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Book Multiscale Modeling  Reformulation  and Efficient Simulation of Lithium ion Batteries

Download or read book Multiscale Modeling Reformulation and Efficient Simulation of Lithium ion Batteries written by Paul Wesley Clairday Northrop and published by . This book was released on 2014 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Book Efficient Simulation and Model Reformulation of Two dimensional Electrochemical Thermal Behavior of Lithium ion Batteries

Download or read book Efficient Simulation and Model Reformulation of Two dimensional Electrochemical Thermal Behavior of Lithium ion Batteries written by and published by . This book was released on 2015 with total page 12 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lithium-ion batteries are an important technology to facilitate efficient energy storage and enable a shift from petroleum based energy to more environmentally benign sources. Such systems can be utilized most efficiently if good understanding of performance can be achieved for a range of operating conditions. Mathematical models can be useful to predict battery behavior to allow for optimization of design and control. An analytical solution is ideally preferred to solve the equations of a mathematical model, as it eliminates the error that arises when using numerical techniques and is usually computationally cheap. An analytical solution provides insight into the behavior of the system and also explicitly shows the effects of different parameters on the behavior. However, most engineering models, including the majority of battery models, cannot be solved analytically due to non-linearities in the equations and state dependent transport and kinetic parameters. The numerical method used to solve the system of equations describing a battery operation can have a significant impact on the computational cost of the simulation. In this paper, a model reformulation of the porous electrode pseudo three dimensional (P3D) which significantly reduces the computational cost of lithium ion battery simulation, while maintaining high accuracy, is discussed. This reformulation enables the use of the P3D model into applications that would otherwise be too computationally expensive to justify its use, such as online control, optimization, and parameter estimation. Furthermore, the P3D model has proven to be robust enough to allow for the inclusion of additional physical phenomena as understanding improves. In this study, the reformulated model is used to allow for more complicated physical phenomena to be considered for study, including thermal effects.

Book Multiscale Simulation Approach for Battery Production Systems

Download or read book Multiscale Simulation Approach for Battery Production Systems written by Malte Schönemann and published by Springer. This book was released on 2017-01-05 with total page 187 pages. Available in PDF, EPUB and Kindle. Book excerpt: Addressing the challenge of improving battery quality while reducing high costs and environmental impacts of the production, this book presents a multiscale simulation approach for battery production systems along with a software environment and an application procedure. Battery systems are among the most important technologies of the 21st century since they are enablers for the market success of electric vehicles and stationary energy storage solutions. However, the performance of batteries so far has limited possible applications. Addressing this challenge requires an interdisciplinary understanding of dynamic cause-effect relationships between processes, equipment, materials, and environmental conditions. The approach in this book supports the integrated evaluation of improvement measures and is usable for different planning horizons. It is applied to an exemplary battery cell production and module assembly in order to demonstrate the effectiveness and potential benefits of the simulation.

Book Multiscale Modeling and Characterization for Performance and Safety of Lithium ion Batteries

Download or read book Multiscale Modeling and Characterization for Performance and Safety of Lithium ion Batteries written by and published by . This book was released on 2015 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Lithium-ion batteries are highly complex electrochemical systems whose performance and safety are governed by coupled nonlinear electrochemical-electrical-thermal-mechanical processes over a range of spatiotemporal scales. In this paper we describe a new, open source computational framework for Lithium-ion battery simulations that is designed to support a variety of model types and formulations. This framework has been used to create three-dimensional cell and battery pack models that explicitly simulate all the battery components (current collectors, electrodes, and separator). The models are used to predict battery performance under normal operations and to study thermal and mechanical safety aspects under adverse conditions. The model development and validation are supported by experimental methods such as IR-imaging, X-ray tomography and micro-Raman mapping.

Book Multiscale Modeling of Degradation in Lithium ion Batteries

Download or read book Multiscale Modeling of Degradation in Lithium ion Batteries written by Fridolin Röder and published by . This book was released on 2019 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a comprehensive methodology for multiscale simulation of degradation in lithium-ion batteries. The work helps to understand battery degradation processes by revealing complex multiscale effects, which cannot be taken into account by single-scale models. A novel numerical method is presented, which dynamically couples molecular models based on kinetic Monte Carlo method with macroscopic models. Moreover, the work provides mathematical models of degradation on various length scales, e.g. heterogeneous side reactions on molecular scale and the restructuring of particle size distributions on electrode scale. Instead of describing processes separately, the multiscale methodology systematically analyzes interaction of degradation processes and cell operation. The presented methodology is certainly applicable to other electrochemical systems with considerable multi-scale nature.

