Physics-based Electrochemical Model Research Articles

Shear force effect of the dry process on cathode contact coverage in all-solid-state batteries

The state-of-the-art all-solid-state batteries have emerged as an alternative to the traditional flammable lithium-ion batteries, offering higher energy density and safety. Nevertheless, insufficient intimate contact at electrode-electrolyte surface limits their stability and electrochemical performance, hindering the commercialization of all-solid-state batteries. Herein, we conduct a systematic investigation into the effects of shear force in the dry electrode process by comparing binder-free hand-mixed pellets, wet-processed electrodes, and dry-processed electrodes. Through digitally processed images, we quantify a critical factor, ‘coverage’, the percentage of electrolyte-covered surface area of the active materials. The coverage of dry electrodes was significantly higher (67.2%) than those of pellets (30.6%) and wet electrodes (33.3%), enabling superior rate capability and cyclability. A physics-based electrochemical model highlights the effects of solid diffusion by elucidating the impact of coverage on active material utilization under various current densities. These results underscore the pivotal role of the electrode fabrication process, with the focus on the critical factor of coverage.

Electrochemical-Electromagnetic Coupled Physics-Based Mathematical Modeling of Li-Ion Batteries: A Theoretical Proof of Concept

This theoretical study presents a novel proof-of-concept modeling approach that couples a P2D physics-based electrochemical model with a 3D electromagnetic model to analyze the behavior of lithium-ion batteries under AC perturbations in the 0.1 Hz–100 kHz frequency range that generates an impedance response in a cylindrical Li-ion battery cell. The coupling between the two models was done by connecting them in series and adding the separate impedances from both models. By considering effective material properties for the electromagnetics model, and by using the Nyquist and Bode plots as figures of merit, it was shown that such a hybrid coupling can be used to predict the impedance of such a system. This research lays the groundwork for future experimental validation and optimization of battery designs in applications involving AC perturbations, offering insights for enhanced energy storage and conversion systems.

Physics based modeling of LiFePO4 cathodes: effects of electrode parameters on cell performance during fast charging

Lithium-iron phosphate (LFP) has emerged as a potential cathode material due to its lower cost and higher stabilities. This work investigates LFP cell behavior at higher C-rates via a detailed simulation study. To facilitate this investigation, a physics-based electrochemical model is calibrated and validated with in-house experimental data. The validated model is used to study the effect of particle size, lithium diffusivity, and electrode thickness on the charge-discharge capacity of Li-LFP cells for a range of C-rates up to 5 C. A detailed discussion is carried out to explain the results of parametric studies, in terms of transport limitations, irreversible losses (overpotentials) and their dependence on different electrode parameters. The model helps us to depict the effect of these parameters on internal profiles of SOC and overpotentials, allowing for a deeper understanding of the cell behavior. Overall, the simulations show that the LFP cell is able to exhibit good capacity at higher C-rates by tuning the particle size and lithium diffusivity. An optimal combination of material and physical parameters is identified to maximize the possible capacity of LFP electrodes.

Simulation of Impedance Changes with Aging in Lithium Titanate-based Cells Using Physics-Based Dimensionless Modeling

Quantifying aging effects in lithium-ion cells with chemistries that have a flat open circuit potential is challenging. We implement a physics-based electrochemical model to track changes in the electrochemical impedance response of lithium titanate-based cells. Frequency domain equations of a pseudo two-dimensional model are made dimensionless, and the corresponding non-dimensional parameters are estimated using a Levenberg-Marquardt routine. The model weighs the relative contributions of changes in diffusion, ionic conduction within the electrolyte phase against solid phase electronic conduction towards cell aging. Solid-phase diffusion, charge transfer resistance and double layer capacitance at the solid-liquid interface are accounted for in the particle impedance. The estimation routine tracks dimensionless parameters using accelerated cycling data from full cells over 1000 cycles. The model can be deployed within a short time for state estimation using physics-based models without requiring prior knowledge of the battery chemistry, format, or capacity.

Physics-Based Electrochemical Model of Vanadium Redox Flow Battery for Low-Temperature Applications

Vanadium redox flow batteries (VRFBs) operate effectively over the temperature range of 10 °C to 40 °C. However, their performance is significantly compromised at low operating temperatures, which may happen in cold climatic conditions. The loss of performance can be attributed to reduced kinetics and decreased diffusivity of ions in the electrolyte. In this paper, we present a physics-based electrochemical model of a vanadium redox flow battery that allows temperature-related corrections to be incorporated at a fundamental level, thereby extending its prediction capability to low temperatures. The model follows the conventional evaluation of the cell overpotential as the sum of contributions from overpotentials associated with activation, ionic conduction and mass transfer polarization. New data-driven models have been proposed to make these sub-models temperature sensitive. The overall model has been validated with a wide range of data from VRFB cells of sizes up to 900 cm2 and operating temperatures down to −10 °C. The model results indicate that enhancement of electrochemical performance of VRFB below subzero temperatures requires electrode and membrane activation and improvement in ionic conductivity of the electrolyte.

High-throughput Li plating quantification for fast-charging battery design

Fast charging of most commercial lithium-ion batteries is limited due to fear of lithium plating on the graphite anode, which is difficult to detect and poses considerable safety risk. Here we demonstrate the power of simple, accessible and high-throughput cycling techniques to quantify irreversible Li plating spanning data from over 200 cells. We first observe the effects of energy density, charge rate, temperature and state of charge on lithium plating, use the results to refine a mature physics-based electrochemical model and provide an interpretable empirical equation for predicting the plating onset state of charge. We then explore the reversibility of lithium plating and its connection to electrolyte design for preventing irreversible Li accumulation. Finally, we design a method to quantify in situ Li plating for commercially relevant graphite|LiNi0.5Mn0.3Co0.2O2 (NMC) cells and compare with results from the experimentally convenient Li|graphite configuration. The hypotheses and abundant data herein were generated primarily with equipment universal to the battery researcher, encouraging further development of innovative testing methods and data processing that enable rapid battery engineering.

A fractional-order model of lithium-ion battery considering polarization in electrolyte and thermal effect

With the growing demand of safety and accurate control for electric vehicles, it is urgent to develop a physics-based electrochemical model of lithium-ion battery with simple calculation and high accuracy over wide temperature range for application in battery management system (BMS). However, traditional electrochemical models are too complex to be applied in real usage, and most of them fail to capture thermal characteristics of the cell. Therefore, a fractional-order model of lithium-ion battery considering polarization in electrolyte and thermal effect (FOMeT) is proposed in this paper. The fractional-order model (FOM) is improved by considering the polarization in electrolyte. The particle thermal model is proposed to describe the heat generation and absorption of the cell. Finally, the FOM considering electrolyte polarization and the particle thermal model are combined to form FOMeT by coupling the cell temperature and dynamics of lithium-ion. The results show that the proposed model performs high voltage accuracy and temperature accuracy over wide temperature range (273.15K∼318.15K) and wide current load range (0.5C∼2C).

Effect of porous structure and morphology of cathode on the degradation of lithium-ion batteries

This study investigates the effect of the micromorphology of cathodes with 3D porous structures and geometries on the degradation and electrochemical performance of lithium-ion batteries. Active particle aggregates with different particle diameters and volume fractions are randomly positioned to generate a 3D structure of the cathode in simulation. A physics-based electrochemical model that describes the degradation of the separator, anode, and cathode is developed. Simulation results show that aggregates with a smaller particle radius have a larger surface area, which leads to a higher capacity with a lower concentration gradient but also severe overall degradation. However, with a larger surface area, the volume fraction of the cathode decreases faster, whereas that of the anode decreases slower because of the difference in the fundamental degradation mechanisms of both electrodes. These results indicate that a cathode with a smaller surface area and an anode with a larger surface area are preferred to minimize battery degradation. This morphological information also impacts the diffusivity, which must be carefully optimized for maximizing the capacity and minimizing the degradation. The model developed in this study is expected to be useful to understand degradation mechanisms and to optimize battery design and manufacturing.

Electrochemical Modeling and Experimental Verification of Lithiation Gradients in Oxide Cathodes of Lithium-Ion Cells

Lithiated nickel-cobalt-manganese oxides, such as NCM523, are used in the positive electrode (cathode) of Li-ion cells. Using operando X-ray diffraction profilometry, lithiation gradients in the cathode matrix can be observed and quantified by expansion into Legendre polynomials with time-dependent weights. These weights (referred to as gradients) increase in magnitude when electric current flows through the cell, decrease during potentiostatic hold and finally relax to zero when the current is interrupted during open circuit rest. Both physics-based electrochemical models and operando X-ray experiments suggest that the time constants for gradient growth and abatement are primarily determined by ionic diffusion in the oxide particles, which in turn depends on their lithium content. In contrast, the magnitude of gradients depends mainly on the applied current. The X-ray profilometry provides a way of directly probing the formation and disappearance of Li gradients across the cathode during fast cycling, which can help to diagnose the effects of material degradation in the cells.

