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 paper reviews efforts in the modeling and simulation of lithium-ion batteries and their use in the design of better batteries. Likely future directions in battery modeling and design including promising research opportunities are outlined.

In this paper, a simple transformation of coordinates is proposed that facilitates the efficient simulation of the non-isothermal lithium-ion pseudo 2-D battery model. The transformed model is then conveniently discretized using orthogonal collocation with the collocation points in the spatial direction. The resulting system of differential algebraic equations (DAEs) is solved using efficient adaptive solvers in time. A series of mathematical operations are performed to reformulate the model to enhance computational efficiency and programming convenience while maintaining accuracy even when non-linear or temperature dependent parameters are used. The transformed coordinate allows for efficient simulation and extension from cell sandwich to stack models. Furthermore, the transformation and reformulation techniques are used to simulate operation of an 8-cell battery stack subject to varying heat transfer coefficients as well as specified temperature boundary conditions. Mathematical modeling and simulation of the operation of lithiumion batteries is not trivial, as concentration and potential fields must be evaluated simultaneously in both solid and liquid phases. This is complicated by the fact that the transport and kinetic parameters which determine battery behavior are highly nonlinear, leading to very complex governing equations. Doyle et al. 1 developed a general model based on concentrated solution theory to describe the internal behavior of a lithium-ion sandwich consisting of positive and negative porous electrodes, a separator, and current collectors. 2 This model proved generic enough to incorporate further advancements in battery systems understanding, leading to the development of a number of similar models. 3-13 Reviews of models for lithium-ion batteries can be found elsewhere in the literature. [10][11][12] Table I depicts a pseudo-twodimensional isothermal model for a lithium-ion battery. 14-16 Table II presents the various expressions used in the model, while Table III shows the physical parameters used in this paper. For analysis and control of lithium-ion batteries in hybrid environments (e.g. with a fuel cell, capacitor, or other electrical components), there is a need to simulate state of charge, state of health, and other parameters of lithium-ion batteries in milliseconds. Full-order physics-based models may simulate discharge curves in several seconds to minutes, depending on the solvers, routines, computers, etc. In contrast, empirical models (based on correlations of past data) can simulate specific operating scenarios in milliseconds. However, use of these models under a different operating condition than for which they were developed may cause abuse or underutilization of electrochemical power sources. This paper presents a coordinate transformation and mathematical analysis for reformulation of physics-based models to solve them quickly, conveniently, and accurately in a way that is valid for a wide range of operating conditions and parameters. The porous electrode model as given in Ta...

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The properties and chemical composition of the solid-electrolyte-interface (SEI) layer have been a subject of intense research due to their importance in the safety, capacity fade, and cycle life of Li-ion secondary batteries. In this paper, Kinetic Monte Carlo (KMC) simulation is applied to explore the formation of the passive SEI layer in the tangential direction of the lithium-ion intercalation in a graphite anode. The simulations are consistent with experimental observations that the active surface coverage decreases with time slowly in the initial stages of the battery operation, and then decreases rapidly. The effects of operating parameters such as the exchange current density, charging voltage, and temperature on the formation of the passive SEI layer are investigated. The active surface coverage at the end of each charging cycle remained constant for more cycles at higher temperature, but was lower at later cycles. The temperature that optimizes the active surface in a lithium-ion battery at cycle 1 can result in much lower active surface for most of the battery life. The potential for coupling the KMC model with porous electrode theory-continuum models is discussed to arrive at a multiscale model for understanding, analyzing, and minimizing capacity fade.

