Model Reduction for Multiscale Lithium-Ion Battery Simulation

In this contribution we are concerned with efficient model reduction for multiscale problems arising in lithium-ion battery modeling with spatially resolved porous electrodes. We present new results on the application of the reduced basis method to the resulting instationary 3D battery model that involves strong non-linearities due to Buttler-Volmer kinetics. Empirical operator interpolation is used to efficiently deal with this issue. Furthermore, we present the localized reduced basis multiscale method for parabolic problems applied to a thermal model of batteries with resolved porous electrodes. Numerical experiments are given that demonstrate the reduction capabilities of the presented approaches for these real world applications

A New Multiscale Modeling Framework for Lithium-Ion Battery Dynamics: Theory, Experiments, and Comparative Study with the Doyle-Fuller-Newman Model

Technological advancements and globalization in recent decades have largely been responsible for the ever-increasing energy and power demands across different industrial sectors. This has led to an extensive use of fossil fuel based resources such as gasoline and diesel, especially in the transportation industry [1]. The consequences of this utilization are excessive emission of greenhouse gases and degradation of air quality, which have raised significant environmental concerns. Added to this, concerns over the eventual depletion of fossil fuels has accelerated the exploration and development of new energy sources. At the same time, increasingly stringent regulations have been imposed to enhance the fuel efficiency and minimize emissions in automobiles. Efforts to meet current and future regulation targets have led to the development of new technologies, some of which are: a) vehicle electrification [2], b) gasoline direct injection technology [3], c) variable valve timing [4], d) advanced exhaust gas recirculation [5], and e) selective catalytic reduction for NOx [6]. On the energy front, wind and solar technologies have been vastly explored [7], but these technologies are time-dependent and intermittent in nature and must be supplemented by energy storage devices. Lithium-ion batteries have been considered the most preferred technology for grid energy storage and electrified transportation because of their higher energy and power densities, better efficiency, and longer lifespan in comparison with other energy storage devices such as lead acid, nickel metal hydride, and nickel cadmium [8]. Lithium-ion batteries are the most dominant technology today in small scale applications such as portable phones and computers [9]. However, their wide-scale adoption in automotive and grid energy storage applications has been hampered by concerns associated with battery life, safety, and reliability. A lack of comprehensive understanding of battery behavior across different environments and operating conditions make it challenging to extract their best performance. Currently, significant trade-offs are being made to optimize battery performance, such as over-sizing and under-utilization in automotive applications. While sensors are used to evaluate battery performance and regulate their operation, their fundamental limitation lies in the inability to measure battery internal states such as state-of-charge (SoC) or state-of-health (SoH). The aforementioned issues with lithium-ion batteries can addressed to a large extent with the help of mathematical modeling. They play an important role in the design and utilization of batteries in an efficient manner with existing technologies, because of their ability to predict battery behavior with minimal expenditure of time and materials [10]. While empirical mathematical models are computationally efficient, they rely on a significant amount of experimental data and calibration effort to predict future battery behavior. In addition, such models do not consider the underlying physicochemical transport processes and hence cannot predict battery degradation. Moreover, the knowledge acquired from such models cannot be generalized across different battery chemistry and geometry. This elucidates the need for fundamental physics-based mathematical models to aid in the development of advanced control strategies through model-based control and virtual sensor deployment. Such models can capture the underlying transport phenomena across various length and time scales, and enhance performance and longevity of batteries while ensuring safe operation. The overarching aim of this dissertation is to present a multiscale modeling approach that captures the behavior of such devices with high fidelity, starting from fundamental principles. The application of this modeling approach is focused on porous lithium-ion batteries. The major outcome of this work is to facilitate the development of advanced and comprehensive battery management systems by: a) developing a high fidelity multiscale electrochemical modeling framework for lithium-ion batteries, b) investigating the temperature-influenced and aging-influenced multiscale dynamics for different battery chemistry and operating conditions, c) formulating a methodology to analytically determine effective ionic transport properties using the electrode microstructure, and d) numerical simulation of the developed physics-based model and comparison analysis with the conventionally used Doyle-Fuller-Newman (DFN) electrochemical model. The new multiscale model presented in this dissertation has been derived using a rigorous homogenization approach which uses asymptotic expansions of variables to determine the macroscopic formulation of pore-scale governing transport equations. The conditions that allow successful upscaling from pore-to-macro scales are schematically represented using 2-D electrode and electrolyte phase diagrams. These phase diagrams are used to assess the predictability of macroscale models for different electrode chemistry and battery operating conditions. The effective transport coefficients of the homogenized model are determined by resolving a unit cell closure variable problem in the electrode microstructure, instead of conventionally employed empirical formulations. The equations of the developed full order homogenized multiscale (FHM) model are implemented and resolved using the finite element software COMSOL Multiphysics®. Numerical simulations are presented to demonstrate the enhanced predictability of the FHM against the traditionally used DFN model, particularly at higher temperatures of battery operation. Model parameter identification is performed by co-simulation studies involving COMSOL Multiphysics® and MATLAB® software using the Particle Swarm Optimization (PSO) technique. The parameter identification studies are performed using data from laboratory experiments conducted on 18650 cylindrical lithium-ion cells of nickel-manganese-cobalt oxide (NMC) cathode chemistry

