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Bayesian parameter inference is useful to improve Li-ion battery diagnostics and can help formulate battery aging models. However, it is computationally intensive and cannot be easily repeated for multiple cycles, multiple operating conditions, or multiple replicate cells. To reduce the computational cost of Bayesian calibration, numerical solvers for physics-based models can be replaced with faster surrogates. A physics-informed neural network (PINN) is developed as a surrogate for the pseudo-2D (P2D) battery model calibration. For the P2D surrogate, additional training regularization was needed as compared to the PINN single-particle model (SPM) developed in Part I. Both the PINN SPM and P2D surrogate models are exercised for parameter inference and compared to data obtained from a direct numerical solution of the governing equations. A parameter inference study highlights the ability to use these PINNs to calibrate scaling parameters for the cathode Li diffusion and the anode exchange current density. By realizing computational speed-ups of ≈2250x for the P2D model, as compared to using standard integrating methods, the PINN surrogates enable rapid state-of-health diagnostics. In the low-data availability scenario, the testing error was estimated to ≈2 mV for the SPM surrogate and ≈10 mV for the P2D surrogate which could be mitigated with additional data.

To plan and optimize energy storage demands that account for Li-ion battery aging dynamics, techniques need to be developed to diagnose battery internal states accurately and rapidly. This study seeks to reduce the computational resources needed to determine a battery’s internal states by replacing physics-based Li-ion battery models – such as the single-particle model (SPM) and the pseudo-2D (P2D) model – with a physics-informed neural network (PINN) surrogate. The surrogate model makes high-throughput techniques, such as Bayesian calibration, tractable to determine battery internal parameters from voltage responses. This manuscript is the first of a two-part series that introduces PINN surrogates of Li-ion battery models for parameter inference (i.e., state-of-health diagnostics). In this first part, a method is presented for constructing a PINN surrogate of the SPM. A multi-fidelity hierarchical training, where several neural nets are trained with multiple physics-loss fidelities is shown to significantly improve the surrogate accuracy when only training on the governing equation residuals. The implementation is made available in a companion repository (https://github.com/NREL/PINNSTRIPES). The techniques used to develop a PINN surrogate of the SPM are extended in Part II (Hassanaly et al., 2024) for the PINN surrogate for the P2D battery model, and explore the Bayesian calibration capabilities of both surrogates.

This paper implements a highly efficient algorithm to extract electrochemical impedance spectra (EIS) from physics-based battery models (e.g., a P2D model). The mathematical approach is different from how EIS is practiced experimentally. Experimentally, the voltage (current) is harmonically perturbed over a wide range of frequencies and the amplitude and phase shift of the corresponding current (voltage) is measured. The experimental approach can be implemented in simulation software, but is computationally expensive. The approach here is to determine locally linear state-space models from the full physical model. The four Jacobian matrices that are the basis of the state-space models can be derived by numerical differentiation of the physical model. The EIS is then extracted from the state-space model using computationally efficient matrix-manipulation techniques. The algorithm can evaluate the full EIS at an instant in time during a transient, independent of whether the battery is in a stationary state. The approach is also able to separate the full-cell impedance to evaluate partial EIS, such as for a battery anode alone. Although such partial EIS is difficult to measure experimentally, the partial EIS provides valuable insights in interpreting the full-cell EIS.

During Li-ion battery operation, (electro)chemical side reactions occur within the cell that can promote or degrade performance. These complex reactions produce byproducts in the solid, liquid, and gas phases. Studying byproducts in these three phases can help optimize battery lifetimes. To relate the measured gas-phase byproducts to species dissolved in the liquid-phase, equilibrium proprieties such as the Henry’s law constants are required. The present work implements a pressure decay experiment to determine the thermodynamic equilibrium concentrations between the gas and liquid phases for ethylene (C2H4) and carbon dioxide (CO2), which are two gases commonly produced in Li-ion batteries, with an electrolyte of 1.2 M LiPF6in 3:7 wt/wt ethylene carbonate/ethyl methyl carbonate and 3 wt % fluoroethylene carbonate (15:25:57:3 wt % total composition). The experimentally measured pressure decay curve is fit to an analytical dissolution model and extrapolated to predict the final pressure at equilibrium. The relationship between the partial pressures and concentration of dissolved gas in electrolyte at equilibrium is then used to determine Henry’s law constants of kC2H4=2.0 × 104kPa for C2H4and kCO2= 1.1 × 104kPa for CO2. These values are compared to Henry’s law constants predicted from density functional theory and show good agreement within a factor of 3.

