Efficient Simulation and Model Reformulation of Two-Dimensional Electrochemical Thermal Behavior of Lithium-Ion Batteries

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....

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“…16,20,21 For convenience, a summary of equations and parameters will be recounted in Table I, Table II, and Table III here.…”

Section: Choice Of the Modelmentioning

confidence: 99%

Data Science Approaches for Electrochemical Engineers: An Introduction through Surrogate Model Development for Lithium-Ion Batteries

Dawson-Elli

Lee

Pathak

et al. 2018

J. Electrochem. Soc.

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“…Other approaches 26,27 have been proposed for efficient simulation of battery models. Northrop et al 28,29 published a reformulated battery model, based on the original P2D model, and the reformulated model was used in this work to obtain the control profiles after implementing GMC. The set of equations and the corresponding parameters of the battery model are listed in Table III, Table IV and Table V (Reference 29).…”

Section: Generic Model Control For Battery Modelsmentioning

confidence: 99%

“…Equation 64 is differentiated with time to get the derivative of potential. In order to find derivative for other terms occurring in 29 …”

Section: Generic Model Control For Battery Modelsmentioning

confidence: 99%

Generic Model Control for Lithium-Ion Batteries

Pathak

Kolluri

Subramanian

2017

J. Electrochem. Soc.

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Battery Management Systems (BMS) are critical to safe and efficient operation of lithium-ion batteries and accurate prediction of the internal states. Smarter BMS that can estimate and implement optimal charging profiles in real-time are important for advancement of the Li-ion battery technology. Estimating optimal profiles using physics-based models is computationally expensive because of the non-linear and stiff nature of the model equations, involving the need for constrained nonlinear optimization. In this work, we present an alternative approach to control batteries called as Generic Model Control, or Reference System Synthesis. This work enables robust stabilization and control of battery models to set-point as an alternative approach, eliminating the need to perform optimization of nonlinear models. As compared to the generic model control approaches implemented by previous researchers, we implement the same concept using direct DAE numerical solvers. The results are presented for single input single objective problems, and for constrained problems for various battery models. Lithium-ion batteries are used in a wide range of applications ranging from cell phones to electric vehicles (EVs) to electric grids. With the expected decline in the price of batteries over the next few years, the market for EVs and grids is growing rapidly. Long recharging times, capacity fade and thermal runaway are some of the main issues that need to be addressed in order to use batteries safely and efficiently for a longer time. This necessitates the use of smarter battery management systems that can derive optimal use strategies by exploiting the dynamics of the battery.Battery models based on transport, physical, electrochemical and thermodynamics principles can be used to monitor the internal states of the battery and to obtain optimal control strategies. Such models are computationally expensive which limits their use in control applications in real-time. Various issues, such as the onset of dynamics of some internal states only during use of batteries at high charge/discharge rates, and several other states which are active only while charging or discharging, adds to the challenges of the observability of these physics-based electrochemical models. Hence, various approximated and reduced order models have been proposed in the past, to make the models strongly observable in local intervals. 1,[2][3][4][5] These models are also highly non-linear in nature, which adds significant challenges to implement control strategies along with the abovementioned issues. Past researchers have shown multivariable control techniques like Dynamic Matrix Control (DMC), 6 Internal Model Control (IMC), 7 and Model Predictive Heuristic Control (MPHC) 8 for a variety of systems. However, these models suffer from their reliability on the linear approximations of the experimentally obtained step-response data and do not directly consider the full nonlinear model explicitly. Several researchers have been working to design optimal charging profiles ...

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“…Recently, this method has also been applied along with coordinate transformation to deal with the non-zero, time-dependent boundary conditions in the solid phase. [25][26][27][28] In this paper, a general, "top-down" process for projection-based model order reduction is proposed to analytically approximate the nonlinear diffusion PDE into a low-order ODE system. First, trial solutions for the electrolyte concentration in the positive electrode, the separator and the negative electrode are firstly assumed as:ĉ…”

Section: Model Order Reduction Of the Nonlinear Diffusion Pdesmentioning

confidence: 99%

Modeling of Li-Ion Cells for Fast Simulation of High C-Rate and Low Temperature Operations

Fan

Pan

Canova

et al. 2016

J. Electrochem. Soc.

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Evaluation of Li-ion cell performance and life requires the ability to predict behavior at extreme conditions, such as low temperatures and high C-rates. Most electrochemical models assuming constant electrolyte diffusion properties fail to accurately predict the electrode and electrolyte potential at such conditions. This study presents a physics-based Extended Single Particle Model (ESPM) designed specifically for accurately predicting the behavior of a Li-ion cell at extreme conditions, incorporating concentrationdependent properties in the electrolyte diffusion dynamics. Since the proposed model aims at supporting long-term simulation, virtual design and optimization studies, minimization of the computational complexity is achieved through analytical Model Order Reduction (MOR) based on a Galerkin projection method. Results show that the implementation of the concentration-dependent diffusion properties leads to significant improvement of model accuracy at extreme conditions. The Reduced Order Model (ROM) can be simulated significantly faster than numerical methods with no loss of accuracy, supporting simulation of long-term usage cycles (10-year) and remaining useful life calculations. Lithium ion batteries are considered the state of the art for energy storage in electric and hybrid vehicles. When batteries operates at low temperature conditions, for instance during a cold start of an electric vehicle, the highly reduced ionic conductivity and diffusivity lead to the formation of large gradients in the electrolyte concentration within the cell domain.1,2 Large concentration gradients can also be established at high C-rate conditions, which typically occur when the battery is subject to fast charge/discharge current loads in cold weather. Therefore, it is important to accurately predict the cell electrochemical behavior and terminal voltage at such conditions, as performing fast charging procedures at low temperatures could severely shorten the cycle life due to lithium deposition on the anode. 1,3,4 Electrochemical battery models based on first principles have shown the ability to accurately predict the concentration dynamics and terminal voltage. [5][6][7][8][9][10][11] In particular, the pseudo two-dimensional model (or the P2D model) based on Porous Electrode Theory 5 and Single Particle Model 12 (SPM) have been widely used for modeling the dynamic response of Lithium ion cells to variable input current profiles. Recently, Extended Single Particle Models (ESPM) [13][14][15][16][17] incorporating the electrolyte dynamics have been developed to capture the cell behavior under high C-rates conditions, albeit with simpler mathematical structure than P2D models.While electrochemical models generally predict well the cell terminal voltage as function of current and temperature, they are characterized by the presence of coupled PDEs and nonlinear algebraic equations, increasing the mathematical complexity and leading to computational challenges when applied to fast simulation and to estimation or control desig...

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Efficient Simulation and Model Reformulation of Two-Dimensional Electrochemical Thermal Behavior of Lithium-Ion Batteries

Cited by 58 publications

References 65 publications

Data Science Approaches for Electrochemical Engineers: An Introduction through Surrogate Model Development for Lithium-Ion Batteries

Data Science Approaches for Electrochemical Engineers: An Introduction through Surrogate Model Development for Lithium-Ion Batteries

Generic Model Control for Lithium-Ion Batteries

Modeling of Li-Ion Cells for Fast Simulation of High C-Rate and Low Temperature Operations

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