A Practical Degradation Simulator for Assembled Li-Ion Batteries with Calibration Functions
Authors: Hayakawa Yukinori , Lin Lei , Fukui Masahiro 
Published: February 2020

Lithium-ion battery system is constructed by an assembled battery for electric vehicles. Deterioration of an assembled battery is based on the deterioration trend of cell battery. However, it is affected by heat distribution, SOC (state of charge) and FCC (full charge capacity) variations. Therefore, we developed a practical battery degradation simulator for assembled batteries. It is necessary to calibrate from parameter of SOC, temperature and current to improve the precise simulation. The system provides the accuracy of the calibration is evaluated by the residual variance of the value of the experimental data and the value by using a model was fitting. The configuration of the assembled battery degradation simulator is shown as Fig.1. First, constitution of the battery and environment is defined by user. Accordingly SOC, heat distribution and current is calculated for each cell. Deterioration is calculated by these parameters and FCC is calculated by deterioration. FCC is used to calculate the state of the next SOC degradation, deterioration of the battery at that time is evaluated by repeating this loop. Fig.2 shows degradation functions.

The battery specifications and the environment to be used are set in the use condition unit. The data from the experiment is assigned to the battery deterioration calculator. It calculates the capacity deterioration and internal resistance deterioration due to save (cycle) and the temperature. The results displayed in graph changes in the capacity and internal resistance due to the deterioration in the result display unit. The deterioration calculation unit, we assume that the capacity deterioration and the increase of R0 are caused by the generation of the SEI (Solid Electrolyte Interface). SEI generation rate is assumed by Arrhenius law related to temperature, the SOC and the current dependency. [1] The FCC loss rate is defined as x [%]. Since root low is established in SEI degradation, the relationship between x [%] and the time t [days] in case of fixing SOC, temperature and current is given as equation (1) in the case of t =0 and x =0. Therefore, loss rate x [%] is given as equation (2) from equation (1). Current dependency is given as equation (3) by defined the lower limit voltage Vmin
[V] and the upper limit voltage Vmax
[V]. Equation (4) is given by integrating equation (2) and (3). [2] Increase of the internal resistance R0 is given as Equation (5) by the Arrhenius low. Equation (5) represents the temperature, current and SOC dependence of R0[Ω]. uocv
[V] is electromotive force, umin
[V] is lower limit electromotive force, I [A]is the charge and discharge current, and a and βis a factor of proportionality.

 The calibration function using the least squares method on data obtained by simulation and actual measurement data of 18650type lithium-ion batteries in degradation simulator. Equation (1) is conducted fitting. Equation (6) is given by defining the coefficient a = A/2B of x
2 and b = e
0/B of x in equation (1). Parameters a, b that a J
1 of equation (6) is minimized is found by the least square method. To construct a matrix equation (7) to find parameters a, b that a J
1 of equation (6) is minimized by the least square method. The equation (8) for the parameter P to minimize the J1 of equation (6) is given by applying the orthogonal principle. In addition, Equation (11) and (12) is given by linearizing the equation (9) and (10). The parameter P that minimizes J
2 of equation (13) is found in the procedure similar to fitting equation (1). Equation (14) and (15) is required in the process. It was calibrated by measuring time-series data of temperature and current dependence of the degradation, FCC and internal resistance in experiments. As a result, values of A/2B = 6088/T-14.9 and e
0/B= 4130.7/T-8.1 was obtained (T [K]: absolute temperature). Fig.3 shows the simulation result. It simulates EV batteries degradation successfully.

 With the development of calibration function was improved the accuracy of secondary battery degradation simulation. This feature is more excellent the versatility of secondary battery degradation simulation since it corresponds to the change of the battery and conditions of target.

[1] M. Broussely, S. Herreyre, P. Biensan, P. Kasztejna, K. Nechev, and R.J. Staniewicz, “Aging mechanism in Li-ion cells and calendar life predictions,” J. of Power Souces, pp. 97-98, 2001.

[2] Scott J. Moura, Joel C. Forman, Saeid Bashash, Jeffrey L. Stein, and Hosam K. Fathy, “Optimal control of film growth in lithium-ion battery packs via relay switches,” IEEE Trans. on Industrial Electronics, vol. 58, no. 8.

Figure 1