#### Date of Award

1-1-2012

#### Document Type

Campus Access Dissertation

#### Department

Chemical Engineering

#### First Advisor

Ralph E White

#### Abstract

Due to high energy density of Li ion cells, rechargeable Li ion batteries are used extensively in different markets and applications ranging from consumer electronics (e.g. laptops, cell phones) to automotive (e.g. Hybrid Electrical Vehicles) and aerospace (e.g. satellite power sources). Battery modeling is a key factor to design, optimize and control Li ion cells. Due to reliability and robustness, physics-based models are of great interests with respect to empirical Equivalent Circuit (EC) models. However, the computation burden restricts the full order physics-based models for on line applications.

In this dissertation, reduced order physics-based Single Particle (SP) model is first compared with an empirical EC model to fit three sets of cell voltage data. The cells are under Low Earth Orbit (LEO) cycling where the charge-discharge rates are less than 1 C-rate. The statistical results indicate that the SP model superiorly predicts all sets of data compared to the EC model, while the computation times of both models are on the same order of magnitude. The SP model is then selected as a preferred model for cell simulation.

Maximization of the cell life by optimizing charge rates during cycling is the first application of the SP model. To simulate the capacity fade during the cell life, the anode side reaction, where some of Li ions are lost, are incorporated into the model. First, we show 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. Then, a new approach based on optimization results is presented to find the optimal charge rates. The new algorithm is able to maximize the cell life 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.

State of charge and loss of active material estimation of a cell under LEO condition by means of the SP model is another work in this dissertation. 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.

Since the SP model is only valid for low rate (¡Ü 1C) applications, we tried to extend the model for higher charge-discharge rates up to 5C by incorporating solution phase charge and material balances into the SP model equations. Li ion concentration and potential profiles in electrolyte phase are approximated by polynomial functions. 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.

#### Recommended Citation

Khaleghi Rahimian, S.(2012). *Optimization and State Estimation of Li Ion Cells Using Single Particle Model.* (Doctoral dissertation). Retrieved from https://scholarcommons.sc.edu/etd/579