. C. Walmsley, and K. Nisancioglu, J. Electrochem. Soc., 157, C313 (2010). E. Senel, Dissertation, Norwegian University of Science and Technology, Trondheim (2013). R. D. Armstrong and K. Edmondson, Electrochim. Acta, 18,937 (1973). R. Ghez, J. Phys. Chem., 58, 1838 (1973).