To sustain the high-rate current required for fast charging electric vehicle batteries, electrodes must exhibit sufficiently high effective ionic diffusion. Additionally, to reduce battery manufacturing costs, wetting time must decrease. Both of these issues can be addressed by structuring the electrodes with mesoscale pore channels. However, their optimal spatial distribution, or patterns, is unknown. Herein, a genetic algorithm has been developed to identify these optimal patterns using a CPU-cheap proxy distance-based model to evaluate the impact of the added pore networks. Both coin-cell and pouch cell form factors have been considered for the wetting analysis, with their respective electrolyte infiltration mode. Regular hexagonal and mud-crack-like patterns, respectively, for fast charging and fast wetting were found to be optimal and have been compared with pre-determined, easier to manufacture, patterns. The model predicts that using cylindrical channels arranged in a regular hexagonal pattern is ∼6.25 times more efficient for fast charging as compared to grooved lines with both structuring strategies being restricted to a 5% electrode total volume loss. The model also shows that only a very limited electrode volume loss (1%–2%) is required to dramatically improve the wetting (5–20 times) compared to an unstructured electrode.

Phase-transformation electrodes have desirable characteristics for lithium-ion batteries. These electrodes have been shown to be abuse resistant, have extended cycle life, and are suitable for fast-charging applications. These new materials have significantly different lithium incorporation behaviors than the more-conventional solid-solution reaction electrodes. This paper explores the implications of phase-transformation physics within a multiparticle electrode that contains a distribution of particle sizes. Phase-transformation physics is such that lithium distributions within the electrode particle ensemble is cycle-path dependent. For example, after charging, any maldistribution of lithium between particles does not naturally redistribute uniformly between all particles, as is the case for solid-solution reaction electrodes. Such maldistribution greatly influences the observed electrochemical impedance spectra. The implications of history-dependent inter-particle lithium distributions is characterized with a mesoscopic model. The model shows how the impedance spectra of a phase-transformation electrode, at a prescribed state of charge, depends on the path history to achieve the state of charge.

The present paper seeks to extract, analyze, and interpret the electrochemical impedance spectra of a LiFePO4-Li4Ti5O12 battery to supplement state-of-charge estimation. A particular challenge in determining the state-of-charge of a LiFePO4-Li4Ti5O12 cell is that the open-circuit voltage is flat over a large range of states of charge. Because the voltage in standard batteries is typically used to inform state-of-charge estimation, a different corrective factor needs to be determined for this cell chemistry. Instead of using the battery voltage, the present study uses the battery's dynamic response to assist state of charge estimation. The present work includes at least three novel contributions: 1) the electrochemical impedance of the LiFePO4-Li4Ti5O12 cell is shown to be strongly history dependent, 2) a novel system-identification technique is implemented to extract the EIS in-situ, and 3) a signature electrochemical impedance spectra attribute is identified that is a strong function of battery state of charge.

A battery's electrochemical impedance response provides great insight about its internal electrochemical dynamics and state-of-health. This paper presents a method to efficiently obtain wide-bandwidth electrochemical impedance spectra using two-level (binary) perturbation sequences. In this study, a physically based battery model's current-voltage response is captured with state-space models using system-identification methods. However, any single identified model is accurate only within a specific, limited frequency range. A stitching procedure combines several state-space models to establish a composite state-space model that is accurate over a wide frequency range. A validation study shows excellent agreement between the impedance of the stitched state-space model and the original physically based battery model. The approach is equally applicable to extracting electrochemical impedance spectra from simulation models as for experimental investigations.