Book Advanced Materials for Battery Separators

Download or read book Advanced Materials for Battery Separators written by Sabu Thomas and published by Elsevier. This book was released on 2024-07-01 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: Advanced Materials for Battery Separators focuses solely on battery separators and their significance, providing the reader with a detailed description of their use in both aqueous and non-aqueous batteries. Topics include separator requirements and classifications, as well as discussions of the different methods for the fabrication of separators, experimental techniques used for the characterization of separators, and their physical and chemical properties. It concludes with a look at the challenges and new technologies developed to improve the performance of separators. This book is a valuable reference for engineers, research scholars, and for graduates and post graduates primarily in the field of material science, electrochemistry, and polymer chemistry. It can also be useful for engineers and technologists working in both industry and the energy field. Provides a detailed discussion of separators used in battery applications Discusses the influence of nanofillers on separator performance and the analytical techniques used for the characterization of separators Explores the challenges and new technologies to improve the performance of separators

Book Efficient Models and Algorithms for Mass Conservation and Morphology Evolution in Lithium Metal Batteries

Download or read book Efficient Models and Algorithms for Mass Conservation and Morphology Evolution in Lithium Metal Batteries written by Taejin Jang and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The demand for energy storage devices with high energy density, coulombic efficiency, long-term stability, and high capacity while ensuring safety has never been higher. However, the efforts towards carbon neutrality and exploration of next-generation batteries for electric vehicles and mobile applications are still insufficient to meet the demands. The development of Lithium-ion batteries is a giant leap in achieving the utilization of lithium, which has high reactivity, mobility, and superior energy density along with high output voltage. However, there is one major area of improvement to advance the conventional lithium-ion batteries: the anode electrode. Lithium metal has the highest energy density among the other potential candidates for anodes, ahead of conventional graphite electrodes which are based on the intercalation of lithium ions. Despite the early research interests, the metal anode was not commercially successful due to safety concerns and inferior cyclability. Even today, those defects are challenging and need further research. Thus, to resolve the above-mentioned difficulties, there is a significant need for a fundamental understanding of the morphology changes during the deposition and stripping, specifically, the anomalies in the microscale, such as the formation of dendrites, local cavitation, and initial surface defects. These translate into macroscale as dendrite growth, depletion of the electrolyte by the continuous solid-electrolyte interface (SEI) layer growth, and formation of isolated regions called 'dead lithium'. This thesis focuses on the physics-based models and algorithms at different scales and varying complexity of the system to simulate the evolution of the anode surface in lithium metal batteries. This includes continuum, mesoscale and multiscale models conserving the system's total mass. The different approaches, such as coordinate transformation and phase-field model, are discussed with proper mathematical reformulation. Lastly, an effective algorithm for fast and accurate simulation is proposed with selected examples

Book Computationally Efficient Online Model Based Control and Estimation for Lithium ion Batteries

