#### Date of Award

1-1-2010

#### Document Type

Campus Access Dissertation

#### Department

Chemical Engineering

#### First Advisor

Ralph E White

#### Abstract

The lithium ion cell has been widely used in portable electronic devices, is used in aerospace and is the most promising power supplier for hybrid electric vehicles (HEV) and electric vehicles (EV) because of its high energy density, no memory effect, and low self-discharge properties. Since the lithium ion cell is gradually becoming an indispensable energy storage device in human life, the studies of mathematical modeling of the lithium ion cell have been extensively scrutinized to better understand the mechanism of the electrochemical process in the cell, to extend the cell life, and to prevent thermal runaway. Among the current models for the lithium ion cell, the physics based pseudo two-dimensional (P2D) model is commonly believed as the most accurate model, but it is also the most time consuming model.

The proper orthogonal decomposition method was also applied to develop an efficient, reduced order electrochemical-thermal model for a lithium ion cell. This model was validated for discharge simulations over a wide range of C rates and various cooling conditions of the cell. The ROM agrees well with the simulation from COMSOL Multiphysics®, a commercial finite element method (FEM) solver, and requires about seven times less computation time than the COMSOL model. The model predictions indicate that the discharge time or percent of capacity removed from the cell at an end of discharge voltage of 3.0V depends on the rate of the discharge and heat transfer rate away from the cell. Also, the heat transfer rate determines whether the capacity removed is limited by mass transfer in the solid phase or mass transfer in the electrolyte.

Accurately approximating the surface concentration in the solid particles plays important role to obtain accurate simulation results using the P2D model for a lithium ion cell in the applications with high rate charge/discharge. The frequency responses of the surface concentration for the various simplified models for the diffusion problem in the spherical particle were compared to the analytical solution. It was turned out that the current simplified models for the diffusion problem fail for the short time period when the frequency is greater than 10 rad/sec. The method of orthogonal collocation on finite elements was introduced to solve the diffusion problem numerically. The effects of the number of collocation points, the locations of the collocation points and the size of the element near the surface on the accuracy of the approximation of the surface concentration for the short time period were analyzed. The reduced order model for the diffusion problem was developed based on the method of the orthogonal collocation on finite elements and the proper orthogonal decomposition. The effects of the locations of the collocation points on the frequency response of the surface concentration predicted by the reduce order model were discussed.

#### Recommended Citation

Cai, L.(2010). *Efficient Modeling of the Lithium Ion Cell Using the Proper Orthogonal Decomposition Method.* (Doctoral dissertation). Retrieved from http://scholarcommons.sc.edu/etd/570