One-dimensional physics-based reduced-order model of lithium-ion dynamics

Lee, James L.; Chemistruck, Andrew; Plett, Gregory L.

doi:10.1016/j.jpowsour.2012.07.075

Cited by 118 publications

(73 citation statements)

References 16 publications

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“…From Equation (9), the fractional-order transfer function in Laplace domain can be given by Equation (10). The integer-order approximation approach of fractional calculus (3) can be then applied to the obtained fractional-order transfer function (10).…”

Section: Mathematical Description Of Fractional-order Modelmentioning

confidence: 99%

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Parameter Sensitivity Analysis for Fractional-Order Modeling of Lithium-Ion Batteries

et al. 2016

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This paper presents a novel-fractional-order lithium-ion battery model that is suitable for use in embedded applications. The proposed model uses fractional calculus with an improved Oustaloup approximation method to describe all the internal battery dynamic behaviors. The fractional-order model parameters, such as equivalent circuit component coefficients and fractional-order values, are identified by a genetic algorithm. A modeling parameters sensitivity study using the statistical Multi-Parameter Sensitivity Analysis (MPSA) method is then performed and discussed in detail. Through the analysis, the dynamic effects of parameters on the model output performance are obtained. It has been found out from the analysis that the fractional-order values and their corresponding internal dynamics have different degrees of impact on model outputs. Thus, they are considered as crucial parameters to accurately describe a battery's dynamic voltage responses. To experimentally verify the accuracy of developed fractional-order model and evaluate its performance, the experimental tests are conducted with a hybrid pulse test and a dynamic stress test (DST) on two different types of lithium-ion batteries. The results demonstrate the accuracy and usefulness of the proposed fractional-order model on battery dynamic behavior prediction.

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Section: Mathematical Description Of Fractional-order Modelmentioning

confidence: 99%

“…The integer-order approximation approach of fractional calculus (3) can be then applied to the obtained fractional-order transfer function (10).…”

Section: Mathematical Description Of Fractional-order Modelmentioning

confidence: 99%

Parameter Sensitivity Analysis for Fractional-Order Modeling of Lithium-Ion Batteries

et al. 2016

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“…Cai and White 11 used proper orthogonal decomposition to find the basis from the solution sets of a high-order model for typical operational modes and truncated trivial responses. Lee et al 12 presented a direct-realization algorithm to identify a discrete time ROM for a given set of electrochemical model parameters at a given state of charge and temperature. The ROMs are useful in various practical applications repeatedly solving a system of differential equations with invariant parameters.…”

mentioning

confidence: 99%

Efficient and Extensible Quasi-Explicit Modular Nonlinear Multiscale Battery Model: GH-MSMD

Kim

Smith

Lawrence-Simon

et al. 2017

J. Electrochem. Soc.

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Complex physics and long computation time hinder the adoption of computer aided engineering models in the design of largeformat battery cells and systems. A modular, efficient battery simulation model-the multiscale multidomain (MSMD) model-was previously introduced to aid the scale-up of Li-ion material & electrode designs to complete cell and pack designs, capturing electrochemical interplay with 3-D electronic current pathways and thermal response. This paper enhances the computational efficiency of the MSMD model using a separation of time-scales principle to decompose model field variables. The decomposition provides a quasi-explicit linkage between the multiple length-scale domains and thus reduces time-consuming nested iteration when solving model equations across multiple domains. In addition to particle-, electrode-and cell-length scales treated in the previous work, the present formulation extends to bus bar-and multi-cell module-length scales. In cutting-edge industries such as automotive and aviation, computer models are valuable tools for reducing the cost of product development, improving manufacturing processes, optimizing designs, and implementing advanced controls. Although the global electricdrive-vehicle market is growing rapidly, the lack of a model that can accurately predict a battery's behavior is recognized as a threat to the automotive industry that has been enhancing its dependence on computer models. In a lithium-ion battery, which is the preeminent candidate powering electric-drive vehicles, physiochemical processes take place in intricate geometries over a wide range of time and length scales. The device response of a battery results from complex nonlinear interplays among material characteristics, design variables, and environmental and operational conditions. The multiscale nonlinear nature of battery physics even more critically affects the device behavior as the size of a battery increases. Without understanding the interplays among the interdisciplinary physicochemical processes occurring across varied scales, it is costly to design long-lasting, highperforming, safe, large batteries.The U.S. Department of Energy's Computer Aided Engineering for Electric Drive Vehicle Battery (CAEBAT) program has supported development of modeling capabilities to help industries accelerate mass-market adoption of electric-drive vehicles and their batteries. In support of the U.S. Department of Energy, National Renewable Energy Laboratory developed the multiscale multidomain (MSMD) model, overcoming challenges in modeling the highly nonlinear multiscale response of battery systems.1,2 The MSMD model introduces separate model domains at particle, electrode, and cell levels, while tightly coupling the physics across the scales. The separation of a model domain and the adoption of local homogeneity assumption are enabled by the intrinsic nature of typical battery systems where substantial time-and length-scale segregation occurs. The MSMD particle-domain models (PDMs) solve collective response of ele...

