For high power equipment, a battery pack which is composed of large number of batteries in series and parallel is necessary. However, after cyclic charging and discharging loops, the uniformity in the parallel-connected battery pack is destroyed; consequently, electrical current appears in the pack between any two batteries with potential difference. Therefore, it can be easily expected that analysis of paralleled batteries becomes more and more complicated while the number of batteries increases. For example, in a set of 100 parallel-connected batteries, 4950 directional branch currents are needed to be manipulated to satisfy Kirchhoff Circuit Laws. Obviously, heavy computational load makes the analysis of mass batteries based on the electrochemical model impossible. In this study, we propose a novel solution in combination with the ESP (enhanced single particle) model as proposed in Ref. [1] to enable an electrochemical analysis even with a huge amount of batteries in the pack.
The main idea of the novel solution originates from the “power allocation”, which means that when an electron leaving a certain battery owns a larger kinetic energy, the current dedicated by this battery accounts for a higher proportion of the total output current. Since the kinetic energy of an electron amounts to the electrical potential difference, the current distribution of a certain battery k in a parallel-connected battery pack with a total of n batteries can be assumed to be Eq.(1), where is the summation of equilibrium currents between the battery k and all the other batteries, and it can be obtained from the view of electrical work as Eq. (2), where is a weighting factor which is related to the convergence. Accordingly, the working current of the battery k at the next time interval () can be calculated from the current and voltage information at the time t, i.e., Eq. (3).
From the simulated discharge-charge curve shown in Fig. 1, it can be seen that by employing this method, the working voltage of the parallel-connected battery pack with 100S120P reaches the same in a dozens of time steps. The corresponding discharge and charge current distributions within each parallel string are presented in Fig. 2 and 3, respectively. This method finds an approximate solution instead of the exact solution from KCL, however, the deviation of the result is only within 10-3~10-5 volt, which is a tolerable error range.
REFERENCES
[1] N. Baba, H. Yoshida, M. Nagaoka, C. Okuda, and S. Kawauchi, J. Power Sources, 252, 214 (2014).