A Modeling Framework for Efficient Reduced Order Simulations of Parametrized Lithium-ion Battery Cells

A Modeling Framework for Efficient Reduced Order Simulations of Parametrized Lithium-ion Battery Cells
Author: Manuel Landstorfer
Publisher:
Total Pages:
Release: 2021
Genre:
ISBN:

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In this contribution we present a new modeling and simulation framework for parametrized Lithium-ion battery cells. We first derive a new continuum model for a rather general intercalation battery cell on the basis of non-equilibrium thermodynamics. In order to efficiently evaluate the resulting parameterized non-linear system of partial differential equations the reduced basis method is employed. The reduced basis method is a model order reduction technique on the basis of an incremental hierarchical approximate proper orthogonal decomposition approach and empirical operator interpolation. The modeling framework is particularly well suited to investigate and quantify degradation effects of battery cells. Several numerical experiments are given to demonstrate the scope and efficiency of the modeling framework.

Parameterization, Simulation and Analysis of Electrode-level Physics-based Battery Model

Parameterization, Simulation and Analysis of Electrode-level Physics-based Battery Model
Author: Sara Wojnar
Publisher:
Total Pages: 0
Release: 2022
Genre:
ISBN:

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An accurate and a computationally efficient Lithium-ion battery model is essential for analyzing battery performance and controlling batteries in real-time. Many battery models that describe cell-level dynamics can be found in existing literature, while electrode-level models have been explored with less frequency. However, investigating the dynamics at the electrode-level can lead to greater insights to identify dominant aging mechanisms and areas where battery designs can be altered in order to improve battery performance and life. In this context, this thesis presents a modeling framework for battery electrode-level dynamics by combining physics-based battery models with data-driven learning models. The modeling framework intends to capture and identify the effect of several uncertainties arising from model inaccuracies and aging related behaviors. Specifically, a single particle model is utilized to capture the Lithium diffusion phenomena in a positive electrode whereas a Gaussian process regression model is used to capture the inaccuracies of the single particle model. Furthermore, a least squares estimator is used to estimate and predict the changes in positive electrode behavior due to cycling-induced aging. The proposed framework is tested using measured data from Lithium-ion battery cells that underwent 90 cycles of continuous charging and discharging. Applying the data-driven technique to the physics-based electrode-level model better predicted the fresh cell voltage of the electrode. The cycle charging time was used to accurately predict the maximum fresh cell voltage uncertainty using a linear fit, although there was more variation in the maximum cell voltage uncertainty in later cycles.

Towards a Systems-level Understanding of Battery Systems

Towards a Systems-level Understanding of Battery Systems
Author: Akshay Subramaniam
Publisher:
Total Pages: 220
Release: 2021
Genre:
ISBN:

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Current imperatives of electrification and decarbonization entail significant improvements in energy density, performance, and cost metrics for battery technology. This has motivated active research into new materials, cell designs, and external controls to ensure safe and efficient operation. Modeling and simulation approaches have a powerful complementary function in this regard, most notably exemplified by the models for Lithium-ion batteries by Newman and co-workers. The overarching theme of this dissertation is thus the development and application of electrochemical modeling approaches at multiple scales in problems relevant to the abovementioned contexts. At the systems level, the development of more intelligent and powerful Battery Management Systems is enabled by fast electrochemical models, which must balance competing considerations of accuracy, computational efficiency, and ease of parameterization. To this end, we report a rigorous and generalized methodology for "upscaling" continuum electrochemical models. This approach, based on the visualization of a battery as Tanks-in-Series, has been demonstrated for both Lithium-ion and more complex Lithium-sulfur batteries. With respect to full models, voltage prediction errors below 20 mV are achieved for high-energy cells in most practical cases. 30 mV errors are achieved for aggressive conditions of high-rate operation at sub-zero ambient temperatures, illustrating their practical utility. This approach results in improved computational speed since each conservation law is replaced by a relatively simple volume-averaged differential or algebraic equation. For examples of large-scale problems, this leads to 10x savings in computation time over fast implementations of conventional models, illustrating competitiveness for real-time applications. In the development of next-generation chemistries, continuum models can serve as a framework for the analysis and interpretation of experimental data, while providing design guidance and helping determine desirable operating regimes. Electrochemical phenomena at different length and time scales are manifested during operation through voltage and temperature signatures, cycle life, and coulombic efficiency. Optimization of cell-level metrics is thus predicated on their correlation with the internal electrochemistry. This entails the integration of electrochemical models at different levels of detail in a computationally efficient and robust manner. To this end, the second half of this dissertation describes our efforts to develop a simulation framework for the modeling of Lithium-metal systems. We first describe a robust computational method to simulate Poisson Nernst Planck (PNP) models for Lithium symmetric cells characterized by thin double layers. This can be leveraged in applications where computational efficiency is of salience, such as cycling simulations and parameterization by coupling kinetic models of interest. This is demonstrated by a systems level method, enabling the quick evaluation of candidate mechanisms appropriately expressed as time-varying rate constants, making it useful for understanding the phenomena underpinning voltage transitions in Lithium symmetric cells. This is followed by a description of a preliminary electrochemical-mechanical model for Li metal interfaces, which is expected to serve as basis for more sophisticated electrochemical-mechanical models for Li metal systems operating under external pressure. We expect these approaches to advance fundamental understanding and design of Li-metal batteries, while creating accessible computational tools to complement experimental studies. Taken together, these contributions are envisaged to advance the knowledge base for model-based design as well as Battery Management Systems, particularly in anticipation of the commercialization of emerging battery chemistries.

