Efficient Reformulation of Solid-Phase Diffusion in Physics-Based Lithium-Ion Battery Models

Ramadesigan, Venkatasailanathan; Boovaragavan, Vijayasekaran; Pirkle, J. Carl; Subramanian, Venkat R.

doi:10.1149/1.3425622

Cited by 137 publications

(94 citation statements)

References 22 publications

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“…This type of volume-averaging 17,18 combined with the polynomial approximation 19,20 has been shown to be accurate for low to medium rates of discharge. [21][22][23][24][25] This step eliminates equations 1.4 and 1.10 from Table I [2] where the subscript i refers to either the positive or negative electrode. This step results in a total of 12 equations that must be solved across the three regions: the positive and negative electrodes, and the separator.…”

mentioning

confidence: 99%

“…Several such approaches can be found in the literature. 15,[21][22][23][24][25] This paper uses the mixed finite difference approach developed by Ramadesigan, et al 25 for simulation of discharge rates greater than 1C. The mixed finite difference approach uses 6 optimally spaced node points (with 6 corresponding governing equations) to describe the behavior of the lithium ion concentration in the radial direction within the solid phase particles.…”

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confidence: 99%

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Coordinate Transformation, Orthogonal Collocation, Model Reformulation and Simulation of Electrochemical-Thermal Behavior of Lithium-Ion Battery Stacks

Northrop¹,

Ramadesigan²,

De³

et al. 2011

J. Electrochem. Soc.

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180

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In this paper, a simple transformation of coordinates is proposed that facilitates the efficient simulation of the non-isothermal lithium-ion pseudo 2-D battery model. The transformed model is then conveniently discretized using orthogonal collocation with the collocation points in the spatial direction. The resulting system of differential algebraic equations (DAEs) is solved using efficient adaptive solvers in time. A series of mathematical operations are performed to reformulate the model to enhance computational efficiency and programming convenience while maintaining accuracy even when non-linear or temperature dependent parameters are used. The transformed coordinate allows for efficient simulation and extension from cell sandwich to stack models. Furthermore, the transformation and reformulation techniques are used to simulate operation of an 8-cell battery stack subject to varying heat transfer coefficients as well as specified temperature boundary conditions. Mathematical modeling and simulation of the operation of lithiumion batteries is not trivial, as concentration and potential fields must be evaluated simultaneously in both solid and liquid phases. This is complicated by the fact that the transport and kinetic parameters which determine battery behavior are highly nonlinear, leading to very complex governing equations. Doyle et al. 1 developed a general model based on concentrated solution theory to describe the internal behavior of a lithium-ion sandwich consisting of positive and negative porous electrodes, a separator, and current collectors. 2 This model proved generic enough to incorporate further advancements in battery systems understanding, leading to the development of a number of similar models. 3-13 Reviews of models for lithium-ion batteries can be found elsewhere in the literature. [10][11][12] Table I depicts a pseudo-twodimensional isothermal model for a lithium-ion battery. 14-16 Table II presents the various expressions used in the model, while Table III shows the physical parameters used in this paper. For analysis and control of lithium-ion batteries in hybrid environments (e.g. with a fuel cell, capacitor, or other electrical components), there is a need to simulate state of charge, state of health, and other parameters of lithium-ion batteries in milliseconds. Full-order physics-based models may simulate discharge curves in several seconds to minutes, depending on the solvers, routines, computers, etc. In contrast, empirical models (based on correlations of past data) can simulate specific operating scenarios in milliseconds. However, use of these models under a different operating condition than for which they were developed may cause abuse or underutilization of electrochemical power sources. This paper presents a coordinate transformation and mathematical analysis for reformulation of physics-based models to solve them quickly, conveniently, and accurately in a way that is valid for a wide range of operating conditions and parameters. The porous electrode model as given in Ta...

