Electrochemical Modeling

This paper proposes a new fast charging strategy for lithium-ion (Li-ion) batteries. The approach relies on an experimentally validated high-fidelity model describing battery electrochemical and thermal dynamics that determine the fast charging capability. Such a high-dimensional nonlinear dynamic model can be intractable to compute in real-time if it is fused with the extended Kalman filter or the unscented Kalman filter that is commonly used in the community of battery management. To significantly save computational efforts and achieve rapid convergence, the ensemble transform Kalman filter (ETKF) is selected and tailored to estimate the nonuniform Li-ion battery states. Then, a health-and safety-aware charging protocol is proposed based on successively applied proportional-integral (PI) control actions. The controller regulates charging rates using online battery state information and the imposed constraints, in which each PI control action automatically comes into play when its corresponding constraint is triggered. The proposed physical constraint-triggered PI charging control strategy with the ETKF is evaluated and compared with several prevalent alternatives. It shows that the derived controller can achieve close to the optimal solution in terms of charging time and trajectory, as determined by a nonlinear model predictive controller, but at a drastically reduced computational cost. Index Terms-Electrochemical model, ensemble transform Kalman filter (ETKF), fast charging, lithium plating, lithiumion (Li-ion) battery. NOMENCLATURE Symbol: C T Battery thermal capacitance (J/K). H Prediction horizon of model predictive control. I I Current due to molar flux of intercalation (A). I app Applied charging current (A). K P , K I Proportional and integral gains. M Order of the submodel for solid-phase diffusion. N j Number of control volumes of a domain. j ∈ {pos, sep, neg}.

In this article, a novel implementation of a widely used pseudo-two-dimensional (P2D) model for lithium-ion battery simulation is presented with a transmission line circuit structure. This implementation represents an interplay between physical and equivalent circuit models. The discharge processes of an NMC-graphite lithium-ion battery under different currents are simulated, and it is seen the results from the circuit model agree well with the results obtained from a physical simulation carried out in COMSOL Multiphysics, including both terminal voltage and concentration distributions. Finally we demonstrated how the circuit model can contribute to the understanding of the cell electrochemistry, exemplified by an analysis of the overpotential contributions by various processes.

In this paper, an advanced charging strategy for improving the charging performance of the Li-ion polymer battery is proposed, which is based on the battery characteristic. Simulation results show that the proposed charging current pattern can improve the charging speed of battery in comparison with the standard CC-CV (constant current-constant voltage) charging strategy and the pulse-charging strategy.

h i g h l i g h t s An extensive review on the simplified P2D model of Li-ion batteries is presented. The necessity, applications and techniques of the reduced model are investigated. Suggestions and challenges of future investigations are discussed.

h i g h l i g h t s An extensive review on the simplified P2D model of Li-ion batteries is presented. The necessity, applications and techniques of the reduced model are investigated. Suggestions and challenges of future investigations are discussed.

h i g h l i g h t s An extensive review on the simplified P2D model of Li-ion batteries is presented. The necessity, applications and techniques of the reduced model are investigated. Suggestions and challenges of future investigations are discussed.

Dimensionless analysis arises as an appropriate methodology to study battery cells behaviour since it brings the opportunity to identify limiting mechanisms in the battery cell performance by analysing a reduced number of dimensionless parameters. These parameters are obtained by condensating the physical dimensional parameters involved in the description of the electrochemical phenomena taking place in the cell. Here, based on the well known Doyle, Fuller and Newman model [M. Doyle, T.F. Fuller, J. Newman, J. Electrochem. Soc., 140(6) 1526-1533 (1993)] (DFN model, in short), a comprehensive set of dimensionless parameters is derived and the information arising from each dimensionless parameter is explained. Application to the design of a solid polymer electrolyte cell is considered, where limiting transport mechanisms are identified through dimensionless parameters analysis and guidelines for a cell redesign are also drawn from this analysis. Predictions made by inspection of the derived comprehensive set of dimensionless parameters are validated both numerically (using the DFN model) and experimentally.

