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Diagnosing imbalances in capacity and resistance within parallel-connected cells in battery packs is critical for battery management and fault detection, but it is challenging given that individual currents flowing into each cell are often unmeasured. This work introduces a novel method useful for identifying imbalances in capacity and resistance within a pair of parallel-connected cells using only voltage and current measurements from the pair. Our method utilizes differential voltage analysis (DVA) when the pair is under constant current discharge and demonstrates that features of the pair's differential voltage curve (dV/dQ), namely its mid-to-high SOC dV/dQ peak's height and skewness, are sensitive to imbalances in capacity and resistance. We analyze and explain how and why these dV/dQ peak shape features change in response to these imbalances, highlighting that the underlying current imbalance dynamics resulting from these imbalances contribute to these changes. Ultimately, we demonstrate that dV/dQ peak shape features can identify the product of capacity imbalance and resistance imbalance, but cannot uniquely identify the imbalances. This work lays the groundwork for identifying imbalances in capacity and resistance in parallel-connected cell groups in battery packs, where commonly only a single current sensor is placed for each parallel cell group., Comment: Accepted to American Control Conference (ACC), Toronto, Canada, July 2024

The battery state of health (SOH) based on capacity fade and resistance increase is not sufficient for predicting Remaining Useful life (RUL). The electrochemical community blames the path-dependency of the battery degradation mechanisms for our inability to forecast the degradation. The control community knows that the path-dependency is addressed by full state estimation. We show that even the electrode-specific SOH (eSOH) estimation is not enough to fully define the degradation states by simulating infinite possible degradation trajectories and remaining useful lives (RUL) from a unique eSOH. We finally define the deepSOH states that capture the individual contributions of all the common degradation mechanisms, namely, SEI, plating, and mechanical fracture to the loss of lithium inventory. We show that the addition of cell expansion measurement may allow us to estimate the deepSOH and predict the remaining useful life., Comment: 6 pages, 3 figures

This paper proposes an analytical framework describing how initial capacity and resistance variability in parallel-connected battery cells may inflict additional variability or reduce variability while the cells age. We derive closed-form equations for current and SOC imbalance dynamics within a charge or discharge cycle. These dynamics are represented by a first-order equivalent circuit model and validated against experimental data. To demonstrate how current and SOC imbalance leads to cell degradation, we developed a successive update scheme in which the inter-cycle imbalance dynamics update the intra-cycle degradation dynamics, and vice versa. Using this framework, we demonstrate that current imbalance can cause convergent degradation trajectories, consistent with previous reports. However, we also demonstrate that different degradation assumptions, such as those associated with SOC imbalance, may cause divergent degradation. We finally highlight the role of different cell chemistries, including different OCV function nonlinearities, on system behavior, and derive analytical bounds on the SOC imbalance using Lyapunov analysis., Comment: 22 pages, 14 figures, submitted to the Journal of Dynamic Systems, Measurement and Control

This work proposes a semi-empirical model for the SEI growth process during the early stages of lithium-ion battery formation cycling and aging. By combining a full-cell model which tracks half-cell equilibrium potentials, a zero-dimensional model of SEI growth kinetics, and a semi-empirical description of cell thickness expansion, the resulting model replicated experimental trends measured on a 2.5 Ah pouch cell, including the calculated first-cycle efficiency, measured cell thickness changes, and electrolyte reduction peaks during the first charge dQ/dV signal. This work also introduces an SEI growth boosting formalism that enables a unified description of SEI growth during both cycling and aging. This feature can enable future applications for modeling path-dependent aging over a cell's life. The model further provides a homogenized representation of multiple SEI reactions enabling the study of both solvent and additive consumption during formation. This work bridges the gap between electrochemical descriptions of SEI growth and applications towards improving industrial battery manufacturing process control where battery formation is an essential but time-consuming final step. We envision that the formation model can be used to predict the impact of formation protocols and electrolyte systems on SEI passivation and resulting battery lifetime., Comment: Submitted to the Journal of the Electrochemical Society on May 24, 2023

Voltage-based battery metrics are ubiquitous and essential in battery manufacturing diagnostics. They enable electrochemical "fingerprinting" of batteries at the end of the manufacturing line and are naturally scalable, since voltage data is already collected as part of the formation process which is the last step in battery manufacturing. Yet, despite their prevalence, interpretations of voltage-based metrics are often ambiguous and require expert judgment. In this work, we present a method for collecting and analyzing full cell near-equilibrium voltage curves for end-of-line manufacturing process control. The method builds on existing literature on differential voltage analysis (DVA or dV/dQ) by expanding the method formalism through the lens of reproducibility, interpretability, and automation. Our model revisions introduce several new derived metrics relevant to manufacturing process control, including lithium consumed during formation and the practical negative-to-positive ratio, which complement standard metrics such as positive and negative electrode capacities. To facilitate method reproducibility, we reformulate the model to account for the "inaccessible lithium problem" which quantifies the numerical differences between modeled versus true values for electrode capacities and stoichiometries. We finally outline key data collection considerations, including C-rate and charging direction for both full cell and half cell datasets, which may impact method reproducibility. This work highlights the opportunities for leveraging voltage-based electrochemical metrics for online battery manufacturing process control., Comment: 27 pages, 6 figures; pre-print for manuscript submitted to Frontiers in Energy Research