Computational modeling of Li-ion batteries

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Phase Separation Dynamics in Isotropic Ion-Intercalation Particles

Lithium-ion batteries exhibit complex nonlinear dynamics, resulting from diffusion and phase transformations coupled to ion intercalation reactions. Using the recently developed Cahn-Hilliard reaction (CHR) theory, we investigate a simple mathematical model of ion intercalation in a spherical solid nanoparticle, which predicts transitions from solid-solution radial diffusion to two-phase shrinking-core dynamics. This general approach extends previous Li-ion battery models, which either neglect phase separation or postulate a spherical shrinking-core phase boundary, by predicting phase separation only under appropriate circumstances. The effect of the applied current is captured by generalized Butler-Volmer kinetics, formulated in terms of diffusional chemical potentials, and the model consistently links the evolving concentration profile to the battery voltage. We examine sources of charge/discharge asymmetry, such as asymmetric charge transfer and surface "wetting" by ions within the solid, which can lead to three distinct phase regions. In order to solve the fourth-order nonlinear CHR initial-boundary-value problem, a control-volume discretization is developed in spherical coordinates. The basic physics are illustrated by simulating many representative cases, including a simple model of the popular cathode material, lithium iron phosphate (neglecting crystal anisotropy and coherency strain). Analytical approximations are also derived for the voltage plateau as a function of the applied current

Capacity Fade Analysis and Model Based Optimization of Lithium-ion Batteries

Electrochemical power sources have had significant improvements in design, economy, and operating range and are expected to play a vital role in the future in a wide range of applications. The lithium-ion battery is an ideal candidate for a wide variety of applications due to its high energy/power density and operating voltage. Some limitations of existing lithium-ion battery technology include underutilization, stress-induced material damage, capacity fade, and the potential for thermal runaway. This dissertation contributes to the efforts in the modeling, simulation and optimization of lithium-ion batteries and their use in the design of better batteries for the future. While physics-based models have been widely developed and studied for these systems, the rigorous models have not been employed for parameter estimation or dynamic optimization of operating conditions. The first chapter discusses a systems engineering based approach to illustrate different critical issues possible ways to overcome them using modeling, simulation and optimization of lithium-ion batteries. The chapters 2-5, explain some of these ways to facilitate: i) capacity fade analysis of Li-ion batteries using different approaches for modeling capacity fade in lithium-ion batteries,: ii) model based optimal design in Li-ion batteries and: iii) optimum operating conditions: current profile) for lithium-ion batteries based on dynamic optimization techniques. The major outcomes of this thesis will be,: i) comparison of different types of modeling efforts that will help predict and understand capacity fade in lithium-ion batteries that will help design better batteries for the future,: ii) a methodology for the optimal design of next-generation porous electrodes for lithium-ion batteries, with spatially graded porosity distributions with improved energy efficiency and battery lifetime and: iii) optimized operating conditions of batteries for high energy and utilization efficiency, safer operation without thermal runaway and longer life

Mechanistic modelling of electrochemical ageing reactions at the graphite anode of lithium-ion batteries