This letter focuses on modeling the electrode heterogeneity by extending the pseudo-two-dimensional model (P2D) with actual particle-size distributions (PSD). The effects of different particle characterization techniques, including the area-weighted, volume-weighted, and number-based methods on cell dynamics are compared. The model with number-based PSD achieves better rate capability (maximum 2.0% improvement in capacity, maximum 2.6% increase in energy). Besides, the effectiveness of the multiparticle (MP) model is evaluated against the single-particle model (SPME) and P2D model under fast charging conditions. Results show that the PSD generates greater heterogeneities of cell internal states at higher C-rates current.

Traditional equivalent circuit models (ECMs) have di culties in estimating battery internal states due to the lack of relevant physics, such as the lithium di usion in active particles. Here we con gure a circuit network to describe the lithium di usion and de ne it as a new high-level circuit element called di usionaware voltage source. The circuit representation is proven equivalent to the discretized di usion equation. The new voltage source gives the electrode potential as a function of the surface concentration and thus automatically incorporates the di usion overpotential. We show that an ECM with the proposed di usionaware voltage sources (called "shell ECM") can reproduce the single particle model simulation results, making it a trustworthy easy-to-implement substitute. Furthermore, the simplest shell ECM consisting of a single di usion-aware voltage source and a resistor is validated against experimental constant-current discharges at various rates. The di usion-aware voltage source can be used to measure di usivity by tting the di usion resistance against experimental data. The viability of the shell ECM for onboard usage is con rmed by implementation into a battery management system of WAE Technologies. By tracking the internal concentration states, the shell ECM demonstrates robustness to dynamic applied-current pro les.

• Degradation by phase transition of nickel-rich layered NMC oxides to rock-salt phase • Effects of LAM, LLI, and resistance increase on cyclic capacity and power fade • High Crates and degradation inhomogeneity allowed by shrinking-core model within P2D • Available in open-source package PyBaMM to be coupled with other degradation mechanisms

Traditional equivalent circuit models (ECMs) have di culties in estimating battery internal states due to the lack of relevant physics, such as the lithium di usion in active particles. Here we con gure a circuit network to describe the lithium di usion and de ne it as a new high-level circuit element called di usionaware voltage source. The circuit representation is proven equivalent to the discretized di usion equation. The new voltage source gives the electrode potential as a function of the surface concentration and thus automatically incorporates the di usion overpotential. We show that an ECM with the proposed di usionaware voltage sources (called "shell ECM") can reproduce the single particle model simulation results, making it a trustworthy easy-to-implement substitute. Furthermore, the simplest shell ECM consisting of a single di usion-aware voltage source and a resistor is validated against experimental constant-current discharges at various rates. The di usion-aware voltage source can be used to measure di usivity by tting the di usion resistance against experimental data. The viability of the shell ECM for onboard usage is con rmed by implementation into a battery management system of WAE Technologies. By tracking the internal concentration states, the shell ECM demonstrates robustness to dynamic applied-current pro les.

The present paper reports on the application of EIS in triboelectrochemistry. Electrochemical measurements were performed at the constant dc current attained during a permanent regime of friction achieved by a rotating Pin-on-Disc (P-o-D) tribometer. A model is then proposed which embodies a classical kinetic description of an active-passive transition into the accepted description of the tribo-electrochemical response of a passive material. From the derivation of the equation at steady-state, a set of parameters were determined allowing to describe correctly both the dc and ac behaviours of the interface and to estimate the different components of the tribo-electrochemical signals.

A model is developed to predict the performance of LiFePO 4 lithium-ion batteries. The developed model (SEMP model) is applicable to any composite cathode material. The SEMP model is applicable for charge/discharge rates as high as 5C. The computational time of this model is significantly reduced. A sensitivity analysis is done over battery design parameters using the SEMP model.

