Maximization of Energy Storage and Minimization of Capacity Fade in Lithium-Ion Battery Pack

Capacity Fade in Lithium-Ion Battery Pack Ravi N. Methekar, Venkatasailanathan Ramadesigan, Venkat R. Subramanian z Department of Energy, Environmental and Chemical Engineering, Washington University, St. Louis, MO 63130 Richard D. Braatz Chemical and Bio-molecular Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801 Electrochemical power sources, especially lithiumion batteries have had significant improvements in design and operating range and are expected to play a vital role in the future in automobiles, power storage, military, and space applications. According to Tesla Motors, at least 16 cells are needed in series to deliver the required power for automobile applications. In such a battery pack, each cell might be at different initial state of charge (SOC). Subsequently, each cell will deliver different power, will be operating under different ranges of SOC and dynamically behave in different ways. Hence, it is difficult to store maximum energy using traditional charging methods wherein only terminal voltage is measurable. On the other hand, it is also difficult and expensive to optimize charging of each cell separately in the pack. Capacity fade in lithium ion batteries with aging is a well known phenomenon and has previously been mentioned in the literature, (2-4) and hence series/ parallel combination of such aged cells will lose its ability to provide maximum power for its application. In this work, we have used the reformulated model, for simulating a single cell out of the series/parallel combination of the cells in battery pack and shown the methodology to optimize energy storage into the battery pack using a single optimizing variable. We assumed that the every cell in the pack is at different initial SOC. This is obtained by estimating the initial conditions for each of the individual cells. The capacity fade in lithium-ion cell is incorporated using the power law equation given by Ramadesigan et al. (6) They quantified the cause of capacity fade in terms of the kinetic and transport parameters contributing to SEI layer growth. The capacity fade is minimized and energy storage is maximized using the optimum profile of current in the charging process of each cell in the pack. The optimum profile of current is estimated using a dynamic optimization technique, especially, control vector parameterization. We considered an optimal control problem formulation as follows: