Literature reports show both benefits and negligible impact when including graded electrodes in battery design, depending upon the exact model and conditions used. In this paper, we use two different optimization approaches for a secondary current distribution porous electrode model with nonlinear kinetics to confirm that computed solutions are correct. We use these confirmed optimal solutions to probe several ways that graded porosity can improve electrode performance. Single objective optimization such as reducing the overall electrode resistance using a graded electrode design provides a modest 4-6% reduction in resistance for typical lithium-ion battery parameters. Multiple objective optimization-for example, simultaneously considering electrode resistance and the overpotential variance and eventually the overpotential average as well-shows that multilayer designs open up a much richer feasible design space for achieving multiple goals. The ultimate answer to the value of graded electrodes will be the techno-economic analysis that links the benefits of an expanded optimal design space to the detrimental costs associated with manufacturing multilayer electrodes. An open-access executable code that can give optimal porosity distribution of any specified chemistry and detailed explanation of the two approaches can be found on the Subramanian group's website. Modeling and mathematical optimization can significantly improve the efficiency of battery design, helping to meet the growing demands for various applications. The idea of using modeling for battery design was first introduced by Tiedemann and Newman in 1975. 1 They used an ohmically limited porous electrode model to maximize the cell's effective capacity by changing the electrode thickness and porosity. Newman later applied the reaction-zone model to maximize the specific energy of the system, taking mass into consideration as well.2 For these two models, the objective function can be directly related to the design variables, thus the optimum can be obtained by simply observing the plot or from the analytical solution. They further optimized the thickness and porosity of a lithium iron phosphate 3 electrode, where they maximized the specific energy using the Ragone plots. Ramadesigan et al.4 went one step further by including the linear electrode kinetics to minimize the internal resistance of the electrode. They used control vector parameterization (CVP) to minimize the ohmic resistance in the positive electrode by varying porosity.With the development of battery modeling, more physical processes have been included, and one of the most popular physics based models is the pseudo-2-Dimensional (P2D) model developed by the Newman group. 5 The P2D model involves a set of nonlinear partial differential equations (PDEs) that can only be solved numerically. Therefore, a numerical optimization approach is required to perform optimization on the system. Du et al. proposed a surrogate-modelbased approach, 6 and later developed a sophisticated framework based on th...
A hybrid analytical-collocation approach for fast simulation of the impedance response for a Li-ion battery using the pseudo-two dimensional model is presented. The impedance response of the spherical diffusion equations is solved analytically and collocation is performed on the resulting boundary value problem across the electrode and separator thickness using an orthogonal collocation scheme based on Gauss-Legendre points. The profiles for a frequency range from 0.5 mHz to 10 kHz are compared with the numerical solution obtained by solving the original model in COMSOL Multiphysics. The internal variable profiles across a wide range of frequencies are compared between the two methods and the accuracy, robustness, and computational superiority of the proposed hybrid analytical-collocation approach is presented. The limitations of the proposed approach are also discussed. A freeware for academic use that reads the various battery parameters and frequencies of interest as input, and predicts the battery impedance for a half cell and full cell, is also developed and a means to access it is reported in this paper.
Background The development of the minimum clinical important difference (MCID) can make it easier for researchers or doctors to judge the significance of research results and the effect of intervention measures, and improve the evaluation system of efficacy. This paper is aimed to calculate the MCID based on anchor and to develop MCID for esophageal cancer scale (QLICP-ES). Methods The item Q29 (How do you evaluate your overall health in the past week with 7 grades answers from 1 very poor to 7 excellent)of EORTC QLQ-C30 was used as the subjective anchor to calculate the score difference between each domain at discharge and admission. MCID was established according to two standards, "one grade difference"(A) and "at least one grade difference"(B), and developed by three methods: anchor-based method, ROC curve method and multiple linear regression models. In terms of anchor-based method, the mean of the absolute value of the difference before and after treatments is MCID. The point with the best sensitivity and specificity-Yorden index at the ROC curve is MCID for ROC curve method. In contrast, the predicted mean value based on a multiple linear regression model and the parameters of each factor is MCID. Results Most of the correlation coefficients of Q29 and various domains of the QLICP-ES were higher than 0.30. The rank of MCID values determined by different methods and standards were as follows: standard B > standard A, anchor-based method > ROC curve method > multiple linear regression models. The recommended MCID values of physical domain, psychological domain, social domain, common symptom and side-effects domain, the specific domain and the overall of the QLICP-ES were 7.8, 9.7, 4.7, 3.6, 4.3, 2.3 and 2.9, respectively. Conclusion Different methods have their own advantages and disadvantages, and also different definitions and standards can be adopted according to research purposes and methods. A lot of different MCID values were presented in this paper so that it can be easy and convenient to select by users.