Download or read book Computationally Efficient Online Model Based Control and Estimation for Lithium ion Batteries written by Ji Liu and published by . This book was released on 2017 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation presents a framework for computationally-efficient, health-consciousonline state estimation and control in lithium-ion batteries. The framework buildson three main tools, namely, (i) battery model reformulation and (ii) pseudo-spectral optimization for (iii) differential flatness. All of these tools already existin the literature. However, their application to electrochemical battery estimationand control, both separately and in an integrated manner, represents a significantaddition to the literature. The dissertation shows that these tools, together, providesignificant improvements in computational efficiency for both online moving horizonbattery state estimation and online health-conscious model predictive battery con-trol. These benefits are demonstrated both in simulation and using an experimentalcase study.Two key facts motivate this dissertation. First, lithium-ion batteries are widelyused for different applications due to their low self-discharge rates, lack of memoryeffects, and high power/energy densities compared to traditional lead-acid and nickel-metal hydride batteries. Second, lithium-ion batteries are also vulnerable to agingand degradation mechanisms, such as lithium plating, some of which can lead tosafety issues. Conventional battery management systems (BMS) typically use model-free control strategies and therefore do not explicitly optimize the performance, lifespan, and cost of lithium-ion battery packs. They typically avoid internal damageby constraining externally-measured variables, such as battery voltage, current,and temperature. When pushed to charge a battery quickly without inducingexcessive damage, these systems often follow simple and potentially sub-optimalcharge/discharge trajectories, e.g., the constant-current/constant-voltage (CCCV)charging strategy. While the CCCV charging strategy is simple to implement,it suffers from its poor ability to explicitly control the internal variables causingbattery aging, such as side reaction overpotentials. Another disadvantage is theinability of this strategy to adapt to changes in battery dynamics caused by aging.Model-based control has the potential to alleviate many of the above limitationsof classical battery management systems. A model-based control system can estimate the internal state of a lithium-ion battery and use the estimated stateto adjust battery charging/discharging in a manner that avoids damaging sidereactions. By doing so, model-based control can (i) prolong battery life, (ii) improvebattery safety, (iii) increase battery energy storage capacity, (iv) decrease internaldamage/degradation, and (v) adapt to changes in battery dynamics resulting fromaging. These potential benefits are well-documented in the literature. However,one major challenge remains, namely, the computational complexity associatedwith online model-based battery state estimation and control. The goal of thisdissertation is to address this challenge by making five contributions to the literature.Specifically: Chapter 2 exploits the differential flatness of solid-phase lithium-ion batterydiffusion dynamics, together with pseudo-spectral optimization and diffusionmodel reformulation, to decrease the computational load associated withhealth-conscious battery trajectory optimization significantly. This contribu-tion forms a foundation for much of the subsequent work in this dissertation,but is limited to isothernal single-particle battery models with significanttime scale separation between anode- and cathode-side solid-phase diffusiondynamics. Chapter 3 extends the results of Chapter 2 in two ways. First , it exploitsthe law of conservation of charge to enable flatness-based, health-consciousbattery trajectory optimization for single particle battery models even in theabsence of time scale separation between the negative and positive electrodes.Second, it performs this optimization for a combined thermo-electrochemicalbattery model, thereby relaxing the above assumption of isothermal batterybehavior and highlighting the benefits of flatness-based optimization for anonlinear battery model. Chapter 4 presents a framework for flatness-based pseudo-spectral combinedstate and parameter estimation in lumped-parameter nonlinear systems.This framework enables computationally-efficient total least squares (TLS)estimation for lumped-parameter nonlinear systems. This is quite relevant topractical lithium-ion battery systems, where both battery input and outputmeasurements can be quite noisy. Chapter 5 utilizes the above flatness-based TLS estimation algorithm formoving horizon state estimation using a coupled thermo-electrochemicalequivalent circuit model of lithium-ion battery dynamics. Chapter 6 extends the battery estimation framework from Chapter 5 to enablemoving horizon, flatness-based TLS state estimation in thermo-electrochemical single-particle lithium-ion battery models, and demonstrates this frameworkusing laboratory experiments.The overall outcome of this dissertation is an integrated set of tools, all of themexploiting model reformulation, differential flatness, and pseudo-spectral methods,for computationally efficient online state estimation and health-conscious controlin lithium-ion batteries.

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

Download or read book A Modeling Framework for Efficient Reduced Order Simulations of Parametrized Lithium ion Battery Cells written by Manuel Landstorfer and published by . This book was released on 2021 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Book Modeling and Simulation of Lithium ion Power Battery Thermal Management

Download or read book Modeling and Simulation of Lithium ion Power Battery Thermal Management written by Junqiu Li and published by Springer Nature. This book was released on 2022-05-09 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Book Efficient Simulation and Abuse Modeling of Mechanical Electrochemical Thermal Phenomena in Li Ion Batteries

Download or read book Efficient Simulation and Abuse Modeling of Mechanical Electrochemical Thermal Phenomena in Li Ion Batteries written by and published by . This book was released on 2019 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This poster covered simultaneous coupling of electrochemical-thermal models with mechanical deformation in lithium ion batteries. Efficiency and stability of mechanical models was significantly enhanced by implementing electrochemical models into LS-DYNA using User-Defined Elements. Six case studies were built and licensed out to participants from Industry for initial testing and their feedback is being incorporated into these tools. Dynamic response of the cells was incorporated by measuring mechanical response of components at strain rates as high as 250 /s. Temperature range for property measurements was expanded (as high as 200 degrees C) to account for property changes at high temperatures experienced by cell components under battery abuse. Multi-cell validation has been expanded to include four different sets of experimental data, with support from various partners. Complex failure modes and fracture response are currently being investigated. These are still very challenging, given the limited amount of prior work available in the literature.

Book Modeling transport properties and electrochemical performance of hierarchically structured lithium ion battery cathodes using resistor networks and mathematical half cell models

Download or read book Modeling transport properties and electrochemical performance of hierarchically structured lithium ion battery cathodes using resistor networks and mathematical half cell models written by Birkholz, Oleg and published by KIT Scientific Publishing. This book was released on 2022-10-05 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hierarchically structured active materials in electrodes of lithium-ion cells are promising candidates for increasing gravimetric energy density and improving rate capability of the system. To investigate the influence of cathode structures on the performance of the whole cell, efficient tools for calculating effective transport properties of granular systems are developed and their influence on the electrochemical performance is investigated in specially adapted cell models.