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“…Smith's SVM approach provides excellent convergence at high current rates (up to 50 C) and has been adopted into the multi-scale multi-dimensional framework 47,48 to model the distributed thermal behavior over large-format cell geometry. Using a similar approach to SVM, Plett and his coworkers 49,50 derived a ROM from the Laplace transfer function by using a discretetime realization algorithm (DRA) and the resulting model was used to simulate the Urban Dynamometer Driving Schedule (UDDS). Plett's approach achieves a significant speedup for the high-frequency simulation as compared with the nonlinear FOM.…”

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confidence: 99%

Nonlinear State-Variable Method for Solving Physics-Based Li-Ion Cell Model with High-Frequency Inputs

Jin

White

2017

J. Electrochem. Soc.

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A nonlinear state-variable method is presented and used to solve the pseudo-2D (P2D) Li-ion cell model under high-frequency input current and temperature signals. The physics-based governing equations are formulated into a nonlinear state variable method (NSVM), in which the mass transfer variables are evaluated using a 1 st order exponential integrator approach at each discrete time point and the electrochemical kinetics (Butler-Volmer) equations are solved by either an iterative or an explicit method. This procedure provides an accurate, computationally efficient method to develop physics-based simulations of the performance of a dual-foil Li-ion cell during practical drive cycles. Physics-based Li-ion cell models are useful tools for analyzing the battery cell performances, characterizing material properties, supporting cell design, and developing battery management systems (BMS). 5 in their work, a dual-foil Li-ion cell was represented by a pseudo-two-dimensional domain; and therefore, this model is usually referred as the "pseudo-2D model (P2D)".3 This model contains several coupled transport phenomena described by nonlinear partial differential equations (PDEs). Due to the numerical complexity of these models, various reduced-order models (ROMs) have been proposed as substitutes for either the single particle (SP) or the P2D full-order model (FOM) in practical online simulation applications.6-16 Also, ROMs have been published to simulate capacity fading 17,18 and for use in parameter estimations. presented an approximate solution to the spherical diffusion problem with a fixed flux which provides high accuracy with only a few terms in a series when compared to the analytic solution with at least 100 terms. This approximate solution provides significant savings in computation time.In order to predict the performance of lithium ion cells operating at higher rates, more complicated models were developed. In 1982, West et al. 4 presented a Nernst-Planck model for porous insertion electrodes for a Li/TiS 2 cell. They pointed out the importance of coupling the transport of lithium ions between the insertion electrode and the electrolyte. In 1993, Mao and White 35 presented a Nernst-Planck model of the Li/TiS 2 cell which included transport of lithium ions through the separator and demonstrated quantitatively how the utilization of the TiS 2 electrode could be improved by decreasing the thickness of the separator. Also in 1993, Doyle et al. 36 published a concentrated solution theory model for a lithium/polymer/TiS 2 cell. Shortly after that in 1994 Fuller et al.5 published a concentrated solution theory model for a dual lithium ion insertion cell ("dual foil"), which is known as "pseudo-2D model (P2D)". In 1996, Doyle et al. 37 published a comparison of their model predictions to experimental data from a Bellcore plastic lithium ion cell. Unfortunately, the computation burden associated with using the program dual foil is too great to use their program for extensive simulations needed for parameter estimation an...

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One-dimensional physics-based reduced-order model of lithium-ion dynamics

Cited by 118 publications

References 16 publications

Parameter Sensitivity Analysis for Fractional-Order Modeling of Lithium-Ion Batteries

Parameter Sensitivity Analysis for Fractional-Order Modeling of Lithium-Ion Batteries

Efficient and Extensible Quasi-Explicit Modular Nonlinear Multiscale Battery Model: GH-MSMD

Nonlinear State-Variable Method for Solving Physics-Based Li-Ion Cell Model with High-Frequency Inputs

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