Electrochemical models for the lithium-ion battery are useful in predicting and controlling its performance. The values of the parameters in these models are vital to their accuracy. However, not all parameters can be measured precisely, especially when destructive methods are prohibited. In this paper, we proposed a parameter estimation approach to estimate the open circuit potential of the positive electrode (Up) using piecewise linear approximation together with all the other parameters of a single particle model. Using the genetic algorithm (GA), Up and 10 more parameters were estimated from a single discharge curve without knowledge of the electrode chemistry. Different case studies were presented for estimating Up with different types of parameters of the battery model. The estimated parameters were then validated by comparing simulations at different C rates with experimental data.
Background: Undergraduate mental health was one of important contents for university and college implement overall education for all-round development. We aimed to explore the association between mental health and the grade point average (GPA) for freshman. Methods: There were 930 freshman whose average age was 17.97±0.68 years old. SAS (Self-Rating Anxiety Scale), SDS (Self-Rating Depression Scale), SCL-90 (Self-reporting Inventory), and IRIDS (Interpersonal Relationship Integrative Diagnostic Scale) were used to assessed the undergraduate mental health in our present study. Logistic regression and Generalized Linear Regression Model (GLM) and Restricted Cubic Splines function (RCS) model were used to explore the mental health and GPA for freshmen.Results: The grade point average in female freshman was higher than male (3.06±0.52 vs 2.77±0.55, P<0.001), and SDS score was higher than male freshman (44.88±11.30 vs 42.43±9.93, P=0.005). After adjusting for age and departments, higher SDS score was associated with the risk of lower grade point average risk (OR=1.41, 95%CI: 1.14, 1.75, P=0.001) for female students. In liner analyses, the SDS score had a negative association with grade point average (β=-0.01, 95%CI: -0.098, -0.001, P=0.002) for female students, and there was Conclusions: The SDS score for female undergraduate was higher than male, and the SDS score was negatively associated with grade point average for female undergraduate.
Background: The minimal clinically important difference (MCID) is an important phrase with big appeal in a field struggling to interpret quality of life (QOL) and other patient-reported outcomes (PRO), is also a bridge between statistics and clinical medicine. This paper is aimed to determine the MCID of esophageal cancer scale among Quality of Life Instruments system for Cancer Patients, QLICP-ES (V2.0). Methods: According to the scoring rule of QLICP-ES (V2.0), the scores of each domain and the overall of the scale were calculated. The MCID values of this scale were established by anchor-based and distribution-based methods. Two criteria A (improves one level after treatments) and B (at least improves one levels after treatments) were defined treatments effects in anchor-based methods, while methods of ES, SEM and RCI were used in distribution-based methods. Results: Using the anchor-based method, according to standard A, the MCID values of physical domain, psychological domain, social domain, common symptom and side-effects domain, the specific domain and the overall were 15.1, 4.4, 3.1, 6.7, 8.5 and 6.0 respectively. According to standard B, the MCID values of above domains and the overall were 19.3, 4.2, 4.8, 7.7, 9.5 and 7.5 respectively. Under the distribution-based methods, the MCID values above calculated by each method (ES, SEM and RCI) are in different ranges from 1.1 to 13.3. Conclusion: All methods have its own advantages and disadvantages to develop the MCID values, so it is necessary to develop the MCID values of QLICP-ES (V2.0) comprehensively with a variety of methods considering the actual situation.
