# Active Equalization of Lithium-Ion Battery Based on Reconfigurable Topology
## 2 Double Layer Equalization Model  
### Inner Layer: Reconfigurable Equalization Topology  
As shown in Figure 1, the series reconfigurable balancing group is composed of \(n\) lithium-ion battery cells and \(2n\) MOSFETs. Each cell is fitted with two MOSFETs. By turning on (or off) one of the switches and turning off (or on) the other, the corresponding cell can be connected to the circuit or be isolated. Accurate SOC estimation is critical to ensure the safe and reliable operation of battery management systems in all applications. Scholars have proposed a variety of effective approaches to estimate the SOC of the battery and diagnose faults in the circuit [25; 26; 27; 28; 29]. Since it is not the focus of this research, we used the measuring port of the battery cell block in Simulink to obtain the value of SOC directly. Assume that in the initial state, \(SOC_{1}\) is the highest in the group, \(SOC_{i}\) is the lowest in the group, and \(SOC_{n}\) lies between them, as shown in Figure 2. To simplify the explanation, we use cell 2 to represent the other cells in the group and assume that \(SOC_{2}\) equals \(SOC_{1}\) (Actually, the two SOCs do not have to be completely the same. The SOCs can be considered equal if the difference between them is less than \(\varepsilon_{1}\)). If each cell has a unique SOC, the system will perform this process several times until the SOCs of all cells are equal. Figure 1: Reconfigurable equalization topology. The equalization process is shown in Figure 3.  
1. At the beginning of the equalization (Figure 3a), the system collects the SOCs of all the cells in the group. The cell with the lowest SOC (cell _i_) is isolated (switch on S_2\(i\) - 1, switch of S_2_i_), and the other cells are connected in series to discharge (switch on S_2, S_4_...S_2\(n\), switch off S_1, S_3_...S_2\(n\) - 1). 2. The series battery group continuously discharges until the SOC of the cell with the highest SOC in step (1) (cell 1) equals the SOC of the cell being isolated (cell _i_) (Figure 3b). Then the cell being isolated (cell _i_) is connected to the working part of the group (switch on S_2\(i\), switch off S_2\(i\) - 1). Meanwhile, the cell with the lowest SOC at this moment (cell _n_) is isolated (switch on S_2\(n\) - 1, switch off S_2_n_). 3. The series battery group repeats steps (1) and (2) until all the SOCs are equal. (Figure 3c). At this moment, all the cells have similar SOCs, and the process of equalization in this group is over. Then all the cells are connected in series to discharge (switch on S_2\(n\), switch off S_2\(n\) - 1). The cell with the lowest SOC is bypassed, and the rest of the cells are connected in series to discharge during the whole equalization process. All the cells are at work state when the equalization is completed. The working part of the group consists of \(n-1\) cells during equalization while \(n\) cells after equalization. When the cells are bypassed, the output voltage of the group gets smaller, and the output current will increase at the same time to ensure constant output power. Ref. [30] has proven that the larger the output current is, the smaller the capacity the battery can discharge. In this study, no more than one cell can  
Figure 3: Equalization process: (**a**) At the beginning of the equalization, battery \(i\) is isolated; (**b**) In the middle of the equalization, battery \(n\) is isolated; (**c**) End of equalization. Figure 2: Initial state of SOC. be bypassed at the same time to reduce the influence of bypassing the cell on the actual discharge capacity. Although this series reconfigurable topology can realize the equalization of the battery group, there are also some problems in practical application: firstly, the output voltage of the battery group during the equalization is the sum of \(n-1\) cell voltages. \[V_{\mathrm{g}}=\sum_{i}^{n}v_{i}-v_{\mathrm{min}} \tag{1}\]  
The output voltage of the battery group after the equalization is the sum of \(n\) cell voltages.