SIMPLIFIED MODEL TO PREDICT CHARGE AND DISCHARGE CYCLES IN LITHIUM ION BATTERIES

E. R. HENQUÍN, P. A. AGUIRRE

Virginia

Conferencia; The 7th Annual Energy Harvesting Workshop and the 2nd Annual CEHMS Conference; 2012

Center for Energy Harvesting Materials and Systems: CEHMS

Abstract Mathematical modeling to predict charge and discharge cycles of lithium ion batteries is important not only to provide state of charge in time, but also to be coupled with the consumption patterns of energy in different devices. Using the developed models has two general purposes: synthesis, design, and evaluation of process performance and control/operation of a real system. Rigorous mathematical models require substantial computer resources and considerable time for resolution. Some authors have proposed modifications to traditional modeling or different mathematical techniques in order to reduce computational time. But even so, it is an arduous task to set up the respective boundary conditions for resolution [1, 2]. In this paper, a simplified mathematical model to predict charge and discharge cycles of lithium ion batteries is proposed. The model is derived by a mass balance in both electrodes and the separator, considering that the lithium flow in the compartments is carried out by diffusion. A simplified model of lithium diffusions into the solid particles is considered in electrodes. Butler-Volmer equation for electrochemical reactions and Ohm´s law in both solid and electrolyte phases are considered in the current balance. The system of ordinary differential equations to be solved consists of an equation for each compartment, two equations for each solid phase in each electrode (inside and outside the spherical particle), which make up a total of 7 equations for the entire battery. This model was validated in comparison with the experimental points [3] (Fig. 4 page 1893) by adjusting parameters such as diffusion on solid and electrolyte phase, and conductivity of both phases. Figure 1 shows the preliminary results of this study. The mathematical model presented in this paper allows properly predicting charge and discharge curves of lithium ion batteries. It is robust enough to be adjusted to other types of lithium batteries. Results are obtained in fractions of seconds in a desktop pc. [1] J. Newman, K. E. Thomas, H. Hafezi, D. R. Wheeler. J. of Power Sources 119–121 (2003) 838–843 [2] P. M. Gomadam, J. W. Weidner, R. A. Dougal, R. E. White. J. of Power Sources 110 (2002) 267–284 [3] M. Doyle and J. Newman. J. of the Electrochem. So. 143, Nº 6, (1996) 1890-1903.