En este trabajo se realizo el analisis del deterioro de los recubrimientos cobre – laton obtenidos via electrodeposicion utilizando las tecnicas de corriente directa, corriente pulsante directa y corriente pulsante inversa, Para este trabajo se empleo la tecnica de curvas de polarizacion Tafel para obtener un valor estimado de la velocidad de la corrosion. Para hallar el modelamiento electrico de la interfase solucion – recubrimiento se utilizo la tecnica de espectroscopia de impedancias electroquimica (EIS). Se encontro que la resistencia a la corrosion se incremento utilizando la tecnica de corriente pulsante inversa.

1Department of Chemical and Biomolecular Engineering, University of California, Los Angeles, 420 Westwood Plaza, Los Angeles, California, 90095, United States. 2Education Ministry Key Lab of Resource Chemistry and Shanghai Key Laboratory of Rare Earth Functional Materials, Department of Chemistry, Shanghai Normal University, Shanghai 200234, P. R. China. 3School of Materials Science and Engineering, Zhejiang University, Hangzhou 310027, P. R. China. 4Department of Mechanical and Aerospace Engineering, University of California, Los Angeles, 420 Westwood Plaza, Los Angeles, California, 90095, United States. 5Chemistry Division, Brookhaven National Laboratory, Upton, NY 11973, United States.

Institute of Technology Rourkela for firstly the opportunity to undertake this project and secondly for their guidance, patience and support throughout my study. They have always pointed me in the right direction with their experience and their contributions to this research are greatly appreciated. He has consistently pushed me to deliver my best, and I am very grateful to him for supervising me throughout the year. I am grateful to the research team of the Biotransport and Biomechanics laboratory here at National institute of technology, Rourkela for giving me an unforgettable experience during my postgraduate studies. There are too many of them to fit this small area, but each and every one of them is remembered for contributing, in one way or another, to the success of this work. I would like to specially thank to my fellow research workers and friends Krishna Reddy, Nakul Dewan and Protima a big thank you for without your humour, listening ears and assistance over a year I doubt this project would hold as special a place in my life. Thank you to my family who always support me no matter what course I embark, so you all become extra special supporters of this work. Lastly, I thank Almighty God with whose blessings I have reached at the completion of my research.

The most commonly used type of lithium-ion battery model in current battery management systems is the equivalent circuit model (ECM), but ECMs can predict only the input/output dynamics of cells but not internal electrochemical states. Since knowledge of these internal electrochemical states is needed to devise controls that can directly mitigate premature aging, researchers increasingly demand advanced control-oriented electrochemical models. Historically, electrochemical models have been computationally complex; in order to reduce this computational complexity many efforts have been made to simplify the original electrochemical model. However, in order to facilitate the application of the electrochemical model, there are still two issues to address: (1) electrochemical parameter identification and (2) taking into account the electric double layer and constantphase-element (CPE) dynamics. In this paper, we first reformulate the original electrochemical model using lumped parameters to produce a full-order model (FOM) with the number of parameters reduced from 36 down to 24. All redundant/unobservable parameters are eliminated, and thus a minimum set of parameters are obtained, making system identification possible. Then, a series of lumped-parameter transfer functions are derived using only the required assumption of linearity. CPEs are added to the transfer functions to capture more accurately dynamic behavior of real cells. The derived lumped-parameter transfer functions are used to generate a lumped-parameter discrete-time state-space model. Time-domain data are generated by a virtual battery cell created via COMSOL using the FOM as a benchmark for comparison. Testing results under different conditions shows an overall improvement in estimation of cell voltage and state variables for a cell having realistic doublelayer capacitance by using the lumped-parameter reduced-order model with CPE.