Physics-Based Equivalent Circuit Model for Lithium-Ion Cells via Reduction and Approximation of Electrochemical Model

<div class="section abstract"><div class="htmlview paragraph">Physics-based electrochemical models and empirical Equivalent Circuit Models (ECMs) are well-established and widely used modeling techniques to predict the voltage behavior of lithium-ion cells. Electrochemical models are typically very accurate and require relatively little experimental data to calibrate, but present high mathematical and computational complexity. Conversely, ECMs are more computationally efficient and mathematically simpler, making them well-suited for applications in controls, diagnosis, and state estimation of lithium-ion battery packs. However, the calibration process requires extensive testing to calibrate the parameters of the model over a wide range of operating conditions.</div><div class="htmlview paragraph">This paper bridges the gap between these two classes of models by developing a method to analytically define the ECM parameters starting from an already-calibrated Extended Single-Particle Model (ESPM). The governing equations of the ESPM were reduced via model order reduction, linearization and by introducing approximations to yield the mathematical structure of a second order ECM. This allowed for analytically defining the parameters of the resulting ECM, without resorting to complex lookup tables and related extensive testing for calibration. The newly defined electrochemistry-based ECM (E-ECM) saw less than 1 mV RMS error increase compared to the ESPM voltage prediction across several test profiles.</div></div>

Enabling high-fidelity electrochemical P2D modeling of lithium-ion batteries via fast and non-destructive parameter identification

Physics-based electrochemical models provide insight into the battery internal states and have shown great potential in battery design optimization and automotive and aerospace applications. However, the complexity of the electrochemical model makes it difficult to obtain parameter values accurately. In this study, a novel non-destructive parameter identification method is proposed to parameterize the most commonly used electrochemical pseudo-two-dimensional model. The whole identification process consists of three key steps. First, in order to find the optimal identification conditions, the sensitivity of model parameters is analyzed, and parameters are classified into three types according to their most sensitive conditions. Second, feasible initial guess values of these unknown parameters are obtained using a deep learning algorithm, which can not only help avoid the divergence problem of the identification algorithm but also speed up the subsequent identification process. Finally, two different approaches are combined and used for parameter identification, and parameters that have high sensitivity are estimated in a step-wise manner. We show that 14 electrochemical parameters can be estimated accurately within 1 h using simulation and experimental data. After estimating the model parameters, the root-mean-square error of the predicted voltage from the model is less than 14 mV.

Impact of Size and Position of Lithium Metal Reference Electrodes on the Measurement of Lithium-Plating Overpotential

Lithium (Li) plating is a major cause of degradation that reduces the capacity of Li-ion batteries. The driving force for the Li plating is dependent on surface overpotential at the graphite-electrolyte interface in the negative electrode (NE). However, there is no experimental method for directly measuring the surface overpotential. Therefore, this overpotential has been estimated by introducing a reference electrode (RE) and measuring the potential difference between the NE current collector and the RE, assuming that the potential difference is the same as Li-plating overpotential. However, this estimation could include significant errors that depend on charging rate, size, and the location of the RE. In this work, we built a pseudo three-dimensional physics-based electrochemical model to understand the trends in the accuracy of prediction of Li-plating overpotential using REs of different sizes placed at different locations. The simulation results indicated that a 50-μm diameter RE could predict the Li-plating overpotential with an error of about 15 mV even at a high charging rate of 3C in the pouch cell. In addition, the RE located inside the cell was expected to have higher accuracy, and its potential provides a conservative estimate for the onset of Li plating of the pouch cell.

