Physics-based Electrochemical Model Research Articles

Highly Accurate Simplification of Physics-Based Electrochemical Model of All-Solid-State Battery for Online State of Charge Estimation

All-solid-state lithium batteries offer superior energy density and safety features, making them highly attractive for electric vehicles and wearable devices. Original physics-based electrochemical model can effectively simulate the internal electrochemical reactions, but they are difficult to be applied to embedded battery management systems. To facilitate the development of real-time applications based on physical models, this paper proposes a SOC prediction method based on a simplified electrochemical model (SEM). First, the transcendental transfer function is converted to third-order transfer functions using the Padé approximation. The electric field in the mass transfer overpotential is then solved using average numerical integration method. Then, the proposed SEM method under variable load conditions is verified by comparing to the results from original partial differential equations. The results show that the developed SEM strikes a balance between high fidelity and computational efficiency. By taking into account the concentration of Li+ ions in the solid electrolyte, the estimation accuracy of SOC in the range of 0.1 to 0.3 is significantly improved, compared with prior studies. Strong support is provided for the advanced control design of smart management systems of ASSBs.

Open Circuit Potential Curve Characterization Method for Cathode Active Materials

The quest to increase battery performance relies on perfecting the components of the batteries as well as improving the battery management system (BMS). As the BMS is responsible for ensuring the safety of the battery, it also governs the optimization of the energy the battery delivers. To improve predictions, classic equivalent circuit models are replaced with physics-based electrochemical models, requiring a deep understanding of the fundamental properties of the battery components. Advanced models not only track the state of charge (SOC) of the cell in the bulk of the materials, but also on the surface. One key parameter for the SOC estimation is the Open Circuit Potential (OCP) of the electrodes as a function of the lithium content, or OCP curve.[1] To provide a highly accurate SOC estimation, the OCP curves need to cover the potential range of the full cell, as well as the potential reached at the surface of the electrodes.This work focuses on characterizing one overlooked aspect of the characterization of the OCP curve of cathode materials: the low potential region.[2-3] We propose a novel method for characterization of the OCP curve of commonly used active materials, striving to provide a standardized mapping from the gravimetric capacity to the lithium concentration, hence increasing the accuracy of the OCP curve. This method allows to characterize the OCP curve up to the lithium content of 1. This newly set scale is then used to align and compare the extensive characterization work already published on various cathode materials.[4] Chaturvedi, N. A., Klein, R., Christensen, J., Ahmed, J. & Kojic, A. Algorithms for Advanced battery-Management Systems. IEEE Control Syst. Mag.49–68 (2010).A. Barai, K. Uddin, M. Dubarry, L. Somerville, A. McGordon, P. Jennings and I. Bloom, Prog. Energy Combust. Sci., 2019, 72, 1–31.C.-H. Chen, F. Brosa Planella, K. O’Regan, D. Gastol, W. D. Widanage and E. Kendrick, J. Electrochem. Soc., 2020, 167, 080534.K. Märker, P. J. Reeves, C. Xu, K. J. Griffith and C. P. Grey, Chem. Mater., 2019, 31, 2545–2554.

Moving Next-Generation Phase-Field Models to BMS Applications - a Case Study That Confirms Professor Uzi Landau's Foresight

Physics-based electrochemical models play an important role in the model-based analysis, virtual engineering, estimation, control, and Battery Management Systems (BMS) of lithium-ion batteries.1 The diffusion process within the cell electrodes has typically been modeled using Fick's laws of diffusion.2 Recently, the intercalation of lithium ions in the electrode particle was posed as a phase change problem, where the area intercalated with lithium undergoes a phase change compared to the pristine material. Researchers have approached this phase change problem in terms of evolving core-shell problems3,4 and, more recently, using phase field models5,6 that may hold certain advantages over the traditional Fickian diffusion models. In this paper, we briefly discuss the relevance and rich physics of phase-field models and show how proper numerical analysis and schemes can help with implementing these models in BMS applications. Further, an investigation of phase-field model-based optimization framework predicts an impulse-like control profile and was designed to reduce capacity degradation. This work was partially inspired by the pulse-charging protocol proposed by Professor Landau in his 2006 work7. An open-source framework is developed and will be shared for predicting the (im)pulse protocol reported in this.

(Battery Student Slam 8 Award Winner) A Comparison of Different Convergence Criteria to Improve the Performance of a P2D Modelling Algorithm of a Lithium-Ion Battery

Lithium-ion batteries (LiBs) are used as the storage for electric vehicles, grid energy and consumer electronics mainly due to the LiBs’ high energy density, long cycle life, and reliable manufacturing. Effective performance and diagnostic management of LiBs is important and is implemented via Battery Management Systems (BMS) [1]. A BMS should also maximise the safety and lifetime of battery packs and therefore, needs to estimate the internal battery states including the state of charge (SoC), state of health (SoH), state of power (SoP), state of function (SoF), and state of safety (SoS) [2]. Accurate estimation of the battery SoX can be realized with the help of a battery model; an algorithm representing the electrochemical, mechanical, electrical, and thermal behaviour of the LiB cells.Cell-level battery models typically fall into three categories: (i) Empirical Models, (ii) Equivalent Circuit Models (ECM) and (iii) Physics-based Electrochemical Models (EM). Electrochemical Models represent the internal cell processes within a cell based on its governing fundamental physical and electrochemical equations [3].The Partial two-dimensional (P2D) model is considered a high-fidelity Electrochemical Model (EM), which in its most basic form, captures three major physio-chemical processes in a cell: mass transfer via reduction/oxidisation (redox) reactions, diffusion of neutral lithium in the electrodes and diffusion of lithium-ions in the electrolyte. The P2D model captures the different physio-chemical phenomena using a set of coupled Partial Differential Algebraic Equations (PDAEs) [4].Despite accuracy, P2D models are complex mathematical models with typically no analytical solution [5]. Therefore, to implement the full-order version of the P2D model, numerical-iterative solver algorithms are required. Multiple works have looked at different methods of optimizing and solving the P2D model. These methods include using different discretisation schemes, such as the finite difference method and the finite volume method, using different iterative solvers and different convergence criteria [5]. However, the different works on iterative solvers we have reviewed to date [5], haven’t investigated the effects of the different criteria on improving the performance of P2D iterative solvers.Hence, in this work, we aim to build on our previous work [6], where we proposed an algorithm to implement the P2D model using the finite volume spatial discretisation method (FVM) and Euler time integration method. We then analyse how the role of (i) the choice of convergence criteria, (ii) the choice of initial guess and (iii) the choice of root-finding method used to converge to the convergence criteria, can be varied to improve the performance of the iterative solver.Therefore, the contributions of this work can be summarised as: An algorithm that implements the isothermal P2D model of a LiB using the Finite Volume Method and Euler integration methods.An analysis of the changes in algorithm performance when the following performance factors are varied; (i) The convergence criteria, (ii) the choice of initial guess and (iii) the choice of root-finding method.An optimal configuration of performance criteria that solves the isothermal-P2D model for a 1C discharge simulation, with an average speed of 3 seconds and a root mean square error of less than 1% when compared to the commercial solver COMSOL. [1] C. P. Grey and D. S. Hall, “Prospects for lithium-ion batteries and beyond—a 2030 vision,” Nature Communications 2020 11:1, vol. 11, no. 1, pp. 1–4, Dec. 2020, doi: 10.1038/s41467-020-19991-4.[2] L. Lu, X. Han, J. Li, J. Hua, and M. Ouyang, “A review on the key issues for lithium-ion battery management in electric vehicles,” Journal of Power Sources, vol. 226. pp. 272–288, Mar. 15, 2013. doi: 10.1016/j.jpowsour.2012.10.060.[3] S. Abada, G. Marlair, A. Lecocq, M. Petit, V. Sauvant-Moynot, and F. Huet, “Safety focused modeling of lithium-ion batteries: A review,” J Power Sources, vol. 306, pp. 178–192, Feb. 2016, doi: 10.1016/J.JPOWSOUR.2015.11.100.[4] M. Doyle, T. F. Fuller, and J. Newman, “Modeling of Galvanostatic Charge and Discharge of the Lithium/Polymer/Insertion Cell,” J Electrochem Soc, vol. 140, no. 6, pp. 1526–1533, Jun. 1993, doi: 10.1149/1.2221597/XML.[5] A. M. Ramos, “On the well-posedness of a mathematical model for Lithium-ion batteries,” Appl Math Model, vol. 40, no. 1, pp. 115–125, May 2015, doi: 10.48550/arxiv.1506.00605.[6] T. Wickramanayake, M. Javadipour, and K. Mehran, “A Novel Root-Finding Algorithm to Solve the Pseudo-2D Model of a Lithium-ion Battery,” 2023 IEEE International Conference on Electrical Systems for Aircraft, Railway, Ship Propulsion and Road Vehicles and International Transportation Electrification Conference, ESARS-ITEC 2023, 2023, doi: 10.1109/ESARS-ITEC57127.2023.10114840.