Advanced battery management is to lithium-ion battery systems as the brain is to the human body. Its performance rests on the use of battery models that are both fast and accurate. However, mainstream equivalent circuit models and electrochemical models have yet to meet this need well, due to struggle with either predictive accuracy or computational complexity. This problem has acquired urgency as some emerging battery applications running across broad current ranges, e.g., electric vertical takeoff and landing aircraft, can hardly find usable models from the literature. Motivated to address the problem, we develop an innovative model in this study. Called BattX, the model is an equivalent circuit model but draws comparisons to a single particle model with electrolyte and thermal dynamics, thus combining their respective merits to be computationally efficient, accurate, and physically interpretable. The model design pivots on leveraging multiple circuits to approximate major electrochemical and physical processes in charging/discharging. Given the model, we develop a multipronged approach to design experiments and identify its parameters in groups from experimental data. Experimental validation proves that the BattX model is capable of accurate voltage prediction for charging/discharging across low to high Crates .

The solid-state spherical diffusion equation with flux boundary conditions is a standard problem in lithium-ion battery simulations. If finite difference schemes are applied, many nodes across a discretized battery electrode become necessary, in order to reach a good approximation of solution. Such a grid-based approach can be appropriately avoided by implementing analytical methods which reduce the computational load. The pseudo-steadystate (PSS) method is an exact analytical solution method, which provides accurate solid-state concentrations at all current densities. The popularization of the PSS method, in the existing form of expression, is however constrained by a solution convergence problem. In this short communication, a modified PSS (MPSS) expression is presented which provides uniformly convergent solutions at all times. To minimize computational runtime, a fast MPPS (FMPPS) expression is further developed, which is shown to be faster by approximately three orders of magnitude and has a constant time complexity. Using the FMPSS method, uniformly convergent exact solutions are obtained for the solid-state diffusion problem in spherical active particles.

The aim of this paper is to study the physical phenomena of Lithium Ion Battery cell from the thermal and electrochemical engineering point of view and to test the behaviors applying different cell operating conditions. Numerical simulation using finite element method is carried out to observe those characteristics of Li-ion Batteries. One dimensional geometry is modeled for finding out electrochemical properties and two-dimensional geometry is modelled for thermal behaviors. From pre-analysis to results, there are many active analytic procedures that are applied in series for determining final results. Firstly, attention is given on electrochemical behavior like electric potential, electrolyte density, impedance, state of charge (SOC) and secondly, on thermal behavior like temperature within the cell, gradient, maximum temperature elevation within the 2D cell model by internal heat generation produced by exothermic reactions of internal chemical kinematics. The results of the present simulation reveal the location of the maximum temperature of the cell body generated and the maximum ohmic heat developed. Furthermore, the result also predicts the isotherms and the isentropic contours within 2D model geometry. Besides, local Nusselt Number of the cell model is determined in radial and vertical direction of the model keeping the respective operating conditions constant.

Developed an efficient data generation for machine learning training. • Accurately predict battery state of charge under various dynamic battery operating conditions. • Achieved very accurate estimation with simple data via a fast training and prediction.

This paper presents a novel approach using a spectral orthogonal collocation method to solve the well-established 'Newman' model for lithium-ion batteries. The resulting system of equations is much lower order and faster to solve than the equation system obtained using the more common finite difference method, but retains the accuracy of the model, with simulation results in good agreement up to high C-rates (40C) compared to the finite difference approach. This approach enables real-time solution of the model to become possible leading to efficient and accurate on-line estimation of physically meaningful states in an advanced battery management system.

A theoretical model of amperometric enzyme electrodes has been developed in which chemical amplification occurs in a single enzyme membrane via cyclic substrate conversion. The system is based on non-stationary diffusion equations with a nonlinear factor related to the Michaelis–Menten kinetics of the enzymatic reaction. By solving the nonlinear equations using the AGM technique, simple analytical expressions of concentration substrate, product, and amperometric current response are derived. Further, biosensor sensitivity, resistance, and gain are obtained from the current. MATLAB programming was used to carry out the digital simulation. The analytical results are validated with the numerical results. The effect of substrate concentration, maximum enzymatic rate, and membrane thickness on biosensor response was evaluated.