Book Progress in Modeling and Simulation of Batteries

Download or read book Progress in Modeling and Simulation of Batteries written by John Turner and published by SAE International. This book was released on 2016-06-15 with total page 98 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modeling and simulation of batteries, in conjunction with theory and experiment, are important research tools that offer opportunities for advancement of technologies that are critical to electric motors. The development of data from the application of these tools can provide the basis for managerial and technical decision-making. Together, these will continue to transform batteries for electric vehicles. This collection of nine papers presents the modeling and simulation of batteries and the continuing contribution being made to this impressive progress, including topics that cover: • Thermal behavior and characteristics • Battery management system design and analysis • Moderately high-fidelity 3D capabilities • Optimization Techniques and Durability As electric vehicles continue to gain interest from manufacturers and consumers alike, improvements in economy and affordability, as well as adoption of alternative fuel sources to meet government mandates are driving battery research and development. Progress in modeling and simulation will continue to contribute to battery improvements that deliver increased power, energy storage, and durability to further enhance the appeal of electric vehicles.

Book Efficient Simulation and Abuse Modeling of Mechanical Electrochemical Thermal Phenomena in Lithium Ion Batteries

Download or read book Efficient Simulation and Abuse Modeling of Mechanical Electrochemical Thermal Phenomena in Lithium Ion Batteries written by and published by . This book was released on 2017 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: NREL's Energy Storage team is exploring the effect of mechanical crush of lithium ion cells on their thermal and electrical safety. PHEV cells, fresh as well as ones aged over 8 months under different temperatures, voltage windows, and charging rates, were subjected to destructive physical analysis. Constitutive relationship and failure criteria were developed for the electrodes, separator as well as packaging material. The mechanical models capture well, the various modes of failure across different cell components. Cell level validation is being conducted by Sandia National Laboratories.

Book A Multi stage Model Order Reduction Framework for Efficient Simulations of Parametrized Lithium ion Battery Cells

Download or read book A Multi stage Model Order Reduction Framework for Efficient Simulations of Parametrized Lithium ion Battery Cells written by Marie-Christin Zumbülte and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Book Towards a Systems level Understanding of Battery Systems

Download or read book Towards a Systems level Understanding of Battery Systems written by Akshay Subramaniam and published by . This book was released on 2021 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Book Effect of Design Parameters and Intercalation Induced Stresses in Lithium Ion Batteries

Download or read book Effect of Design Parameters and Intercalation Induced Stresses in Lithium Ion Batteries written by Sumitava De and published by . This book was released on 2014 with total page 131 pages. Available in PDF, EPUB and Kindle. Book excerpt: Electrochemical power sources, especially lithium ion batteries have become major players in various industrial sectors, with applications ranging from low power/energy demands to high power/energy requirements. But there are some significant issues existing for lithium ion systems which include underutilization, stress-induced material damage, capacity fade, and the potential for thermal runaway. Therefore, better design, operation and control of lithium ion batteries are essential to meet the growing demands of energy storage. Physics based modeling and simulation methods provide the best and most accurate approach for addressing such issues for lithium ion battery systems. This work tries to understand and address some of these issues, by development of physics based models and efficient simulation of such models for battery design and real time control purposes. This thesis will introduce a model-based procedure for simultaneous optimization of design parameters for porous electrodes that are commonly used in lithium ion systems. The approach simultaneously optimizes the battery design variables of electrode porosities and thickness for maximization of the energy drawn for an applied current, cut-off voltage, and total time of discharge. The results show reasonable improvement in the specific energy drawn from the lithium ion battery when the design parameters are simultaneously optimized. The second part of this dissertation will develop a 2-dimensional transient numerical model used to simulate the electrochemical lithium insertion in a silicon nanowire (Si NW) electrode. The model geometry is a cylindrical Si NW electrode anchored to a copper current collector (Cu CC) substrate. The model solves for diffusion of lithium in Si NW, stress generation in the Si NW due to chemical and elastic strain, stress generation in the Cu CC due to elastic strain, and volume expansion in the Si NW and Cu CC geometries. The evolution of stress components, i.e., radial, axial and tangential stresses in different regions in the Si NW are studied in details. Lithium-ion batteries are typically modeled using porous electrode theory coupled with various transport and reaction mechanisms with an appropriate discretization or approximation for the solid phase diffusion within the electrode particle. One of the major difficulties in simulating Li-ion battery models is the need for simulating solid-phase diffusion in the second radial dimension r within the particle. It increases the complexity of the model as well as the computation time/cost to a great extent. This is particularly true for the inclusion of pressure induced diffusion inside particles experiencing volume change. Therefore, to address such issues, part of the work will involve development of efficient methods for particle/solid phase reformulation - (1) parabolic profile approach and (2) a mixed order finite difference method. These models will be used for approximating/representing solid-phase concentration variations within the active material. Efficiency in simulation of particle level models can be of great advantage when these are coupled with macro-homogenous cell sandwich level battery models.