Lithium-ion battery plays a vital role in electric vehicles and energy storage systems. In order to monitor, predict and control the status of lithium-ion batteries, model-based battery management systems (BMS) have been intensively studied and developed by researchers(1). The accuracy and predictability of the model used are of great importance to these systems, which heavily depends on the precision of the parameters needed in these models. Recently, Battery Informatics, Inc., a spin-off startup company from the Subramanian group proposed the concept of self-learning BMS. One of the objectives for self-learning BMS is to estimate parameters online as battery operates, where the ability to accurately and quickly estimate parameters that matches charge/discharge curves is essential. Estimating parameters for the lithium-ion batteries is challenging due to the complexity of the governing equations, and the possibility of multiple set of parameters that might provide the same accuracy of fitting discharge curves. Parameter estimation of various lithium-ion battery systems has been done for different models, including equivalent circuit model(2), single particle model(3), and pseudo 2D (P2D) model(4, 5). Most of these models are built on known open circuit voltage curves for individual electrodes, base parameters for cathode/anode thickness, porosities etc.. Recently, Qi et al (6)estimated open circuit potential of a single electrode together with other parameters using single particle model from a battery discharge curve. In this presentation, we will show the estimation of electrode open circuit potential together with other parameters of the P2D model. We will attempt to address the possibility and relative importance/impact of estimating all the parameters needed for the P2D model from charge-discharge curves. This will be facilitated using our past results in model reformulation(7) and parameter estimation for fade analysis (8). Acknowledgements The authors thank the United States Department of Energy (DOE) for the financial support for this work through the Advanced Research Projects Agency-Energy (ARPA-E) award #DEAR0000275. References 1. V. Ramadesigan, P. W. C. Northrop, S. De, S. Santhanagopalan, R. D. Braatz and V. R. Subramanian, J. Electrochem. Soc., 159, R31 (2012). 2. Y. Hu, S. Yurkovich, Y. Guezennec and B. J. Yurkovich, Control Eng. Pract., 17, 1190 (2009). 3. A. P. Schmidt, M. Bitzer, Á. W. Imre and L. Guzzella, J. Power Sources, 195, 5071 (2010). 4. J. C. Forman, S. J. Moura, J. L. Stein and H. K. Fathy, J. Power Sources, 210, 263 (2012). 5. S. Santhanagopalan, Q. Guo and R. E. White, J. Electrochem. Soc., 154, A198 (2007). 6. Y. Qi, S. Kolluri, V. R. Subramanian, D. T. Schwartz and S. Santhanagopalan, Meeting Abstracts, MA2016-02, 366 (2016). 7. P. W. Northrop, V. Ramadesigan, S. De and V. R. Subramanian, Journal of The Electrochemical Society, 158, A1461 (2011). 8. V. Ramadesigan, K. Chen, N. A. Burns, V. Boovaragavan, R. D. Braatz and V. R. Subramanian, Journal of The Electrochemical Society, 158, A1048 (2011).
There are a wide range of battery models at different scales, from empirical models to molecular dynamics models, that can describe the battery behavior. The Pseudo 2-Dimensional (P2D) model considers the porous electrode theory, concentrated solution theory, Ohm’s law, kinetic relationships, as well as charge and material balances.1 These physic-based behaviors are described by a set of stiff nonlinear partial differential algebraic equations (DAEs) which can be only solved numerically. In this talk, we discuss and review different methods to simulate the battery models, specifically about integration in the time domain. As the P2D model discretized in spatial coordinates by using any suitable method such as finite difference2-3, finite volume4 and spectral methods5-8, it results in a system of nonlinear DAEs. Typically, nonlinear DAEs can be solved based on Runge-Kutta (RK) methods (explicit or implicit) or multistep methods. The different orders of accuracy will affect the accuracy of the numerical solutions for each time step and it will further affect the computational efficiency. However, most of the time the stability region becomes smaller when the order of accuracy of the method increases. For the multistep method, Backward Differentiation Formula (BDF) method is commonly used, because we can get more than second order of accuracy without increasing the number of variables.9 Both RK and BDF methods will be reviewed for simulating battery models. Subtle differences among different methods and efficiency improvement and robustness of all these methods will be analyzed and discussed. In particular, the compromise between, stability, accuracy, and ease of programming will be discussed. Implementation in different programming languages and platforms will also be compared. Acknowledgements The authors are thankful for the financial support of this work by the Clean Energy Institute (CEI) at the University of Washington. References 1. W. Tiedemann and J. Newman, J. Electrochem. Soc., 122, 1482–1485 (1975) 2. M. Doyle, T. F. Fuller, and J. Newman, J. Electrochem. Soc., 140, 1526–1533 (1993). 3. G. G. Botte, V. R. Subramanian, and R. E. White, Electrochim. Acta, 45, 2595–2609 (2000). 4. M. Torchio, L. Magni, R. B. Gopaluni, R. D. Braatz, and D. M. Raimondo, J. Electrochem. Soc., 163, A1192–A1205 (2016). 5. V. R. Subramanian, V. Boovaragavan, V. Ramadesigan, and M. Arabandi, J. Electrochem. Soc., 156, A260–A271 (2009). 6. P. W. C. Northrop, V. Ramadesigan, S. De, and V. R. Subramanian, J. Electrochem. Soc., 158, A1461–A1477 (2011). 7. V. Ramadesigan, V. Boovaragavan, J. C. Pirkle, and V. R. Subramanian, J. Electrochem. Soc., 157, A854–A860 (2010). 8. V. R. Subramanian, V. D. Diwakar, and D. Tapriyal, J. Electrochem. Soc., 152, A2002–A2008 (2005). 9. K. Brenan, S. Campbell, and L. Petzold, Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations. Society for Industrial and Applied Mathematics (1995).
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.