## 2 Proposed Modular Cell Balancing Circuit
### Proposed Modular Cell Balancing Circuit
#### 2.2.2 Proposed Modular Cell Balancing Circuit  
1.System structure for proposed MCBC  
The system structure of the proposed MCBC is shown in Figure 8. This circuit is constructed by dividing the SCBS into two modules (\(M_{1}\), \(M_{2}\)) and each module contains \(N\) cells in series-connection in which each cell in the SCBS connects the switch \(S_{\text{k}}\) and the primary side winding of the MWTs in intra-module balancers. Each MWT has a secondary side winding in connection with one diode  
Figure 7: Modular circuit balancing concept: (**a**) Conventional cell balancer; (**b**) Modular cell balancer; (**c**) The modular cell balancer based on outer-module. to reset the magnetizing inductance of transformers (\(L_{\rm m}\)) to prevent saturation of the MWTs. Each module connects with the intra-module balance individually, and all modules are connected to the outer-module balancer. In the intra-module balancer, a number of the transformer's primary windings are equal to a number of the cells inside each module. The magnetizing energy of the MWT is to balance the cell voltages in each module, and a charge/discharge process of a module balancing capacitor (\(C_{\rm m}\)) is to balance the module voltages. In this proposed circuit, the energy is transferred from a high voltage level to a low voltage level in both the cells inside each module and modules simultaneously by the MWTs and the modular balancing capacitor, respectively. The \(C_{\rm m}\) is used to equalize the energy between the modules through the outer-module balancer. It is controlled by the switches \(S_{\rm a1}\), \(S_{\rm a2}\) and \(S_{\rm b1}\), \(S_{\rm b2}\) which are controlled by PWM signals, as shown in Figure 9. Voltage sensors and intelligent control circuit are not used in this MCBC. Therefore, the circuit has been simply designed and controlled. Figure 8: The proposed modular cell balancing circuit. 2. Operational principle  
The operational principle of the proposed MCBC is similar to that of the MWTFC and the SCC individually. In particular, the switches in the MWTFC and the SCC are driven by two fixed duty ratios (\(D\)) and (\(D_{1}\)), respectively. In order to simply analyze operating modes for the circuit, the following assumptions are made:  
* All the switches, capacitor, diodes and transformer are ideal. * Each module contains four cells. Figure 9: Operational waveforms of the proposed modular cell balancing circuit (MCBC). * The relationship among voltage of the battery cells is arranged in decreasing order from \(Cell_{11}\) (\(V_{\text{cell11}}\)) to \(Cell_{24}\) (\(V_{\text{cell24}}\)), and \(V_{\text{cell111}}>V_{\text{cell12}}>V_{\text{aver1}}>V_{\text{cell13}}>V_{\text{ cell14}}>V_{\text{cell21}}>V_{\text{cell22}}>V_{\text{ave2}}\)\(>V_{\text{cell23}}>V_{\text{cell24}}\) (the module 1 voltage: \(V_{\text{M1}}=V_{\text{Cell11}}+V_{\text{Cell12}}+V_{\text{Cell13}}+V_{\text {Cell14}}\); the average voltage of \(M_{1}\): \(V_{\text{aver1}}=V_{\text{M1}}/4\); the module 2 voltage: \(V_{\text{M2}}=V_{\text{Cell21}}+V_{\text{Cell22}}+V_{\text{Cell23}}+V_{\text {Cell24}}\); the average voltage of \(M_{2}\): \(V_{\text{aver2}}=V_{\text{M2}}/4\); \(V_{\text{M1}}>V_{\text{M2}}\)). There are four operating modes during one switching period (\(T_{\text{s}}\)) of the proposed MCBC. These modes based on the switching states of the primary side switches (\(S_{11}\), \(S_{12}\), \(S_{13}\), \(S_{14}\), \(S_{21}\), \(S_{22}\), \(S_{23}\), \(S_{11}\), and \(S_{24}\)) in the intra-module balancer and the switches (\(S_{\text{a1}}\), \(S_{\text{a2}}\), and \(S_{\text{b1}}\), \(S_{\text{b2}}\)) in the outer-module balancer. The theoretical waveforms and operating modes of the proposed circuit are shown in Figures 9 and 10, respectively.