Lithium-Ionen-Batterien spielen eine wichtige Rolle in einer Gesellschaft, die immer mehr von den Auswirkungen des Klimawandels betroffen ist. Daher ist es notwendig, die CO2-Emissionen und den Verbrauch fossiler Brennstoffe zu reduzieren. Gegenwärtig scheinen Lithium-Ionen-Batterien die idealen Kandidaten für diese Herausforderung zu sein, aber es bedarf weiterer Forschung und Entwicklung, um ihr Verhalten zu verstehen, ihre Grenzen zu kennen und dadurch ihre Leistung zu verbessern. Hierbei haben sich mathematische Modelle und numerische Simulation als Standardtechniken in der Forschung und Entwicklung von Lithium-Ionen-Batterien etabliert und als sehr nützlich erwiesen, um experimentelle Arbeiten zu unterstützen und die Genauigkeit von Modellen zur Lebenserwartungsvorhersage zu erhöhen. Diese Arbeit konzentriert sich auf die elektrochemischen Alterungsreaktionen in der Anode, insbesondere auf das Thema Lithium-Plating und dessen Wechselwirkung mit dem Solid-Electrolyte-Interface (SEI). Ziel dieser Arbeit ist ein tieferes Verständnis dieser Degradationsprozesse durch die Verwendung verfeinerter Modellierungsansätze und der Analyse von Simulationen über einen weiten Bereich von Betriebsbedingungen. Die zugrunde liegenden Gleichungen sind im hauseigenen multiphysikalischen Softwarepaket DENIS implementiert, für die elektrochemische Modellbeschreibung wird der Open Source Code für chemische Kinetik CANTERA verwendet. Die Entwicklung, Parametrierung und experimentelle Validierung eines umfassenden pseudo-dreidimensionalen Multiphysik-Modells einer kommerziellen Lithium-Ionen-Zelle mit Mischkathode und Graphitanode wird vorgestellt. Dieses Modell ist in der Lage, sowohl den Wärme- und Massentransport auf mehreren Skalen, als auch komplexe elektrochemische Reaktionsmechanismen zu beschreiben und zu simulieren, einschließlich der Fähigkeit, eine Mischelektrode zu simulieren, in der mehrere Aktivmaterialien einer Interkalations-/Deinterkalations-Reaktion ausgesetzt sind. Es folgt eine Erweiterung, um den reversiblen Lithium-Plating Vorgang darstellen zu können und die Vorhersage des Alterungsverhaltens über einen weiten Bereich von Bedingungen vorher sagen zu können, wobei der Schwerpunkt auf hohen Strömen und niedrigen Temperaturen liegt, die insbesondere im Feld der Schnellladung interessant sind. Dieses erweiterte Modell wird durch Vergleich mit veröffentlichten experimentellen Ergebnissen überprüft, die ein Spannungsplateau und einen Spannungsabfall als Plating-Indikatoren zeigen, und beinhaltet optional eine explizite Reinterkalationsreaktion, die makroskopische Hinweise auf Plating im speziellen Fall einer Zelle, die keine offensichtlichen Plattierungszeichen zeigt, unterdrückt. Dieses Modell wird verwendet, um Degradationskarten über einen weiten Bereich von Bedingungen und eine eingehende raum-zeitliche Analyse des Anodenverhaltens auf der mesoskopischen und mikroskopischen Skala zu erstellen, um die dynamische und nichtlineare Wechselwirkung zwischen der Interkalations-Reaktion und den Plating-Reaktionen zu demonstrieren. Es wird ein vertiefender Ausblick auf die SEI-Bildung und das SEI-Wachstum gegeben, zusammen mit der qualitativen Beschreibung von drei verschiedenen 1D-Modellen mit abnehmendem Detaillierungsgrad, die mit dem Ziel entwickelt wurden, in Zukunft idealerweise in umfassendere Multiskalen-Modelle einbezogen zu werden. Schließlich wird das erweiterte Modell erfolgreich mit einem zuvor entwickelten SEI-Modell gekoppelt, so dass ein umfassendes Modellgerüst entsteht, das in der Lage ist, sowohl Degradationsprozesse als auch deren kontinuierliche positive Rückkopplung zu simulieren