## Operating Principle of the Proposed Dual-Mode Control Strategy for the DAB Converter
### Light Load  
Under light load conditions, the proposed DAB converter adopts the PWM control to drive two full-bridges, which lowers the loss of backflow power and improves the efficiency of the DAB converter. Figure 5 demonstrates the theoretical waveforms of the proposed control strategy for the DAB converter in PWM mode under light load conditions.  
Figure 5: Theoretical waveforms of the proposed control strategy for the DAB converter in PWM mode under light load conditions.  
State 1 (\(t_{0}\leq t\leq t_{1}\)):  
As shown in Figure 5, due to the discharge of energy stored in \(C_{OSSI}\), \(C_{OSSI}\), \(C_{OSSS}\), and \(C_{OSSS}\) to zero during the dead time in the previous state, switches \(S_{1}\), \(S_{4}\), \(S_{5}\), and \(S_{8}\) are turned on with ZVS at \(t=t_{0}\). Since \(L_{M}\) and \(L_{K}\) have not discharged their stored energy completely, currents \(i_{LM}\) and \(i_{LK}\) keep flowing in the same direction as their previous state until their stored energy is discharged to zero. The detailed current path is shown in Figure 6a.  
State 2 (\(t_{1}\leq t\leq t_{2}\)):  
As shown in Figure 5, at \(t=t_{1}\), switches \(S_{1}\), \(S_{4}\), \(S_{5}\), and \(S_{8}\) remain on. The energy stored in \(L_{K}\) has been discharged to zero, causing \(L_{K}\) to change its state from discharging to charging. Nevertheless, the energy stored in \(L_{M}\) has not been discharged to zero. In this case, \(V_{DCbus}\) will charge \(L_{K}\) and combine with the \(L_{M}\), transferring the energy to the low-voltage side to provide the load. The detailed current path is shown in Figure 6b.  
State 3 (\(t_{2}\leq t\leq t_{3}\)):  
As shown in Figure 5, at \(t=t_{2}\), switches \(S_{1}\), \(S_{4}\), \(S_{5}\), and \(S_{8}\) remain on. At this time, \(L_{M}\) has discharged its stored energy to zero, thus transitioning from discharge to charge energy. \(V_{DCbus}\) charges inductors \(L_{M}\) and \(L_{K}\), as well as supplies energy to the load. The detailed current path is shown in Figure 6c.  
State 4 (\(t_{3}\leq t\leq t_{4}\)):  
At \(t=t_{3}\), switches \(S_{1}\), \(S_{4}\), \(S_{5}\), and \(S_{8}\) are turned off. The period from \(t_{3}\) to \(t_{4}\) is the dead time of the high- and low-voltage side switches. At this time, currents \(i_{LM}\) and \(i_{LK}\)  
Figure 6: (**a–f**) The current flow path of the DAB converter in PWM control mode.  
flow in the same direction. The high-voltage side current discharges \(C_{OSS2}\) and \(C_{OSS3}\) to charge \(C_{OSS1}\) and \(C_{OSS4}\), combining with \(L_{M}\) to transfer energy to the low-voltage side. The low-voltage side current discharges \(C_{OSS6}\) and \(C_{OSS7}\), charging \(C_{OSS5}\) and \(C_{OSS8}\), and providing energy to the load. The detailed current path is shown in Figure 6d.  
Note that after the energy stored in \(C_{OSS2}\), \(C_{OSS3}\), \(C_{OSS6}\), and \(C_{OSS7}\) has been discharged to zero, intrinsic diodes \(D_{2}\), \(D_{3}\), \(D_{6}\), and \(D_{7}\) conduct the current during the remainder of this state. The detailed current path is shown in Figure 6e.  
State 5 (\(t_{4}\leq t\leq t_{5}\)):  
As shown in Figure 5, due to the discharge of energy stored in \(C_{OSS2}\), \(C_{OSS3}\), \(C_{OSS6}\), and \(C_{OSS7}\) to zero during the dead time in state 4, switches \(S_{2}\), \(S_{3}\), \(S_{6}\), and \(S_{7}\) are turned on with ZVS at \(t=t_{4}\). Since \(L_{M}\) and \(L_{K}\) have not discharged their stored energy completely, currents \(i_{LM}\) and \(i_{LK}\) keep flowing in the same direction as their previous state until their stored energy is discharged to zero. The detailed current path is shown in Figure 6f.  
States 6 to 8 work the same way as states 2 to 4; the only difference is that switches \(S_{2}\), \(S_{3}\), \(S_{6}\), and \(S_{7}\) take the place of switches \(S_{1}\), \(S_{4}\), \(S_{5}\), and \(S_{8}\). Therefore, there will be no further explanation.