Reconstructing the Pseudo-2-Dimensional (p2D) Model in Comsol Multiphysics Using Mathematical Interfaces

The classic ‘pseudo-2-dimensional’ (p2D) model of Newman and co-workers (also known as the DFN model), with its different efficient implementations, is the state-of-the-art physics-based electrochemical model for lithium-ion batteries. COMSOL Multiphysics (COMSOL) is a popular modeling software for multiphysics simulations, and its Battery Design Module for Li-ion batteries is widely used in the battery modeling community. This work presents a step-wise model development for reconstructing the detailed p2D model equations. This includes variable model parameters and weak-form implementation for the solid-phase diffusion, eliminating the need for non-local couplings and approximations for modeling the pseudo radial-dimension in the solid-phase.To model and understand the effect of capacity degradation on lithium-ion cells, the battery models in COMSOL need to incorporate additional degradation mechanisms. In this work, we have followed the approach of equation-based modeling in COMSOL, which enables us to formulate the p2D model using the mathematical PDE interfaces. This approach provides us with a lot of flexibility in terms of battery degradation model formulation and helps develop a clearer understanding of the p2D model equation in light of the assumptions involved.The steps in the model development involved writing the conservation equations in the generic mathematics interfaces coupled with the additional equations for the degradation mechanisms. The efforts were centered on developing cycling simulations based on Events for practically relevant operating conditions. This custom model was validated against the results from COMSOL’s Battery Interface, in-house codes, and baseline cycle data from the experiments and further developed as a physicochemical degradation model for automotive, large-format Lithium-ion batteries.This equation-based COMSOL model with cycling works without the requirement for Battery Design Module, LiveLink and Application Builder and can be adopted for a variety of electrochemical modeling applications by the electrochemical modeling community.

Development of a Fast Running Equivalent Circuit Model with Thermal Predictions for Battery Management Applications

Equivalent circuit modelling (ECM) is a powerful tool to study the dynamic and non-linear characteristics of Li-ion cells and is widely used for the development of the battery management system (BMS) of electric vehicles. The dynamic parameters described by the ECM are used by the BMS to estimate the battery state of charge (SOC), which is crucial for efficient charging/discharging, range calculations, and the overall safe operation of electric vehicles. Typically, the ECM approach represents the dynamic characteristics of the battery in a mathematical form with a limited number of unknown parameters. Then, the parameters are calculated from voltage and current information of the lithium-ion cell obtained from controlled experiments. In the current work, a faster and simplified first-order resistance–capacitance (RC) equivalent circuit model was developed for a commercial cylindrical cell (LGM50 21700). An analytical solution was developed for the equivalent circuit model incorporating SOC and temperature-dependent RC parameters. The solution to the RC circuit model was derived using multiple expressions for different components like open circuit voltage (OCV), instantaneous resistance (R0), and diffusional parameters (R1 and C1) as a function of the SOC and operating temperature. The derived parameters were validated against the virtual HPPC test results of a validated physics-based electrochemical model for the voltage behavior. Using the developed RC circuit model, a polynomial expression is derived to estimate the temperature increase of the cell including both irreversible and reversible heat generation components. The temperature predicted by the proposed RC circuit model at different battery operating temperatures is in good agreement with the values obtained from the validated physics model. The developed method can find applications in (i) onboard energy management by the BMS and (ii) quicker evaluation of cell performance early in the product development cycle.

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.