Improving the efficiency and utilization of battery systems can increase the viability and cost-effectiveness of existing technologies for electric vehicles (EVs). Developing smarter battery management systems and advanced sensing technologies can circumvent problems arising due to capacity fade and safety concerns. This paper describes how efficient simulation techniques and improved algorithms can alleviate some of these problems to help electrify the transportation industry by improving the range of variables that are predictable and controllable in a battery in real-time within an electric vehicle. The use of battery models in a battery management system (BMS) is reviewed. The effect of different simulation techniques on computational cost and accuracy are also compared, and the validity of implementation in a microcontroller environment for model predictive control (MPC) is addressed. Using mathematical techniques to add more physics without losing efficiency is also discussed. Behavioral predictions can be made using mathematical models without the need to directly observe the states using expensive and time consuming physical experiments. Such predictions allow for more intelligent design of new systems, which is generally limited by the mathematical techniques used and the computational resources available. An improved modeling and simulation approach can achieve the following goals when applied to engineering systems: r More accurate predictions by using more meaningful models r Faster simulation with fewer computational resources r Optimization of design parameters r Better control, allowing aggressive performance while maintaining safetyHere we focus on the application of such principles to the use of physics-based battery models in battery management systems in electric vehicles.In recent years, battery electric vehicles (BEV) have increased in popularity to reduce the dependence on fossil fuels. Lithium-ion batteries are a popular choice as an energy storage medium for high demand applications due to their large energy density but are not utilized to their full capacity in BEV applications; operating a Li-ion battery too aggressively can lead to reduced cycle life and unpredictable thermal runaway reactions. These challenges reduce the functional capacity of the battery available for propulsion.The consumer expects the vehicle's performance and capabilities to remain uniform regardless of the state of charge or age of the battery, as they have become accustomed to internal combustion engines. When the battery is nearly depleted, it is difficult or impossible to satisfy high power demand, which is aggravated as the battery ages. To avoid these difficulties, the BMS shuts off the battery with a large amount of energy unused, so that Li-ion batteries for EVs are greatly overdesigned and carry extra weight and volume, reducing efficiency and increasing cost.1 Research is underway to better understand the internal limitations of Li-ion batteries including SEI layer growth, side * Electrochemical Society ...

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 paper, the reformulated model is used to allow for more complicated physical phenomena to be considered for study, including thermal effects. There is an increasing societal pressure to utilize alternative energy sources to supplant the high use of fossil fuels. As energy and power demand is continually increasing, both in terms of grid usage and for transportation, there has been more interest in developing renewable energy sources. One problem with renewable energy sources is the intermittent nature and short-term unpredictability of supply of sources such as wind and solar. Thus, in order to match supply and demand, some form of energy storage is required, and lithium-ion battery technologies are one possible solution. Furthermore, electric vehicles are increasing in popularity as the price of liquid fuels generally increase. Lithium-ion batteries are a popular choice for electric vehicles because of their high energy and power density compared to other battery chemistries.The performance of lithium-ion batteries is highly dependent on the conditions at which they are exposed as well as the state of the internal variables. This has led to the development of several mathematical models to simulate battery behavior, ranging from simple empirical-based models or circuit based models 1,2 to computationally expensive mole...

Capacity fade experienced by electric vehicle (EV) and plug-in hybrid electric vehicle (PHEV) batteries will affect the economic and technological value of the battery pack during EV life as well as the value of the battery at the end of life. The growth of the solid-electrolyte interface (SEI) layer is a major cause of capacity fade. We studied the fade caused by SEI layer growth for eight different driving cycles (which include regenerative braking), and six charging protocols. In addition, we looked at the growth caused by varying the depth of discharge during cycling. Constant current and constant current-constant voltage charging patterns at differing rates were studied. Results showed that for half of the driving cycles regenerative braking increased the life-time energy utilization of the battery in addition to increasing the capacity during a single cycle. For the other half of the driving cycles it is shown that while regenerative braking may be beneficial during a single cycle, over the life of the battery it can decrease the total usable energy. These cases were studied using a reformulated porous electrode pseudo two dimensional model that included SEI layer growth as a side reaction. While working electric vehicles (EV) have been in existence for over a century (a lead-acid battery powered car achieved speeds of 30m/s in 1899), the price of EVs has not become competitive with their internal combustion engine (ICE) counterparts.1 EV sales are currently aided by subsidies ranging from $3,000 in China to $7,500 in the US and Western Europe to $10,000 in Japan.2 One of the causes of the high prices of EVs is the expensive nature of the vehicle's battery pack, which is not required by ICE vehicles running entirely on gas (hybrids operate on a combination of both systems with plug-in hybrid electric vehicles (PHEV) being able to operate in an all-electric mode). Most currently available and planned EVs (and PHEVs) use a lithium-ion (Li-ion) battery chemistry. Li-ion EV battery pack costs are estimated at between $600-$1,200 per kWh of energy capacity. 2,3 This price can cause battery packs to cost in excess of $10,000 per vehicle and account for 30-50% of total vehicle cost. 4 Decreasing the price of the battery pack will be extremely important in making EVs price competitive in the automobile market.As EV and PHEVs age, their battery packs will have to be replaced due to capacity and power fade. Power fade is defined as the loss of cell power caused by increased cell impedance from aging. Capacity fade is defined as the loss of energy storage capacity due to degradation caused by cycling.5 Based on present requirements, EV batteries that have lost 20% of their initial factory capacity are no longer useful for automotive use and should be replaced. 6 Typically, an EV battery will last between 5 to 10 years within its automotive application depending on driving and charging patterns. Nissan estimates that the battery installed in the 2011 Nissan Leaf will contain approximately 80% of its original capacity ...

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