Mathematical Modeling of Lithium Batteries

Mathematical Modeling of Lithium Batteries
Author: Krishnan S. Hariharan
Publisher: Springer
Total Pages: 213
Release: 2017-12-28
Genre: Technology & Engineering
ISBN: 3319035274

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This book is unique to be the only one completely dedicated for battery modeling for all components of battery management system (BMS) applications. The contents of this book compliment the multitude of research publications in this domain by providing coherent fundamentals. An explosive market of Li ion batteries has led to aggressive demand for mathematical models for battery management systems (BMS). Researchers from multi-various backgrounds contribute from their respective background, leading to a lateral growth. Risk of this runaway situation is that researchers tend to use an existing method or algorithm without in depth knowledge of the cohesive fundamentals—often misinterpreting the outcome. It is worthy to note that the guiding principles are similar and the lack of clarity impedes a significant advancement. A repeat or even a synopsis of all the applications of battery modeling albeit redundant, would hence be a mammoth task, and cannot be done in a single offering. The authors believe that a pivotal contribution can be made by explaining the fundamentals in a coherent manner. Such an offering would enable researchers from multiple domains appreciate the bedrock principles and forward the frontier. Battery is an electrochemical system, and any level of understanding cannot ellipse this premise. The common thread that needs to run across—from detailed electrochemical models to algorithms used for real time estimation on a microchip—is that it be physics based. Build on this theme, this book has three parts. Each part starts with developing a framework—often invoking basic principles of thermodynamics or transport phenomena—and ends with certain verified real time applications. The first part deals with electrochemical modeling and the second with model order reduction. Objective of a BMS is estimation of state and health, and the third part is dedicated for that. Rules for state observers are derived from a generic Bayesian framework, and health estimation is pursued using machine learning (ML) tools. A distinct component of this book is thorough derivations of the learning rules for the novel ML algorithms. Given the large-scale application of ML in various domains, this segment can be relevant to researchers outside BMS domain as well. The authors hope this offering would satisfy a practicing engineer with a basic perspective, and a budding researcher with essential tools on a comprehensive understanding of BMS models.

Model Order Reduction of Multi-dimensional Partial Differential Equations for Electrochemical-thermal Modeling of Large-format Lithium-ion Batteries

Model Order Reduction of Multi-dimensional Partial Differential Equations for Electrochemical-thermal Modeling of Large-format Lithium-ion Batteries
Author: Guodong Fan
Publisher:
Total Pages:
Release: 2016
Genre:
ISBN:

