Publications

The physics-based single particle (SP) model was compared to the semi-empirical equivalent circuit analog (ECA) model to predict the cell voltage under constant current charge and discharge for different sets of Li-ion cell data. The parameters of the models were estimated for each set of data using nonlinear least squares regression. In order to enhance the probability of finding the global optima, a combination of the trust region method with a genetic algorithm was applied to minimize the objective function (the sum of squared residuals). Several statistical quantities such as sum of the squared errors, adjusted R2, root mean squared error, confidence intervals of the parameters, and prediction bounds were included to compare the models. A significance test (t test) on the parameters and the analysis of the variances (F and $\chi$2 tests) were also performed to discriminate between the goodness of the fit obtained from the two models. The statistical results indicate that the SP model superiorly predicts all sets of data compared to the ECA model, while the computation times of both models are on the same order of magnitude. © 2011 Elsevier B.V. All rights reserved.

A semianalytical methodology based on the integral transform technique is proposed to solve the diffusion equation with concentration dependent diffusion coefficient in a spherical intercalation electrode particle. The method makes use of an integral transform pair to transform the nonlinear partial differential equation into a set of ordinary differential equations, which is solved with less computational efforts. A general solution procedure is presented and two illustrative examples are used to demonstrate the usefulness of this method for modeling of diffusion process in lithium ion battery electrode. The solutions obtained using the method presented in this study are compared to the numerical solutions. © 2010 Elsevier B.V.

The single-particle model presented by Santhanagopalan et al. J. Power Sources, 156, 620 (2006) is extended to include an energy balance. The temperature dependence of the solid phase diffusion coefficient of the lithium in the intercalation particles, the electrochemical reaction rate constants, and the open circuit potentials (OCPs) of the positive and negative electrodes are included in the model. The solution phase polarization is approximated using a nonlinear resistance, which is a function of current and temperature. The model is used to predict the temperature and voltage profiles in a lithium-ion cell during galvanostatic operations. The single-particle thermal model is validated by comparing the simulated voltage and temperature profiles to the results obtained using a distributed porous electrode model. The simulation results from the single-particle thermal model also show good agreement with experimental voltage data obtained from lithium-ion pouch cells under different discharge rates (C/33, C/2 and C) at different temperatures (15, 25, 35, and 45C).

Inthis work, a mathematical thermal model for lithium ion batterypack with specific configuration was developed by coupling the singleparticle model and energy balance equation with basic circuit constraints.The temperature variation at different parts of the battery packwas considered in charge/discharge operations, and the dependency of cellparameters on temperature were taken into account. The model wasvalidated by comparing the simulated current, voltage, and temperature profileswith experimental data. Case studies such as battery balancing andcircuit interruption were also performed and discussed. 2011 The Electrochemical Society

The existing lithium ion battery model in Multiphysics (MP) software (COMSOL Inc., Palo Alto, CA) is extended to include the thermal effects. The thermal behavior of a lithium ion battery is studied during the galvanostatic discharge process with and without a pulse. © 2011 Elsevier B.V. All rights reserved.

A cathode half cell physics-based model for a St. Jude Medical fabricated silver vanadium oxide (SVO) cathode coin cell battery was constructed. The model is based on a single particle Fick s second law approach with the open-circuit potential modeled with a Redlich-Kister equation. By assuming that lithium ions intercalate only through the ends of the cuboid SVO particles, the model is able to predict accurately the discharge profile of experimental cathode half cell coin cells. © 2011 Elsevier B.V.

The optimum charge rate for a lithium ion cell at each cycle is determined to maximize the useful life of the cell without using optimization algorithms. In previous work, we showed that by applying a dynamic optimization routine the number of cycles can be increased by approximately 29.4% with respect to the case with one optimal charge current [7]. The dynamic optimization results indicated that the optimum charge rates are the minimum currents at which the constraints for the useful life are satisfied. This is due to the minimum charge rate resulting in minimum side reaction rate and capacity fade. Useful cell life is defined as the number of cycles before the end of discharge voltage (EODV) drops below 3.0 V or the cell discharge capacity becomes less than 20% of the original discharge capacity. The new approach presented in this work is able to find the optimal charge rates in a few minutes while the previous optimization algorithm takes at least one day, and improves the useful cell life by approximately 41.6% with respect to using only one optimal charge current. © 2011 Elsevier B.V. All rights reserved.

A new continuation method, which applies a new homotopy that is a combination of the fixed-point and Newton homotopies (FPN), is developed for seeking all real solutions to a nonlinear equation, written as f(x)=0, without having to specify a bounded interval. First, the equation to be solved is multiplied by (x-x0), where x0 is the starting value, which is set to zero unless the function does not exist at x0, in which case x0 becomes a tracking initiation point that can be set arbitrarily to any value where the function does exist. Next, the new function, (x-x0)f(x)=0, is incorporated into the FPN homotopy. The initial step establishes a single bifurcation point from which all real roots can be found. The second step ensures a relatively simple continuation path that consists of just two branches that stem from the bifurcation point and prevents the formation of any isola. By tracking the two branches of the homotopy path, all real roots are located. Path tracking is carried out with MATLAB, using the continuation toolbox of CL\_MATCONT, developed by Dhooge et al. (2006), based on the work of Dhooge, Govaerts, and Kuznetsov (2003), which applies Moore-Penrose predictor-corrector continuation to track the path, using convergence-dependent step-size control to negotiate turning points and other sharp changes in path curvature. This new method has been applied, without failure, to numerous nonlinear equations, including those with transcendental functions. As with other continuation methods, f(x)must have twice-continuous derivatives. © 2010 Elsevier Ltd.

A new homotopy developed for finding all real roots to a single nonlinear equation is extended to a system of nonlinear algebraic and transcendental equations written as f\x\ = 0 to find all real roots, including those on isolas. To reach roots that may lie on isolas, the functions are squared. This causes all roots to be bifurcation points that are connected to each other through stemming branches. As a result, a new system of homotopy functions, including numerous bifurcation points, is formed as H\x,t\ = (x - x0)(1 + f2 - t), where x0 is the starting point. Because the functions are squared, many systems of equations must be solved to find a starting point on a reduced system of homotopy functions written as H\x,t\ = 1 + f2 - t. Therefore, robustness is achieved at the expense of increased computation time. To improve the efficiency of the algorithm, the Levenberg-Marquardt method is used to find the starting point for the reduced homotopy system by solving a system of nonlinear equations with the degree of freedom equal to one. Then, a continuation method is used to track the paths from the resulting starting point to seek at least one root. Because all roots are bifurcation points, tracking the stemming branches from each subsequent root is the final step. The new algorithm was able to find successfully all the reported roots for 20 test problems that included a variety of algebraic and transcendental terms. In some cases additional roots were obtained. © 2011 American Chemical Society.

Using a dynamic optimization method, the optimum charge currents as a function of cycle number during cycling for the lithium-ion cell are obtained. A single particle physics-based model, which includes capacity fade, was applied to simulate the cell performance under low earth-orbit (LEO) cycling conditions. Useful cell life is defined as the number of cycles before the end of discharge voltage drops below 3.0 V or the cell discharge capacity becomes less than 20% of the original discharge capacity. The simulated useful cell life can be increased by ∼29.28% by varying the charge current. © 2010 The Electrochemical Society.