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.
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.
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.
The use of energy is required to make human life comfortable and energy storage is as critical as energy supply. Among the different systems that can be utilized for the storage of energy, batteries are one of the most common and portable ones. Moreover, there has been a growing demand for lithium-ion Batteries (LIBs) over the last few decades due to their high performance within cycle life, energy and power density. One of the major concerns of LIBs is the safe operations and the prevention of a battery causing fire or explosion, which is known as “thermal runaway”. In this study, two different ways to prevent catastrophic thermal runaway will be investigated. One way is to develop a thermoelectrochemical model to predict thermal behavior of a battery. In this case, the investigation of thermodynamic quantities such as entropy change is essential as it is directly related to temperature prediction of the system. In this study, the typical methodologies to measure the entropy change were investigated. It has been shown that side reactions of cells can interfere with obtaining accurate measurement results of entropy changes. Moreover, a physics-based electrochemical model was introduced for the new methodology to measure entropy change which is known as “the frequency-domain method”. Differing from the initial frequency domain method, the change of entropy is physically coupled to the internal state changes of batteries. This method reduces the time of the entropy change measurement by scale of 100, in comparison to the traditional methods. Solid-state batteries are another potential solution to preventing thermal runaway as they have excellent thermal stability. In this study, an electrochemical model for the all-solid-state lithium-ion batteries has been developed. For the purpose of maintaining efficient control algorithm development, the model was simplified. A sensitivity analysis was conducted to observe the model accuracy in the simplified models. It was concluded from the simulation results that all the simplified models have sufficient accuracies in the voltage and capacity prediction; and it can serve as a useful tool for the state estimation.
Electric vehicles contain hundreds of high-energy density lithium-ion batteries. The crashworthiness of these vehicles can be improved by better understanding the response of these batteries in an event of an accident or abusive loads. These loads can induce short-circuit and thermal runways in extreme cases. Therefore, an efficient finite element model of a battery that can precisely predict the coupled multi-physics behavior of a cell in a real-world application is desired. This investigation incorporates detailed and homogenized multi-physics modeling of various form factors of lithium-ion batteries. In the first two chapters of this thesis, a multi-physics homogenized model of a pouch cell was developed and validated in a wide range of multi-disciplines of the battery. In contrast to other similar models described in the literature, which are only applicable in certain scenarios, this model has a much broader range of applications due to the innovative techniques developed for material calibration and cell modeling. In addition, due to the homogenized nature and computational cost efficiency of this technique, the developed model has significance in the crashworthiness analysis of battery packs and electric vehicles where hundreds of these batteries exist. In the final chapter, a detailed layered model of an 18650 cylindrical cell was developed. Component and cell-level tests were performed on the cell to calibrate the material properties and extract the geometries of all the components of the cell. This model is the first of its kind that precisely predicts the load-displacement response and shape of deformation in various loading scenarios. This developed model has crucial importance in the safety assessment of the batteries by providing insight into the sequence of deformation of the internal layers and components and their interplay during mechanical abuse loadings. Overall, the two developed models in this thesis provide battery-related industries with a tool to improve the safety of future electrified industries.
Understanding the combined electrochemical-thermal and mechanical response of a system has a variety of applications, for example, structural failure from electrochemical fatigue and the potential induced changes of material properties. For lithium-ion batteries, there is an added concern over the safety of the system in the event of mechanical failure of the cell components. In this work, we present a generic multi-scale simultaneously coupled mechanical-electrochemical-thermal model to examine the interaction between mechanical failure and electrochemical-thermal responses. We treat the battery cell as a homogeneous material while locally we explicitly solve for the mechanical response of individual components using a homogenization model and the electrochemical-thermal responses using an electrochemical model for the battery. A benchmark problem is established to demonstrate the proposed modeling framework. The model shows the capability to capture the gradual evolution of cell electrochemical-thermal responses, and predicts the variation of those responses under different short-circuit conditions.
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.
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.
Energy-storing electrochemical batteries are the most critical components of high energy density storage systems for stationary and mobile applications. Lithium-ion batteries have received considerable interest for hybrid electric vehicles (HEV) because of their high specific energy, but face inherent thermal management challenges that have not been adequately addressed. In the present investigation, a fully coupled electrochemical and thermal model for lithium-ion batteries is developed to investigate the impact of different thermal management strategies on battery performance. This work represents the first ever study of these coupled electrochemical-thermal phenomena in batteries from the electrochemical heat generation all the way to the dynamic heat removal in actual HEV drive cycles. In contrast to previous modeling efforts focused either exclusively on particle electrochemistry on the one hand or overall vehicle simulations on the other, the present work predicts local electrochemical reaction rates using temperature-dependent data on commercially available batteries designed for high rates (C/LiFePO4) in a computationally efficient manner. Simulation results show that conventional external cooling systems for these batteries, which have a low composite thermal conductivity (~1 W/m-K), cause either large temperature rises or internal temperature gradients. Thus, a novel, passive internal cooling system that uses heat removal through liquid-vapor phase change is developed. Although there have been prior investigations of phase change at the microscales, fluid flow at the conditions expected here is not well understood. A first-principles based cooling system performance model is developed and validated experimentally, and is integrated into the coupled electrochemical-thermal model for assessment of performance improvement relative to conventional thermal management strategies. The proposed cooling system passively removes heat almost isothermally with negligible thermal resistances between the heat source and cooling fluid. Thus, the minimization of peak temperatures and gradients within batteries allow increased power and energy densities unencumbered by thermal limitations.
Vehicle crashes can lead to crushing of the battery, damaging lithium ion battery cells and causing local shorts, heat generation, and thermal runaway. Simulating all the physics and geometries at the same time is challenging and takes a lot of effort; thus, simplifications are needed. We developed a material model for simultaneously modeling the mechanical-electrochemical-thermal behavior, which predicted the electrical short, voltage drop, and thermal runaway behaviors followed by a mechanical abuse-induced short. The effect of short resistance on the battery cell performance was studied.
