Discrete-time realization of transcendental impedance models, with application to modeling spherical solid diffusion

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

doi:10.1016/j.jpowsour.2012.01.134

Cited by 58 publications

(41 citation statements)

References 19 publications

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“…Solid phase diffusion.-To transform the solid particle diffusion PDE into a state equation, we used an approximate transfer function approach presented earlier, as shown in Appendix A, which is also used by Smith et al, 12 Lee et al 48 and Leek et al 49 The resulting transfer function is:…”

Section: Variable Name Symbolmentioning

confidence: 99%

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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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Section: Variable Name Symbolmentioning

confidence: 99%

“…and the state variables at the next time point, x k , can be calculated through the following equation: [49] where that if λ i = 0, the corresponding diagonal element in Equation 48 is estimated by taking the limit for λ i → 0:…”

Section: Variable Name Symbolmentioning

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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“…In Ref. [8], a discrete-time state space model is derived from a known transfer function. And then it is converted into a continuous-time state space model.…”

Section: Introductionmentioning

confidence: 99%

“…In both Refs. [7,8], analytical transfer functions are assumed to be known, and thus both methods are limited to spherical particles. The method discussed in this paper can be extended to particles of any shape.…”

Section: Introductionmentioning

confidence: 99%

Model order reduction for solid-phase diffusion in physics-based lithium ion cell models

Xiao

Stanton

Cai

et al. 2012

Journal of Power Sources

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“…Toward the first challenge, several control-oriented reformulations for the P2D model have been proposed, including the state-variablemodeling (SVM) approach by Smith et al 5 and the discrete-time realization algorithm (DRA) by Leek et al 6 and Lee et al 7 These methods require linearization of the electrochemical equations and thus lose accuracy. Also, the gain and pole values used by the SVM or DRA method need to be pre-determined through implicit approaches and there are parameterization issues to implement these algorithms.…”

mentioning

confidence: 99%

An Adaptive Reduced-Order-Modeling Approach for Simulating Real-Time Performances of Li-Ion Battery Systems

Jin

White

2017

J. Electrochem. Soc.

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In this work, a reduced-order-modeling(ROM) approach is introduced to simulate a battery system with multiple cells. The ROM is described by only two state variable equations and several explicit expressions. While running a stand-alone pseudo-2D (P2D) model by the nonlinear state variable modeling (NSVM) algorithm at a specified current, several parameters can be estimated through the NSVM procedure; and with these parameters, the cell voltage under additional current perturbations can be computed approximately by the ROM. This modeling scheme was tested for a 24P battery module in a co-simulation process: the stand-alone P2D model is solved at the battery-average current to estimate certain parameters to share with its ROM, then the ROM is implemented to evaluate the voltage response of each cell at its respective cell current. The ROM shows excellent accuracy and a much higher speed than the full-order-model with P2D models used for each cell. The battery management system (BMS) plays a crucial role in electrical vehicles (EV). During a standard vehicle development cycle, in-loop simulation is a useful technique to test and verify complex real-time embedded systems.1-3 To conduct in-loop simulation, the embedded system to be tested is connected to a mathematical representation of all related dynamic systems, because this arrangement lowers cost and improves safety as compared with using the real system. The mathematical representation interacting with embedded system is referred as "plant simulation". For the BMS software development, the plant simulation is performed by system-level battery models while the corresponding embedded system includes certain battery control and management algorithms. Therefore an accurate plant model for the battery system is vital for a successful BMS design. Besides accuracy, the plant battery model is also expected to work under high frequency inputs with noise and generate real-time output signals at low computational costs.The pseudo-2D (P2D) model developed by Fueler et al. 4 is a physical model that can be used to provide reliable predictions for the transport and electrochemical phenomena in Li-ion cells. However, it is still difficult to use the P2D model in plant simulation. The first challenge is the numerical issues in solving the nonlinear partialdifferential-equations (PDEs) contained in the P2D model at highfrequency inputs. During practical driving modes, the power requests from the powertrain to the EV battery change very quickly with time, and the currents and voltages are processed as discrete-time electrical signals. Most multi-physics PDE solvers (e.g., COMSOL) are designed to model continuous-time processes (e.g., constant current) and are slow for high-frequency simulation cases. Another challenge is the high computational costs to scale-up the P2D model from celllevel to pack-level. A single-cell P2D model normally includes more than 100 discretized state variables even using a very coarse mesh. To meet the high power and energy demands, typical EV battery...

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Discrete-time realization of transcendental impedance models, with application to modeling spherical solid diffusion

Cited by 58 publications

References 19 publications

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

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

Model order reduction for solid-phase diffusion in physics-based lithium ion cell models

An Adaptive Reduced-Order-Modeling Approach for Simulating Real-Time Performances of Li-Ion Battery Systems

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