Cycle Life Modeling of Lithium-Ion Batteries (original) (raw)

A first-principles-based charge-discharge model was developed to simulate the capacity fade of Li-ion batteries. The model is based on the loss of active lithium ions due to solvent reduction reaction and on the rise of the anode film resistance. The effect of parameters such as exchange current density, depth of discharge DOD, end of charge voltage, film resistance, and the overvoltage of parasitic reaction were studied quantitatively. The model controls the required DOD by controlling the discharge time and estimates the end of discharge voltages as a function of cycle number. Accelerated cycle life testing and developing correlations based on this data are critical for the capacity fade evaluation of batteries. 1-3 Darling and Newman 4 made a first attempt to model the parasitic reactions in lithium-ion batteries by incorporating a solvent oxidation into a lithium-ion battery model. Spotnitz 5 developed polynomial expressions for estimation of irreversible and reversible capacity loss due to solid electrolyte interphace SEI film growth and dissolution in lithium-ion batteries. Ramadass et al. 6 developed a capacity fade prediction model for Li-ion cells based on a semi-empirical approach. Recently, Christensen and Newman 7 simulated the influence of the anode film resistance on the charge/discharge performance of a lithium-ion battery. In this model the loss of reversible lithium ions and increase in the anode film resistance were incorporated into the first-principles model developed by Doyle et al. 8 Process parameters such as charge rate CR, the depth of discharge DOD, end-of-charge voltage EOCV, and the discharge rate DR which influence the capacity fade 9 were not considered in the above-mentioned models. We developed a first-principles-based model to simulate the capacity fade of Li-ion batteries in which incorporation of a continuous occurrence of the solvent reduction reaction during constant current and constant voltage CC-CV charging explains the capacity fade of the battery. 10 Initially the model estimates the capacity fade parameters as a function of cycle number. Next it is necessary to run the lithium-ion intercalation model with the updated parameters to estimate the performance of the battery at a specific cycle number. However, to run both models takes a long computational time. Also, the model does not consider the discharge process, which leads to inaccurate estimation of the total reaction time for the parasitic reaction. In this paper, a charge-discharge capacity fade model was developed based on the loss of active lithium ions due to solvent reduction reaction. The rise of the surface film resistance at the anode due to the parasitic reaction occurring was also considered in the model. The model considers process parameters such as: CR, DOD, EOCV, and the DR. It controls the required DOD by controlling the discharge time and estimates the discharge voltage as a function of cycle number. To decrease the computational time, the transport of lithium in the liquid phase was neglected. It takes only 10 h using a computer with 2.0 GHz CPU and 512 Mb RAM to run the model and to estimate the capacity fade and the charge-discharge performance of a battery cycled up to 2000 times. Model Development The simulations were carried out based on the experimental data obtained for a pouch lithium-ion cell 2.187 Ah, which consists of Li x CoO 2 positive electrode and mesocarbon microbead MCMB negative electrode. The charge-discharge simulations were performed by using a direct charge current of 0.334 A to a specified EOCV of 4.0 or 4.2 V. Next, the voltage was held constant until the charge current decreased to 50 mA. Subsequently, the battery was discharged under a direct current of 0.835 A to a specified DOD of 0.4 or 0.6. There was no rest time between charging and discharging. For simulation of the capacity check, the battery was initially discharged using a discharge current of 0.835 A to 3.0 V. Next, the battery was charged by applying a conventional CC-CV protocol 0.334 A to 4.2 V with a 50 mA cutoff current. The fully charged battery was discharged for second time to 3.0 V. The value of discharge capacity estimated in the second discharge process was used for capacity fade analysis. Both charge-discharge and the capacity check simulations terminate when the battery reaches a voltage lower than 3.0 V. As shown in Fig. 1, during discharge, the lithium ions deinterca-late from the negative electrode and intercalate into the positive electrode. Inside the porous electrode, the intercalation/ deintercalation processes take place at the electrode/electrolyte interface. A rigorous model based on porous electrode theory, concentrated solution theory, Ohm's law, and intercalation/deintercalation kinetics was developed previously which simulates the galvanostatic charge/discharge behavior of a Li-ion rechargeable battery. 8 In the model suggested in this paper, the variation of Li concentration in the liquid phase along the current path was neglected because low-to-medium charge/discharge currents were used in the simulations. The variation in the solid phase potential at the anode or at the cathode is negligible because of good conductivity of the electrode materials. It was also assumed that the active electrode materials are made from uniform spherical particles with a radius of R i and that the diffusion is the only mechanism of lithium transport inside the particles. The direction normal to the surface of the particles was taken to be the r-direction. The model equation that describes the diffusion of lithium in the solid phase is given by Fick's 2nd law