The solid-state spherical diffusion equation with flux boundary conditions is a standard problem in lithium-ion battery simulations. If finite difference schemes are applied, many nodes across a discretized battery electrode become necessary, in order to reach a good approximation of solution. Such a grid-based approach can be appropriately avoided by implementing analytical methods which reduce the computational load. The pseudo-steadystate (PSS) method is an exact analytical solution method, which provides accurate solid-state concentrations at all current densities. The popularization of the PSS method, in the existing form of expression, is however constrained by a solution convergence problem. In this short communication, a modified PSS (MPSS) expression is presented which provides uniformly convergent solutions at all times. To minimize computational runtime, a fast MPPS (FMPPS) expression is further developed, which is shown to be faster by approximately three orders of magnitude and has a constant time complexity. Using the FMPSS method, uniformly convergent exact solutions are obtained for the solid-state diffusion problem in spherical active particles.

The thermal behavior of Li-ion cells is an important safety issue and has to be known under varying thermal conditions. The main objectives of this work is to gain a better understanding of the temperature increase within the cell considering different heat sources under specified working conditions. With respect to the governing physical parameters, the major aim is to find out under which thermal conditions a so called Thermal Runaway occurs. Therefore, a mathematical electrochemical-thermal model based on the Newman model has been extended with a simple combustion model from reaction kinetics including various types of heat sources assumed to be based on an Arrhenius law. This model was realized in COMSOL Multiphysics modeling software. First simulations were performed for a cylindrical 1860 cell with a LiCoO2-cathode to calculate the temperature increase under two various simple electric load profiles and to compute critical system parameters. It has been found that the critical...

This paper presents a review of studies on mathematical modeling of solid oxide fuel cells (SOFCs) with respect to the tubular and planar configurations. In this work, both configurations are divided into five subsystems and the factors such as mass/energy/momentum transfer, diffusion through porous media, electrochemical reactions with and without CO oxidation, shift and reforming reactions, and polarization losses inside the subsystems are discussed. Using variety of fuels fed to SOFCs is issued and their effect on the system is compared briefly. A short review of solid oxide fuel cell configurations and different flow manifolding are also presented in this study. Novel models based on statistical data-driven approach existing in the literatures are considered shortly. Although many studies on solid oxide fuel cells modeling have been done, still more research needs to be done to improve the models in order to predict the fuel cell behaviors more accurately. At the end of this pap...

A physics-based equivalent circuit model (ECM) is derived by applying the finite volume method to a pseudotwo-dimensional (P2D) model of lithium-ion (Li-ion) batteries. Only standard passive components are used to construct the equivalent circuit, which reflects the fact that a Li-ion battery is an energy storage device. Voltages across and currents through the circuit elements in the ECM are identified with the respective internal electrochemical processes in the battery, thus allowing the parametric values of circuit elements to be expressed as functions of the Li-ion concentrations and temperature. Variations in the parametric values across the thickness of the battery lead to a distributed-parameter ECM amenable for a wide range of applications. Furthermore, in contrast to existing reduced-order models of Li-ion battery which are described by differential-algebraic equations, the ECM is governed by ordinary differential equations wherein all the circuit components are expressed as explicit functions of the state and input variables. Hence, the developed model allows the solution to be found directly using matrix algebra, resulting in rapid simulation study suitable for the development of computationally efficient real-time battery control algorithms. Results of simulation based on the developed distributed-parameter ECM show close agreement with those obtained from a partial differential equation based P2D model under a wide range of applied current rates, but at a much reduced computational burden.

