Lithium ion cell design optimization during the cyclic process

AGUIRRE PIO; AIMO, CORINA E.

Antofagasta

Workshop; 7th International Workshop on Lithium, Industrial Minerals and Energy (IWLiME 2020); 2020

​CELiMIN, Universidad de Antofagasta

Systems based on renewable energy sources require a basic electrical storage device for their efficient and safe utilization. Lithium battery systems offer a very good ratio of supplied energy density in relation to their size and present a higher efficiency compared to other energy storage devices, allowing the use of a greater number of charge-discharge cycles. Furthermore, these batteries lack the undesirable memory effects, conserving their capacity even with incomplete charges. However, the net effect of batteries is critically dependent on the design of the power-consuming device, the technical design of the battery, the time pattern of power delivery, charging times, and system capabilities to charge the batteries.The energy demand profiles required by a technological application during its operation could be interpreted as charging, discharging, and shutdown sequences imposed on the battery. If these sequences are repeated identically in continuous periods, a cyclic process is set up. It is characterized by the repetition of a pattern over time, in which the variables involved recover those values they had at the beginning of the cycle. Most of the current technological applications for rechargeable batteries are designed to work in cyclic processes.Studies of the influence of variables such as temperature [1] and aging mechanisms under these conditions [2] are presented in the bibliography. However, further optimization studies are considered necessary during a complete charge/discharge cycle and in multiple cycles including cell design variables [3].In the present work it is proposed to obtain the optimal design of a lithium-ion whole-cell based on a certain power profile defined by a cyclic discharge and charge process using a mathematical programming approach. The main design variables correspond to the amount of active material, which is what defines the cell capacity, and electrode thicknesses, which influence the potential drops due to diffusion phenomena of the active material within the solid, and therefore in energy efficiency. The cell mass per unit area depends on these design variables, therefore it is also optimized. The objective function of the proposed problem consists of maximizing the cell capacity throughout the cycle, subject to certain predefined charging and discharging times.To achieve this goal, a lithium cell mathematical model is used in an optimization environment, specifically in GAMS (General Algebraic Modeling System). The model was developed and validated with experimental data in [4] and it consists of a system of algebraic and ordinary differential equations dependent on the temporal variable. The latter define mass balances of salt and lithium in the compartments (anode, separator and cathode) and in the particles. In addition, current equations are rigorously defined, considering the total current that circulates through the collectors as the sum of average current that circulates through electrolytic phase and average current that circulates in solid phase inside the cell. Thus, potential drops in these phases are considered, in addition to overpotentials defined by Butler-Volmer kinetics to calculate cell voltage. This model was efficiently applied to optimize the design and operating conditions for simple discharging [5] and charging [6] processes. With the background obtained in these works, it was possible to adapt and apply the optimization schemes to the study of cyclic processes. Since the high non-linearity of the model, a deep understanding of how it works in the different optimization schemes is necessary for the correct definition of simpler problems as initialization steps to achieve convergence towards the optimal solution desired in the minimum possible computational time.The simultaneous optimization of design variables allowed a 60% increase in cell capacity with respect to the initial design taken from the literature, for a cycle consisting of a six-hour discharge, followed by a charge of the same duration. On the other hand, when the optimal design obtained operating in a cyclic process was compared against the optimal design obtained for the simple charging process, considering the same objective function, cells of different characteristics were obtained. This is because the charging and discharging processes have different nature and in a cyclic process an agreement must be reached between capacity and energy efficiency.