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Lithium ion batteries are considered the state of the art for energy storage in electric and hybrid vehicles. However, there are still several major challenges, such as battery safety, durability and cost, limiting the widespread application of Li-ion batteries in electrified vehicles. Understanding and predicting the chemical and physical processes in Li-ion cells is possible through multi-scale characterization methods. However, ``in-situ" quantification of such processes on a vehicle is not yet achievable due to the absence of direct measurements. Hence, high-fidelity, first-principles models are an essential investigation tool for the prediction of the battery performance and life. While such multi-scale, multi-dimensional first-principles models allow one to characterize the distribution of electrochemical and thermal properties within the cell, they require significant calibration effort and computation time, due to the presence of large scale coupled Partial Differential Equations (PDEs) and nonlinear algebraic equations, ultimately preventing their application to estimation and control algorithm design and verification. This dissertation presents the reduced order electrochemical-thermal models derived from first principles and suitable for real-time simulation, estimation and control design, through the systematic use of projection methods to achieve direct Model Order Reduction (MOR) from linear and nonlinear parabolic PDEs to low-order Ordinary Differential Equations (ODEs). The proposed methodology is applied to an electrochemical-thermal model for the simulation of large-scale Lithium ion battery cells. The resulting reduced-order multi-scale, multi-dimensional model is validated against numerical solutions and experimental data at various input current conditions. The physics-based, ultra-fast modeling tools developed within this research will enable accurate prediction of the electrochemical and thermal distributions within the battery cells, supporting simulation and analysis of performance and remaining usable life of the Li-ion batteries in electrified vehicles.

Multiscale Modeling, Reformulation, and Efficient Simulation of Lithium-ion Batteries

Multiscale Modeling, Reformulation, and Efficient Simulation of Lithium-ion Batteries
Author: Paul Wesley Clairday Northrop
Publisher:
Total Pages: 202
Release: 2014
Genre: Electronic dissertations
ISBN:

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Lithium-ion batteries are ubiquitous in modern society, ranging from relatively low-power applications, such as cell phones, to very high demand applications such as electric vehicles and grid storage. The higher power and energy density of lithium-ion batteries compared to other forms of electrochemical energy storage makes them very popular in such a wide range of applications. In order to engineer improved battery design and develop better control schemes, it is important to understand internal and external battery behavior under a variety of possible operating conditions. This can be achieved using physical experiments, but those can be costly and time consuming, especially for life-studies which can take years to perform. Here using mathematical models based on porous electrode theory to study the internal behavior of lithium-ion batteries is examined. As the physical phenomena which govern battery performance are described using several nonlinear partial differential equations, simulating battery models can quickly become computationally expensive. Thus, much of this work focuses on reformulating the battery model to improve simulation efficiency, allowing for use to solve problems which require many iterations to converge (e.g. optimization), or in applications which have limited computational resources (e.g. control). Computational time is improved while maintaining accuracy by using a coordinate transformation and orthogonal collocation to reduce the number of equations which must be solved using the method of lines. Orthogonal collocation is a spectral method which approximates all dependent variables as a series solution of trial functions. This approach discretizes the spatial derivatives with higher order accuracy than standard finite difference approach. The coefficients are determined by requiring the governing equation be satisfied at specified collocation points, resulting in a system of differential algebraic equations (DAEs) which must be solved with time as the only differential variable. The system of DAEs can be solved using standard time-adaptive integrating solvers. The error and simulation time of the battery model of orthogonal collocation is analyzed. The improved computational efficiency allows for more physical phenomena to be considered in the reformulated model. Lithium-ion batteries exposed to high temperatures can lead to internal damage and capacity fade. In extreme cases this can lead to thermal runaway, a dangerous scenario in which energy is rapidly released. In the other end of the temperature spectrum, low temperatures can significantly impede performance by increasing diffusion resistance. Although accounting for thermal effects increases the computational cost, the model reformulation allows for these important phenomena to be considered in single cell as well as 2D and multicell stack battery models. The growth of the solid electrolyte interface (SEI) layer contributes to capacity fade by means of a side reaction which removes lithium from the system irreversibly as well as increasing the resistance of the transfer lithium-ion from the electrolyte to the active material. As the reaction kinetics are not well understood, several proposed mechanisms are considered and implemented into the continuum reformulated model. The effects of SEI layer growth on a lithium-ion cell over 10,000 cycles is simulated and analyzed. Furthermore, a kinetic Monte Carlo model is developed and implemented to study the heterogeneous growth of the solid electrolyte layer. This is a stochastic approach which considers lithium-ion diffusion, intercalation, and side reactions. As millions of individual time steps may be performed for a single cycle, it is very computationally expensive, but allows for simulation of surface phenomena which are ignored in continuum models.