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confidence: 99%

mentioning

confidence: 99%

Coordinate Transformation, Orthogonal Collocation, Model Reformulation and Simulation of Electrochemical-Thermal Behavior of Lithium-Ion Battery Stacks

Northrop¹,

Ramadesigan²,

De³

et al. 2011

J. Electrochem. Soc.

Self Cite

180

204

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show abstract

“…As lithium ions (Li + ) intercalate into and out of the electrodes in the pseudo-dimension r (the direction normal to the surface of the electrodes, shown in Fig. 1), the diffusion equations for the solid phase are expressed in both the x-direction and the pseudo-dimension r [19]. Variations of lithium ion concentration in the solid phase can be expressed using Fick's laws of diffusion [15,20], assuming c s,k = c s,k (x, r, t):…”

Section: Species Conservation For Solid Phasementioning

confidence: 99%

Parameter estimation of an electrochemistry-based lithium-ion battery model

Masoudi

Uchida

McPhee

2015

Journal of Power Sources

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Parameters for an electrochemistry-based Lithium-ion battery model are estimated using the homotopy optimization approach. A high-fidelity model of the battery is presented based on chemical and electrical phenomena. Equations expressing the conservation of species and charge for the solid and electrolyte phases are combined with the kinetics of the electrodes to obtain a system of differential-algebraic equations (DAEs) governing the dynamic behavior of the battery. The presence of algebraic constraints in the governing dynamic equations makes the optimization problem challenging: a simulation is performed in each iteration of the optimization procedure to evaluate the objective function, and the initial conditions must be updated to satisfy the constraints as the parameter values change. The ε-embedding method is employed to convert the original DAEs into a singularly perturbed system of ordinary differential equations, which are then used to simulate the system efficiently. The proposed numerical procedure demonstrates excellent perfor- * Corresponding author. The final publication is available at Elsevier via http://doi.org/10.1016/j.jpowsour.2015.04.154 © 2015 mance in the estimation of parameters for the Lithium-ion battery model, compared to direct methods that are either unstable or incapable of converging. The obtained results and estimated parameters demonstrate the efficacy of the proposed simulation approach and homotopy optimization procedure.

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“…Efforts in numerical methods have been summarized by Ramadesigan et al [53] and Zeng et al [54]. Although we know that D s varies with concentration and temperature by experiments, an effective mathematical method is still needed to treat variable D s approximately and obtain simulation results in acceptable accuracy.…”

Section: Superposition Integral and Variable D Smentioning

confidence: 99%

Simulation of temperature rise in Li-ion cells at very high currents

Mao

Tiedemann²,

Newman

2014

Journal of Power Sources

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h i g h l i g h t sA radial mass-transport coefficient is used to modify the thermal-electrochemical Dualfoil model. Simulation of current and temperature under very-high-current discharge is achieved. Mass-transport limitation decreased by high cell temperature causes a rapid temperature rise. Effective heat transfer outside the cell center is critical. a b s t r a c tThe Dualfoil model is used to simulate the electrochemical behavior and temperature rise for MCMB/ LiCoO 2 Li-ion cells under a small constant-resistance load, approaching a short-circuit condition. Radial mass transport of lithium from the center of the pore to the pore wall has been added to the model to describe better current limitations at very high discharge currents. Electrolyte and solid-surfaceconcentration profiles of lithium ions across the cell at various times are developed and analyzed to explain the lithium-ion transport limitations. Sensitivity tests are conducted by changing solution and solid-state diffusion coefficients, and the heat-transfer coefficient. Because diffusion coefficients increase at high temperature, calculated discharge curves can show currents dropping initially but then rising to a second peak, with most of the available capacity being consumed in the second peak. Conditions which lead to such a second peak are explored.Published by Elsevier B.V.

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Efficient Reformulation of Solid-Phase Diffusion in Physics-Based Lithium-Ion Battery Models

Cited by 137 publications

References 22 publications

Coordinate Transformation, Orthogonal Collocation, Model Reformulation and Simulation of Electrochemical-Thermal Behavior of Lithium-Ion Battery Stacks

Coordinate Transformation, Orthogonal Collocation, Model Reformulation and Simulation of Electrochemical-Thermal Behavior of Lithium-Ion Battery Stacks

Parameter estimation of an electrochemistry-based lithium-ion battery model

Simulation of temperature rise in Li-ion cells at very high currents

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