Numerous technologies, such as batteries and fuel cells, depend on electrochemical kinetics. In some cases, the responsible electrochemistry and charged-species transport is complex. However, to date, there are essentially no general-purpose modeling capabilities that facilitate the incorporation of thermodynamic, kinetic, and transport complexities into the simulation of electrochemical processes. A vast majority of the modeling literature uses only a few (often only one) global charge-transfer reactions, with the rates expressed using Butler-Volmer approximations. The objective of the present paper is to identify common aspects of electrochemistry, seeking a foundational basis for designing and implementing software with general applicability across a wide range of materials sets and applications. The development of new technologies should be accelerated and improved by enabling the incorporation of electrochemical complexity (e.g., multi-step, elementary charge-transfer reactions and as well as supporting ionic and electronic transport) into the analysis and interpretation of scientific results. The spirit of the approach is analogous to the role that Chemkin has played in homogeneous chemistry modeling, especially combustion. The Cantera software, which already has some electrochemistry capabilities, forms the foundation for future capabilities expansion.

•A system theoretic analysis of battery charging.•When does optimal charging include sinusoidal components?•Analytical relationship between battery impedance and energy optimal charging.•Simple test for a constrained charging sequence to optimize total stored charge.

Phase-transformation electrodes have desirable characteristics for lithium-ion batteries. These electrodes have been shown to be abuse resistant, have extended cycle life, and are suitable for fast-charging applications. These new materials have significantly different lithium incorporation behaviors than the more-conventional solid-solution reaction electrodes. This paper explores the implications of phase-transformation physics within a multiparticle electrode that contains a distribution of particle sizes. Phase-transformation physics is such that lithium distributions within the electrode particle ensemble is cycle-path dependent. For example, after charging, any maldistribution of lithium between particles does not naturally redistribute uniformly between all particles, as is the case for solid-solution reaction electrodes. Such maldistribution greatly influences the observed electrochemical impedance spectra. The implications of history-dependent inter-particle lithium distributions is characterized with a mesoscopic model. The model shows how the impedance spectra of a phase-transformation electrode, at a prescribed state of charge, depends on the path history to achieve the state of charge.

The present paper seeks to extract, analyze, and interpret the electrochemical impedance spectra of a LiFePO4-Li4Ti5O12battery to supplement state-of-charge estimation. A particular challenge in determining the state-of-charge of a LiFePO4-Li4Ti5O12cell is that the open-circuit voltage is flat over a large range of states of charge. Because the voltage in standard batteries is typically used to inform state-of-charge estimation, a different corrective factor needs to be determined for this cell chemistry. Instead of using the battery voltage, the present study uses the battery’s dynamic response to assist state of charge estimation. The present work includes at least three novel contributions: 1) the electrochemical impedance of the LiFePO4-Li4Ti5O12cell is shown to be strongly history dependent, 2) a novel system-identification technique is implemented to extract the EIS in-situ, and 3) a signature electrochemical impedance spectra attribute is identified that is a strong function of battery state of charge.

Numerous technologies, such as batteries and fuel cells, depend on electrochemical kinetics. In some cases, the responsible electrochemistry and charged-species transport is complex. However, to date, there are essentially no general-purpose modeling capabilities that facilitate the incorporation of thermodynamic, kinetic, and transport complexities into the simulation of electrochemical processes. A vast majority of the modeling literature uses only a few (often only one) global charge-transfer reactions, with the rates expressed using Butler–Volmer approximations. The objective of the present paper is to identify common aspects of electrochemistry, seeking a foundational basis for designing and implementing software with general applicability across a wide range of materials sets and applications. The development of new technologies should be accelerated and improved by enabling the incorporation of electrochemical complexity (e.g., multi-step, elementary charge-transfer reactions and as well as supporting ionic and electronic transport) into the analysis and interpretation of scientific results. The spirit of the approach is analogous to the role that Chemkin has played in homogeneous chemistry modeling, especially combustion. The Cantera software, which already has some electrochemistry capabilities, forms the foundation for future capabilities expansion.

A battery’s electrochemical impedance response provides great insight about its internal electrochemical dynamics and state-of-health. This paper presents a method to efficiently obtain wide-bandwidth electrochemical impedance spectra using two-level (binary) perturbation sequences. In this study, a physically based battery model’s current-voltage response is captured with state-space models using system-identification methods. However, any single identified model is accurate only within a specific, limited frequency range. A stitching procedure combines several state-space models to establish a composite state-space model that is accurate over a wide frequency range. A validation study shows excellent agreement between the impedance of the stitched state-space model and the original physically based battery model. The approach is equally applicable to extracting electrochemical impedance spectra from simulation models as for experimental investigations.