Modeling and Simulation of Lithium-ion Power Battery Thermal Management

Modeling and Simulation of Lithium-ion Power Battery Thermal Management
Author: Junqiu Li
Publisher: Springer Nature
Total Pages: 343
Release: 2022-05-09
Genre: Technology & Engineering
ISBN: 9811908443

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This book focuses on the thermal management technology of lithium-ion batteries for vehicles. It introduces the charging and discharging temperature characteristics of lithium-ion batteries for vehicles, the method for modeling heat generation of lithium-ion batteries, experimental research and simulation on air-cooled and liquid-cooled heat dissipation of lithium-ion batteries, lithium-ion battery heating method based on PTC and wide-line metal film, self-heating using sinusoidal alternating current. This book is mainly for practitioners in the new energy vehicle industry, and it is suitable for reading and reference by researchers and engineering technicians in related fields such as new energy vehicles, thermal management and batteries. It can also be used as a reference book for undergraduates and graduate students in energy and power, electric vehicles, batteries and other related majors.

Electrochemical Transport Simulation of 3D Lithium-ion Battery Electrode Microstructures

Electrochemical Transport Simulation of 3D Lithium-ion Battery Electrode Microstructures
Author: Bradley Louis Trembacki
Publisher:
Total Pages: 278
Release: 2015
Genre:
ISBN:

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Lithium-ion batteries are commonly modeled using a volume-averaged formulation (porous electrode theory) in order to simulate battery behavior on a large scale. These methods utilize effective material properties and assume a simplified spherical geometry of the electrode particles. In contrast, a particle-scale (non-porous electrode) simulation applied to resolved electrode geometries predicts localized phenomena. Complete simulations of batteries require a coupling of the two scales to resolve the relevant physics. A central focus of this thesis is to develop a fully-coupled finite volume methodology for the simulation of the electrochemical equations in a lithium-ion battery cell at both the particle scale and using volume-averaged formulations. Due to highly complex electrode geometries at the particle scale, the formulation employs an unstructured computational mesh and is implemented within the MEMOSA software framework of Purdue’s PRISM (Prediction of Reliability, Integrity and Survivability of Microsystems) center. Stable and efficient algorithms are developed for full coupling of the nonlinear species transport equations, electrostatics, and Butler-Volmer kinetics. The model is applied to synthetic electrode particle beds for comparison with porous electrode theory simulations and to evaluate numerical performance capabilities. The model is also applied to a half-cell mesh created from a real cathode particle bed reconstruction to demonstrate the feasibility of such simulations. The second focus of the thesis is to investigate 3D battery electrode architectures that offer potential energy density and power density improvements over traditional particle bed battery geometries. A singular feature of these geometries is their interpenetrating nature, which significantly reduces diffusion distance. Advancement of micro-scale additive manufacturing techniques has made it possible to fabricate these electrode microarchitectures. A fully-coupled finite volume methodology for the transport equations coupled to the relevant electrochemistry is implemented in the PETSc (Portable, Extensible Toolkit for Scientific Computation) software framework which allows for a straightforward scalable simulation on orthogonal hexahedral meshes. Such scalability becomes important when performing simulations on fully resolved microstructures with many parameter sweeps across multiple variables. Using the computational model, a variety of 3D battery electrode geometries are simulated and compared across various battery discharge rates and length scales in order to quantify performance trends and investigate geometrical factors that improve battery performance. The energy density and power density of the 3D battery microstructures are compared in several ways, including a uniform surface area to volume ratio comparison as well as a comparison requiring a minimum manufacturable feature size. Significant performance improvements over traditional particle bed electrode designs are observed, and electrode microarchitectures derived from minimal surfaces are shown to be superior under a minimum feature size constraint. An average Thiele modulus formulation is presented to predict the performance trends of 3D microbattery electrode geometries. As a natural extension of the 3D battery particle-scale modeling, the third and final focus of the thesis is the development and evaluation of a volume-averaged porous electrode theory formulation for these unique 3D interpenetrating geometries. It is necessary to average all three material domains (anode, cathode, and electrolyte) together, in contrast to traditional two material volume-averaging formulations for particle bed geometries. This model is discretized and implemented in the PETSc software framework in a manner similar to the particle-scale implementation and enables battery-level simulations of interpenetrating 3D battery electrode architectures. Electrode concentration gradients are modeled using a characteristic diffusion length, and results for plate and cylinder electrode geometries are compared to particle-scale simulation results. Additionally, effective diffusion lengths that minimize error with respect to particle-scale results for gyroid and Schwarz P electrode microstructures are determined, since a theoretical single diffusion length is not easily calculated. Using these models, the porous electrode formulation for these 3D interpenetrating geometries is shown to match the results of particle-scale models very well.