Publications

An isothermal reduced order physics-based Li ion battery model is developed by incorporating solution phase charge and material balances into single particle (SP) model. Li ion concentration and potential profiles in electrolyte phase are approximated by polynomial functions. A cubic polynomial is used for electrolyte concentration and potential inside electrodes, while separator liquid phase potential and concentration are estimated by parabolas. Diffusion inside solid particles is also simplified using an approximate solution based on analytical solution for the solid concentration. Applying the aforementioned reduction techniques decreases the degree of freedom of full order model by more than 100, while the cell voltage relative error of proposed model is less than 1% at different charge-discharge rates up to 5C. © 2012 Elsevier B.V. All rights reserved.

A more accurate method (comparing to the Euler, Runge-Kutta, and implicit Runge-Kutta methods) for the numerical solutions of ordinary differential equations (ODEs) is presented in this paper. The coefficients in the approximate solution for the ODE using the proposed method are divided into two groups: the fixed coefficients and the free coefficients. The fixed coefficients are determined by using the same way as in the traditional Taylor series method. The free coefficients are obtained optimally by minimizing the error of the approximate solution in each time interval. Examples are presented to compare the numerical solutions of the Rahmanzadeh, Cai, and White s method (RCW) to those of other popular ODEs methods. © 2013 Elsevier Ltd.

A model order reduction method is developed and applied to the solid-phase diffusion problem used in physics-based lithium ion cell models. The reduced order model is in the form of a state space model. Model identification is performed in the frequency-domain using the vector fitting method. The method allows the user to control the order of the model, the frequency band for model identification, and optionally a weight function to give a certain frequency band more weight. The model can be used for spherical and non-spherical particles. For spherical particles, the results from using the reduced order model are compared with those from analytical solutions, and excellent agreement is achieved using 3rd and 5th order models. When the approach is applied to non-spherical particles, the transfer functions need to be calculated numerically. Two methods, step response and complex exponential, are proposed to calculate the required transfer function. While the step response method is more suitable for low frequencies, the exponential method is more accurate for high frequencies. © 2012 Elsevier B.V.

Lithium ion batteries have conventionally been manufactured in small capacities but large volumes for consumer electronics applications. More recently, the industry has seen a surge in the individual cell capacities, as well as the number of cells used to build modules and packs. Reducing cell-to-cell and lot-to-lot variations has been identified as one of the major means to reduce the rejection rate when building the packs as well as to improve pack durability. The tight quality control measures have been passed on from the pack manufactures to the companies building the individual cells and in turn to the components. This paper identifies a quantitative procedure utilizing impedance spectroscopy, a commonly used tool, to determine the effects of material variability on the cell performance, to compare the relative importance of uncertainties in the component properties, and to suggest a rational procedure to set quality control specifications for the various components of a cell, that will reduce cell-to-cell variability, while preventing undue requirements on uniformity that often result in excessive cost of manufacturing but have a limited impact on the cells performance.

A 1D mathematical model, which aims at modeling the formation of calcareous deposits on the surface of cathodically polarized steel in seawater, was developed in this paper. The current model is related to mass transport phenomenon, electrochemical reactions, precipitation reactions and homogenous reactions. The model is also capable of tracking the growth interface of the calcareous deposits via the arbitrary Lagrangian-Eulerian method. The current model predicted time-dependent changes of the physical properties of calcareous deposits, including thickness, deposit porosity, coverage rate and electric resistance, and the numerical results are in good agreement with existing experiments. © 2012 Elsevier Ltd.

A one dimensional mathematical model is presented for a high temperature lithium-aluminum, iron disulfide molten salt battery system. Multi-physics transport phenomena in the electrolyte, charge balances in the solid phases and electrolyte, complex multi-step electrochemical and chemical reactions in the electrodes are described in this model. The model includes the effects of precipitation salt on active area in the electrode and the discharge capacity. In addition the model also takes the change in volume of the active material into account during the electrochemical reactions by incorporating the change in porosity of the electrode and the change in dimension of the electrode. The model results are compared to the existing model in literature and available experimental data. © 2011 Published by Elsevier B.V. All rights reserved.

The state of charge (SOC) and the loss of active material of the electrodes of a Li ion cell under Low Earth Orbit condition (LEO) have been estimated using Kalman filtering methods, by means of the physics-based single particle (SP) model. Zero mean Gaussian noise was added to the charge-discharge curves obtained by the SP model to generate synthetic data. Afterwards, nonlinear Filtering approaches including Extended Kalman Filtering (EKF) and Unscented Kalman Filtering (UKF) were applied to predict the true SOC and the electrodes degradation, by minimizing the measurement residuals between the model prediction and the synthetic data. The results indicated that UKF is a far superior candidate than EKF for the SOC estimation for a Li-ion cell during the cycling. Moreover, the proposed method is able to predict the loss of active material for each electrode during the cell life. © 2012 The Electrochemical Society.

Physics-based lithium ion models are widely used to predict the electrochemical behavior of lithium ion cells. The implementation of such a model typically requires solving a diffusion problem in solid particles. A linear time-invariant (LTI) model is proposed for the solid-phase diffusion problem. This LTI model can be used for spherical and non-spherical particles. For spherical particles, results from using the LTI model are compared with those from solving full diffusion equation, and excellent agreement is achieved. The LTI model solves only a few equations, and thus it runs much faster than the model solving the full diffusion equation. Impact of particle shapes on the electrochemical behavior is investigated after the model is validated. © 2012 Elsevier B.V. All rights reserved.

The physics-based pseudo two-dimensional (P2D) model for lithium ion cells requires significant computation time. To reduce this burden, the orthogonal collocation on finite elements (OCFE) method is applied here. The number of node points both in the macro-scale and in the micro-scale in the P2D model is reduced by optimally locating the node points. This OCFE method is shown to be better than other approximate methods for the spherical diffusion equation with flux boundary conditions. This OCFE method is also used to solve the P2D model equations and the results are compared to those obtained from COMSOL (a commercial differential/algebraic equation solver using FEM). © 2012 Elsevier B.V. All rights reserved.

An approximate solution is presented for the spherical diffusion equation for the spherical particles in a physics-based lithium-ion battery model. This approximate solution is compared to different numerical and analytic solutions for various boundary conditions. These comparisons reveal that our approximate solution can provide accuracy and time-efficiency in simulation. This approximate solution is much faster than the numerical and truncated analytical solutions at high current rate, and shows better long-time accuracy than the short-time analytical solution. This approximate solution can also be used as the porous electrode model. © 2011 Elsevier B.V. All rights reserved.