In this work, we derive analytical expressions governing state-of-charge and current imbalance dynamics for two parallel-connected batteries. The model, based on equivalent circuits and an affine open circuit voltage relation, describes the evolution of state-of-charge and current imbalance over the course of a complete charge and discharge cycle. Using this framework, we identify the conditions under which an aged battery will experience a higher current magnitude and state-of-charge deviation towards the end of a charge or discharge cycle. This work enables a quantitative understanding of how mismatches in battery capacities and resistances influence imbalance dynamics in parallel-connected battery systems, helping to pave a path forward for battery degradation modeling in heterogeneous battery systems., Comment: 7 pages, 4 figures, conference paper (MECC 2022)

A data-driven model augmentation framework, referred to as Weakly-coupled Integrated Inference and Machine Learning (IIML), is presented to improve the predictive accuracy of physical models. In contrast to parameter calibration, this work seeks corrections to the structure of the model by a) inferring augmentation fields that are consistent with the underlying model, and b) transforming these fields into corrective model forms. The proposed approach couples the inference and learning steps in a weak sense via an alternating optimization approach. This coupling ensures that the augmentation fields remain learnable and maintain consistent functional relationships with local modeled quantities across the training dataset. An iterative solution procedure is presented in this paper, removing the need to embed the augmentation function during the inference process. This framework is used to infer an augmentation introduced within a Polymer electrolyte membrane fuel cell (PEMFC) model using a small amount of training data (from only 14 training cases.) These training cases belong to a dataset consisting of high-fidelity simulation data obtained from a high-fidelity model of a first generation Toyota Mirai. All cases in this dataset are characterized by different inflow and outflow conditions on the same geometry. When tested on 1224 different configurations, the inferred augmentation significantly improves the predictive accuracy for a wide range of physical conditions. Predictions and available data for the current density distribution are also compared to demonstrate the predictive capability of the model for quantities of interest which were not involved in the inference process. The results demonstrate that the weakly-coupled IIML framework offers sophisticated and robust model augmentation capabilities without requiring extensive changes to the numerical solver.

With the increased pervasiveness of Lithium-ion batteries, there is growing concern for the amount of retired batteries that will be entering the waste stream. Although these batteries no longer meet the demands of their first application, many still have a significant portion of their initial capacity remaining for use in secondary applications. Yet, direct repurposing is generally not possible and each cell in a battery must be evaluated, increasing the cost of the repurposed packs due to the time intensive screening process. In this paper, a rapid assessment of the internal resistance of a cell is proposed. First, this method of measuring the resistance is completed on cells from twelve retired battery packs and one fresh pack using a hybrid pulse power characterization (HPPC) test as a benchmark for the analysis. Results from these tests show relatively constant resistance measurements across mid to high terminal voltages, allowing this metric to be independent of state of charge (SOC). Then, the relation between internal resistance and capacity across the various packs is discussed. Initial experimental results from this study show a correlation between internal resistance and capacity which can be approximated with a linear fit, suggesting internal resistance measurements taken above a threshold cell terminal voltage may be a suitable initial screening metric for the capacity of retired cells without knowledge of the SOC., Comment: 6 pages, 7 figures, Submitted to IFAC AAC 2022 Conference

Fast charging of lithium-ion batteries is crucial to increase desirability for consumers and hence accelerate the adoption of electric vehicles. A major barrier to shorter charge times is the accelerated aging of the battery at higher charging rates, which can be driven by lithium plating, increased solid electrolyte interphase growth due to elevated temperatures, and particle cracking due to mechanical stress. Lithium plating depends on the overpotential of the negative electrode, and mechanical stress depends on the concentration gradient, both of which cannot be measured directly. Techniques based on physics-based models of the battery and optimal control algorithms have been developed to this end. While these methods show promise in reducing degradation, their optimization algorithms' complexity can limit their implementation. In this paper, we present a method based on the constant current constant voltage (CC-CV) charging scheme, called CC-CV$\eta \sigma$T (VEST). The new approach is simpler to implement and can be used with any model to impose varying levels of constraints on variables pertinent to degradation, such as plating potential and mechanical stress. We demonstrate the new CC-CV$\eta \sigma$T charging using an electrochemical model with mechanical and thermal effects included. Furthermore, we discuss how uncertainties can be accounted for by considering safety margins for the plating and stress constraints., Comment: In press; Modeling, Estimation and Control Conference 2021

