## 3 Power Loss Analysis of the Cell Balancing System  
The proposed cell balancing system, as shown in Figure 3, is realized through the bidirectional flyback converter topology where Vbn is the voltage of nth cell, \(S_{n}\) is the photoMOS array, \(L_{m}\) is the field inductor of the transformer, \(N\) is the turn ratio of the transformer, and \(Q_{1}\) and \(Q_{2}\) are the MOSFET for switching. The designed cell balancing system utilizes a 6S1P lithium ternary battery module. The cells' state of charge will determine the operation mode of the photoMOS relay and the MOSFETs. Figure 4 shows that the proposed has two operation modes, where \(I_{1}\) is the balancing current, and \(I_{2}\) is the current at high side. Mode A is a boost mode. For example, when the voltage \(V_{B1}\) of the first cell is higher than the voltage of other cells in the module, the photoMOS \(S_{1}\) will be turned on, and the MOSFET \(Q_{1}\) will work as the main switch to control the circuit. The field inductor \(L_{m}\) of the transformer will store the energy of the cell, and transfer it to the battery module. The MOSFET \(Q_{2}\) will be operated with synchronous rectification control to reduce the conduction loss of the rectifier diode, as shown in Figure 4a; When the voltage \(V_{B1}\) of the first cell is less than the voltage of other cells in the module, the proposed system will operate in mode B. The photoMOS \(S_{1}\) will turn on, and the MOSFET \(Q_{2}\) will work as the main switch to control the circuit. The field inductor \(L_{m}\) of the transformer will store the energy of the battery module, and then transfer it to the cell. At this time, the MOSFET \(Q_{1}\) will be operated with synchronous rectification control to reduce the conduction loss of the rectifier diode, as shown in Figure 4b. By operating in these two modes alternately, after multiple balancing actions, the balancing system can achieve the equilibrium of the battery module. Figure 4: Schematic diagram of active cell balancing circuit based on bidirectional flyback converter in (**a**) boost mode (**b**) buck mode. Figure 3: Diagram of active cell balancing circuit based on bidirectional flyback converter. To determine the best balance current to achieve the highest efficiency and the least losses of the proposed system, it is necessary to estimate the losses caused by each component of the balancing architecture during the energy transfer. In the cell balancing situation, to implement the bidirectional flyback converter, the designed converter will only operate in continuous conduction mode (CCM) to prevent the energy inversion. Therefore, all the losses are considered in CCM. The losses caused by gate drivers, differential voltage sensors, or photoMOS relays will not be taken into account either because the power loss analysis proposed by this research attempts to find the relation between operating current and the bidirectional flyback converter's efficiency. In this case, the auxiliary power of those components is supplied by DC power manufactured by Gwinstek Company. The losses are mainly composed of the conduction and switching losses of the power switch, the copper and iron loss of the transformer, and the line loss. This research discusses the loss model of the proposed circuit operating in buck mode. As shown in Figure 5, this loss model replaces the battery module with the ideal voltage source \(V_{puck}\). The cell is replaced by the ideal voltage source \(V_{Bn}\). \(R_{s}\) is the wire resistance, \(R_{L}\) is the resistance of the transformer, \(R_{ds1(on)}\) is the on-resistance of MOSFET \(Q_{1}\), \(R_{ds2(on)}\) is the on-resistance of MOSFET \(Q_{2}\), and \(L_{m}\) is the field inductor of the transformer.