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...

Data science, hailed as the fourth paradigm of science, is a rapidly growing field which has served to revolutionize the fields of bio-informatics and climate science and can provide significant speed improvements in the discovery of new materials, mechanisms, and simulations. Data science techniques are often used to analyze and predict experimental data, but they can also be used with simulated data to create surrogate models. Chief among the data science techniques in this application is machine learning (ML), which is an effective means for creating a predictive relationship between input and output vector pairs. Physics-based battery models, like the comprehensive pseudo-two-dimensional (P2D) model, offer increased physical insight, increased predictability, and an opportunity for optimization of battery performance which is not possible with equivalent circuit (EC) models. In this work, ML-based surrogate models are created and analyzed for accuracy and execution time. Decision trees (DTs), random forests (RFs), and gradient boosted machines (GBMs) are shown to offer trade-offs between training time, execution time, and accuracy. Their ability to predict the dynamic behavior of the physics-based model are examined and the corresponding execution times are extremely encouraging for use in time-critical applications while still maintaining very high (∼99%) accuracy. Data science, also known as data-intensive scientific discovery, is hailed as the fourth paradigm of science.1 A field focused on extracting knowledge or understanding from data, it includes the subdomains of machine learning, classification, data mining, databases, and data visualization. In the age of internet-scale data, these techniques are not only powerful, but also necessary to extract the signal from the noise and to have the throughput to do so in a reasonable amount of time. It has revolutionized the fields of bio-informatics, climate science, word recognition, advertising, medicine, and is finding more applications daily. In Google's Translate application, substantial improvements over previous methods were achieved using artificial neural network (ANN) structures, making 60% fewer errors than the previous state-ofthe-art algorithm.2 In climate science, where models are sophisticated and numerous, data science techniques are used to determine which of 20 models will give the best prediction on future and historical data, the accuracy of which surpasses the accuracy of the average of all models, the current benchmark.3 As chemical engineers are increasingly tasked with the analysis of more complex data sets, these same data science tools which have revolutionized other fields become more relevant. 4 When data sets grow, they must be managed intentionally in order to be useful. Data management, a subfield of data science, fills this role and gives the tools to be able to correct for missing data points, ensure consistency of the data, and transform the content of the data such that it is suitable for use in other aspects of data science....

This article introduces a lumped electrochemical model for lithium-ion batteries. The governing equations of the standard ‘pseudo 2-dimensional’ (p2D) model are volume-averaged over each region in a cathode-separator-anode representation. This gives a set of equations in which the evolution of each averaged variable is expressed as an overall balance containing internal source terms and interfacial fluxes. These quantities are approximated to ensure mass and charge conservation. The averaged porous domains may thus be regarded as three ‘tanks-in-series’. Predictions from the resulting equation system are compared against the p2D model and simpler Single Particle Model (SPM). The Tanks-in-Series model achieves substantial agreement with the p2D model for cell voltage, with error metrics of <15 mV even at rates beyond the predictive capability of SPM. Predictions of electrochemical variables are examined to study the effect of approximations on cell-level predictions. The Tanks-in-Series model is a substantially smaller equation system, enabling solution times of a few milliseconds and indicating potential for deployment in real-time applications. The methodology discussed herein is generalizable to any model based on conservation laws, enabling the generation of reduced-order models for different battery types. This can potentially facilitate Battery Management Systems for various current and next-generation batteries.

Dalvi and Suresh (AIChE J.20115713291338) proposed a model for the kinetics of a reaction between two particulate solids A and B, where B is the diffusing component, in terms of the average number of contact points N AB between the two types of particles. In the present work, the applicability and validity of the model is studied, taking the formation of tricalcium aluminate from its immediate precursors as a candidate reaction. Partial analytical solutions to the Dalvi–Suresh model have been derived, and a simple parameter-estimation methodology has been developed. The data clearly show an influence of N AB, and use of the Ginstling–Brounshtein model (Appl. Chem. USSR19502313271338) for parameter estimation leads to diffusivity values that depend on N AB in a systematic way. Parameters estimated using the Dalvi–Suresh model, on the other hand, show only a random scatter and also show reasonable agreement with the values of diffusivity of Ca in oxides.

Optimal operation of lithium-ion batteries requires robust battery models for advanced battery management systems (ABMS). A nonlinear model predictive control strategy is proposed that directly employs the pseudo-two-dimensional (P2D) model for making predictions. Using robust and efficient model simulation algorithms developed previously, the computational time of the nonlinear model predictive control algorithm is quantified, and the ability to use such models for nonlinear model predictive control for ABMS is established.