Internal short circuits are a leading cause of battery thermal runaway, and hence a major safety issue for electric vehicles. An internal short circuit with low resistance is called a hard internal short, which causes a high internal current flow that leads to an extremely fast temperature rise, gas generation, cell swelling, and ultimately battery rupture and failure. Thus it is crucial to detect these faults immediately after they get triggered. In large battery packs with many cells in parallel, detecting an internal short circuit event using voltage is difficult due to suppression of the voltage signal from the faulty cell by the other healthy cells connected in parallel. In contrast, analyzing the gas composition in the pack enclosure can provide a robust single cell failure detection method. At elevated temperature, decomposition of the battery materials results in gas generation and cell swelling. The cell structure is designed to rupture at a critical gas pressure and vent the accumulated $CO_2$ gas, in order to prevent explosive forces. In this paper, we extend our previous work by combining the models of cell thermal dynamics, swelling, and $CO_2$ gas generation. In particular, we developed a fast and high confidence level detection method of hard internal short circuit events for a battery pack by measuring cell expansion force and monitoring $CO_2$ concentrations in a pack enclosure., Comment: 6 pages, 4 figures. This work has been accepted to IFAC World Congress 2020 for publication

Recent data-driven approaches have shown great potential in early prediction of battery cycle life by utilizing features from the discharge voltage curve. However, these studies caution that data-driven approaches must be combined with specific design of experiments in order to limit the range of aging conditions, since the expected life of Li-ion batteries is a complex function of various aging factors. In this work, we investigate the performance of the data-driven approach for battery lifetime prognostics with Li-ion batteries cycled under a variety of aging conditions, in order to determine when the data-driven approach can successfully be applied. Results show a correlation between the variance of the discharge capacity difference and the end-of-life for cells aged under a wide range of charge/discharge C-rates and operating temperatures. This holds despite the different conditions being used not only to cycle the batteries but also to obtain the features: the features are calculated directly from cycling data without separate slow characterization cycles at a controlled temperature. However, the correlation weakens considerably when the voltage data window for feature extraction is reduced, or when features from the charge voltage curve instead of discharge are used. As deep constant-current discharges rarely happen in practice, this imposes new challenges for applying this method in a real-world system., Comment: 7 pages, 7 figures, Submitted to American Controls Conference 2021

Accurate tracking of the internal electrochemical states of lithium-ion battery during cycling enables advanced battery management systems to operate the battery safely and maintain high performance while minimizing battery degradation. To this end, techniques based on voltage measurement have shown promise for estimating the lithium surface concentration of active material particles, which is an important state for avoiding aging mechanisms such as lithium plating. However, methods relying on voltage often lead to large estimation errors when the model parameters change during aging. In this paper, we utilize the in-situ measurement of the battery expansion to augment the voltage and develop an observer to estimate the lithium surface concentration distribution in each electrode particle. We demonstrate that the addition of the expansion signal enables us to correct the negative electrode concentration states in addition to the positive electrode. As a result, compared to a voltage only observer, the proposed observer can successfully recover the surface concentration when the electrodes' stoichiometric window changes, which is a common occurrence under aging by loss of lithium inventory. With a 5% shift in the electrodes' stoichiometric window, the results indicate a reduction in state estimation error for the negative electrode surface concentration. Under this simulated aged condition, the voltage based observer had 9.3% error as compared to the proposed voltage and expansion observer which had 0.1% error in negative electrode surface concentration., Comment: 6 pages, 4 figures, Submitted to American Controls Conference 2021

We present a coupled continuum formulation for the electrostatic, chemical, thermal and mechanical processes in battery materials. Our treatment applies on the macroscopic scale, at which electrodes can be modelled as porous materials made up of active particles held together by binders and perfused by the electrolyte. Starting with the description common to the field, in terms of reaction-transport partial differential equations for ions, variants of the classical Poisson equation for electrostatics, and the heat equation, we add mechanics to the problem. Our main contribution is to model the evolution of porosity as a consequence of strains induced by intercalation, thermal expansion and mechanical stresses. Recognizing the potential for large local deformations, we have settled on the finite strain framework. We present a detailed computational study of the influence of the dynamically evolving porosity, upon ion distribution, electrostatic potential fields, charge-discharge cycles and mechanical force generated in the cell., Comment: 43 pages, 24 figures, appear in J. Electrochem. Soc