Implementation of a Physics-Based Model for Half-Cell Open-Circuit Potential and Full-Cell Open-Circuit Voltage Estimates: Part I. Processing Half-Cell Data

Physics-based electrochemical models of lithium-ion cells require knowledge of electrode open-circuit potential (OCP) as a function of stoichiometry. To determine the OCP relationships for a cell built from unknown active materials, we might run low-rate constant-current laboratory tests on half cells built from harvested electrodes to collect related discharge and charge data. However, processing data from these tests must overcome three problems: the “data-quality problem,” the “missing-data problem,” and the “inaccessible-lithium problem.” This paper introduces a simple histogram-based method to overcome the data-quality problem and compares five different approaches to overcome the missing-data and inaccessible-lithium problems. These methods rely in part on a physics-based thermodynamic model for multiple-species multiple-reaction (MSMR) systems, which is flexible enough to accommodate different cell chemistries and simple enough to be utilized in real-time battery management systems. The five methods are validated in simulations and are then applied to physical half-cell data to produce OCP estimates for graphite and NMC electrodes from a commercial cell.

Control-Oriented Modeling of Lithium-Ion Batteries

Abstract Battery management systems (BMSs), which monitor and optimize performance while ensuring safety, require control-oriented models, i.e., models tailored to the design and implementation of estimation and control algorithms. Physics-based electrochemical models describe detailed battery phenomena, but are too computationally intensive for use in estimation and control applications. Single particle models (SPMs), which retain some of the physics of electrochemical models, are often used for control-oriented battery modeling since they are computationally efficient; however, they are only valid over very low frequency ranges and C-rates. Empirical equivalent circuit models (ECMs) are also used for control-oriented battery modeling since they are computationally efficient and can describe battery behavior over wide frequency ranges; however, they provide no physical understanding of the battery and, therefore, have limited applicability. Further, fractional order terms (e.g., Warburg impedances) are often employed, making the models unwieldy for use in the time domain. This work provides a control-oriented battery model that combines the benefits of SPM and ECM models, while overcoming their limitations. The proposed model incorporates some of the battery physics found in electrochemical models, can easily be used in both the time and frequency domains, and describes battery behavior over its entire frequency range. A linearized single particle model, which incorporates key electrochemical parameters, is used for modeling battery physics at very low frequencies. For low frequencies, integer-order linear systems are used to approximate diffusion physics described by Warburg impedances, and high frequency behavior is modeled by the double layer capacitance effect. The proposed battery model is more computationally efficient than full electrochemical models since it does not require the solution of PDEs, is accurate for a wider frequency range than the SPM considered in this paper, and does not suffer from the unwieldiness and limited applicability of empirical ECMs. The model is validated in the time and frequency domains via a comparison to pseudo-two-dimensional (P2D) model simulations and experimental data.

Enabling fast charging of lithium-ion batteries through secondary-/dual- pore network: Part II - numerical model

To increase the market share of electric vehicles, it is desirable to reduce the battery charge times, which are significantly limited by poor electrolyte transport. A high rate charging is achievable by using expensive and low energy density cells with thin electrodes. For higher energy density cells, new electrolytes with improved conductivity and diffusivity and/or electrodes with advanced architecture are required to boost the electrolyte transport, leading to a more uniform utilization of active materials. In our previous work, an analytical model was developed to investigate the effect of secondary pore network (SPN) on electrolyte transport and the configuration of SPN was optimized by enforcing equal characteristic diffusion times in through-plane and in-plane directions. To evaluate the effect of SPN on the fast-charging capability of lithium-ion batteries, a 2D physics-based electrochemical model is developed with SPN in either one or both electrodes. The effect of SPN on cell energy density and lithium plating is investigated for cells with different loadings and electrode porosities. Combining SPN with elevated charging temperatures, the model predicts that the volumetric discharge energy density of a 3 mA h/cm2 cell can reach 270 Wh/L after a 6C constant-current charging.

Modeling the effect of electrode thickness on the performance of lithium-ion batteries with experimental validation

Manufacturing process for composite electrodes in lithium-ion batteries generally results in non-uniform micro-structure geometrical distribution in the through-thickness direction of a porous electrode. Inhomogeneity of the porous electrode thus affects the lithium ions transport in the electrolyte and their diffusion in the active materials. Quantifying the relationship between mass transport-related parameters and the electrode thickness is very important for studying the effect of the electrode thickness on the performance of lithium-ion batteries. The objective of this work is to study how the Lix(Ni1/3Mn1/3Co1/3)O2 (NMC111) electrode thickness affects the battery performance by developing an improved physics-based electrochemical model. In this model, the Bruggeman coefficient and the effective diffusion coefficient of NMC111 cathode with various thicknesses ranging from 31 μm to 130 μm are estimated by comparing simulation results with experimental data. The proposed electrochemical model is validated experimentally for cells with various electrode thicknesses. The simulation results indicate that increasing electrode thickness reduces the rate capabilities of lithium-ion batteries. The reason is discussed by analyzing the ohmic and diffusion limitation for cells will various electrode thicknesses under different discharge C-rates.