We present a reduced order model for a lithium ion battery in which Padé approximants are used to simplify complex, transcendental, transfer functions associated with the linearized, pseudo 2-dimensional (P2D) electrochemical model of the battery. The resulting transfer functions take the form of simple, rational polynomial functions, which can be used to compute any variable at any location within a one-dimensional representation of the battery domain. Corrections for nonlinear behavior are also incorporated into the reduced model. The results obtained using the reduced model compare favorably to those from the full (nonlinear) P2D model and the computational time required to produce these results is significantly reduced. Importantly, the form of the reduced model means that variables can be evaluated at specific discrete locations within the cell domain, without the need to compute all values of the variable at all discrete locations, as is the case with the spatial discretization methods most commonly used to implement the P2D model. We show that this results in further significant time savings and enhances the suitability of the model for variety of applications.

A microscopic model of a lithium battery is developed, which accounts for lithium diffusion within particles, transfer of lithium from particles to the electrolyte and transport within the electrolyte assuming a dilute electrolyte and Butler-Volmer reaction kinetics. Exploiting the small size of the particles relative to the electrode dimensions, a homogenised model (in agreement with existing theories) is systematically derived and studied. Details of how the various averaged quantities relate to the underlying geometry and assumptions are given. The novel feature of the homogenisation process is that it allows the coefficients in the electrode-scale model to be derived in terms of the microscopic features of the electrode (e.g. particle size and shape) and can thus be used as a systematic way of investigating the effects of changes in particle design. Asymptotic methods are utilised to further simplify the model so that one-dimensional behaviour can be described with relatively simpler expressions. It is found that for low discharge currents, the battery acts almost uniformly while above a critical current, regions of the battery become depleted of lithium ions and have greatly reduced reaction rates leading to spatially nonuniform use of the electrode. The asymptotic approximations are valid for electrode materials where the OCV is a strong function of intercalated lithium concentration, such as Li x C 6 , but not for materials with a flat discharge curve, such as LiFePO 4 .

A thermal–electrochemical model of lithium-ion batteries is presented and a Luenberger observer is derived for State-of-Charge (SoC) estimation by recovering the lithium concentration in the electrodes. This first-principles based model is a coupled system of partial and ordinary differential equations, which is a reduced version of the Doyle–Fuller–Newman model. More precisely, the subsystem of Partial Differential Equations (PDEs) is the Single Particle Model (SPM) while the Ordinary Differential Equation (ODE) is a model for the average temperature in the battery. The observer is designed following the PDE backstepping method. Since some coefficients in the coupled ODE–PDE system are time-varying, this results in the time dependency of some coefficients in the kernel function system of the backstepping transformation and it is non-trivial to show well-posedness of the latter system. Adding thermal dynamics to the SPM serves a twofold purpose: improving the accuracy of SoC estimation and keeping track of the average temperature which is a critical variable for safety management in lithium-ion batteries. Effectiveness of the estimation scheme is validated via numerical simulations.

Increasing complexity of mathematical models demands techniques of model order reduction (MOR) that enable an efficient numerical simulation. For example, network approaches yield systems of differential algebraic equations (DAEs) in electric circuit simulation. Thereby, miniaturization and increasing packing densities result in extremely large DAE systems. MOR methods are well developed for linear systems of ordinary differential equations (ODEs), whereas the nonlinear case represents still an open field of research. We consider MOR for semi-explicit systems of DAEs. Techniques for ODEs can be generalized to semi-explicit DAEs by a direct or an indirect approach. In the direct approach, we introduce artificial parameters in the system. Accordingly, MOR methods for ODEs can be applied to the regularized system. Numerical simulations using the constructed MOR strategies are presented.

The response modeling of whole-cell biochip represents the link between cellular biology and transducer output, allowing better system engineering. It provides the mathematical background for signal and noise modeling, performance prediction and data analysis. Here we describe an analytical model for whole- cell biosensors with electrochemical detection for single use, test and dispose applications. In this system the electrochemical signal is generated by the oxidation of the by-products of the reaction between an external substrate and the enzyme alkaline phosphatase. The enzyme expression can be either normal or enhanced due to the response of the biological cell to an external excitation. The electrochemical oxidation current is measured as a function of time. The model is based on the electrochemical reaction rate equations; an analytical solution is presented, compared to data and discussed.