Physics-based control-oriented reduced-order degradation model for LiNiMnCoO2 - graphite cell

Li-ion battery performance degrades with aging and usage, and the degradation highly depends on how the cell is operated. As such, models used for system design and optimization should ideally capture the impact of those effects, and battery management system should take degradation into consideration and control cell operation carefully. Physics-based electrochemical models have shown the capability of predicting cell performance and degradation, but are computationally time consuming, often precluding its use in control-oriented design/optimization. Based on the constitutive laws which are widely adopted in the electrochemical models, a control-oriented reduced-order degradation model for a commercial LiNiMnCoO2/graphite cell is derived to improve computational efficiency without sacrificing model fidelity. Three primary degradation mechanisms that occur in a typical Li-ion cell are captured: 1) Solid Electrolyte Interface (SEI) layer growth, 2) SEI layer fracture and re-healing, and 3) Active Material loss. The extensive validation against a wide range of experimental data illustrates the ability of the model to accurately predict the capacity loss.

A Physics-Based Electrochemical Model for Lithium-Ion Battery State-of-Charge Estimation Solved by an Optimised Projection-Based Method and Moving-Window Filtering

State-of-charge (SOC) is one of the most critical parameters in battery management systems (BMSs). SOC is defined as the percentage of the remaining charge inside a battery to the full charge, and thus ranges from 0% to 100%. This percentage value provides important information to manufacturers about the performance of the battery and can help end-users identify when the battery must be recharged. Inaccurate estimation of the battery SOC may cause over-charge or over-discharge events with significant implications for system safety and reliability. Therefore, it is crucial to develop methods for improving the estimation accuracy of battery SOC. This paper presents an electrochemical model for lithium-ion battery SOC estimation involving the battery’s internal physical and chemical properties such as lithium concentrations. To solve the computationally complex solid-phase diffusion partial differential equations (PDEs) in the model, an efficient method based on projection with optimized basis functions is presented. Then, a novel moving-window filtering (MWF) algorithm is developed to improve the convergence rate of the state filters. The results show that the developed electrochemical model generates 20 times fewer equations compared with finite difference-based methods without losing accuracy. In addition, the proposed projection-based solution method is three times more efficient than the conventional state filtering methods such as Kalman filter.

Estimation of Transport and Kinetic Parameters of Vanadium Redox Batteries Using Static Cells

Mathematical models of Redox Flow Batteries (RFBs) can be used to analyze cell performance, optimize battery operation, and control the energy storage system efficiently. Among many other models, physics-based electrochemical models are capable of predicting internal states of the battery, such as temperature, state-of-charge, and state-of-health. In the models, estimating parameters is an important step that can study, analyze, and validate the models using experimental data. A common practice is to determine these parameters either through conducting experiments or based on the information available in the literature. However, it is not easy to investigate all proper parameters for the models through this way, and there are occasions when important information, such as diffusion coefficients and rate constants of ions, has not been studied. Also, the parameters needed for modeling charge-discharge are not always available. In this paper, an efficient way to estimate parameters of physics-based redox battery models will be proposed. This paper also demonstrates that the proposed approach can study and analyze aspects of capacity loss/fade, kinetics, and transport phenomena of the RFB system.

Comparison of Lithium-Ion Anode Materials Using an Experimentally Verified Physics-Based Electrochemical Model

Researchers are in search of parameters inside Li-ion batteries that can be utilized to control their external behavior. Physics-based electrochemical model could bridge the gap between Li+ transportation and distribution inside battery and battery performance outside. In this paper, two commercially available Li-ion anode materials: graphite and Lithium titanate (Li4Ti5O12 or LTO) were selected and a physics-based electrochemical model was developed based on half-cell assembly and testing. It is found that LTO has a smaller diffusion coefficient (Ds) than graphite, which causes a larger overpotential, leading to a smaller capacity utilization and, correspondingly, a shorter duration of constant current charge or discharge. However, in large current applications, LTO performs better than graphite because its effective particle radius decreases with increasing current, leading to enhanced diffusion. In addition, LTO has a higher activation overpotential in its side reactions; its degradation rate is expected to be much smaller than graphite, indicating a longer life span.