The Single-Phase-Shift (SPS) modulation is the most fundamental and widely adopted control method for the Dual Active Bridge (DAB) converter. Under SPS control, both the primary-side full bridge (Bridge 1) and the secondary-side full bridge (Bridge 2) operate at a fixed 50% duty cycle. The diagonal switch pairs of each bridge (such as Q1/Q4 and Q5/Q8) are turned on and off synchronously .

The core control variable in this scheme is the external phase-shift angle $\varphi$ introduced between the primary-side square-wave voltage (V_p) and the secondary-side square-wave voltage (V_s). This phase shift angle directly regulates the direction and magnitude of the power flow across the high-frequency isolation transformer T1, as shown in Figure 2-4.

The average power P₁₂ transferred between the two bridges is governed by the energy stored and released in the series leakage inductor L_s, which can be mathematically expressed as :

Where V₁ is the input DC voltage, V₂ is the output DC voltage, f_s is the switching frequency, and N is the transformer turns ratio (N = N1/N2) .

• Forward Power Mode ( $0\le \varphi \le \pi$ ): V_p leads V_s, causing energy to flow from the primary side to the secondary side .
• Reverse Power Mode ( $-\pi \le \varphi \le 0$ ): V_p lags V_s, causing energy to seamlessly flow back from the secondary side to the primary side.

The maximum power capability (P_max) is strictly limited by the hardware parameters L_s and f_s, and is achieved when the phase-shift angle $\varphi$ equals $\pi /2$ :

To minimize switching losses and achieve high total system efficiency, the SPS-DAB relies entirely on the reactive energy stored in the leakage inductor L_s to discharge and charge the MOSFET parasitic output capacitances C_oss, thereby facilitating Zero Voltage Switching (ZVS). Figure 2-5 shows complete waveforms of PWM and current . Taking the forward operation mode as a reference, a typical switching cycle progresses through the following key intervals:

• Interval 1 ( $t_0$ to $t_0^{\text{'}}$ - Dead Time Realization, as shown in Figure 2-6): Prior to $t_0$ , the switches Q1 and Q4 are turned off . During this dead-time interval, the inductor current I_L must remain negative ( $I_L\left(t_0\right)<0$ ). This negative current forces the energy stored in L_s to discharge the output capacitances of Q1 and Q4 while charging those of Q2 and Q3, creating the necessary zero-voltage condition across Q1 and Q4 prior to their turn-on .
  Figure 2-6 DAB converter operating stage during Interval 1
• Interval 2 ( $t_0^{\text{'}}$ to $t_1$ - Primary Channel Conduction, as shown in Figure 2-7): At $t_0^{\text{'}}$ , switches Q1 and Q4 are turned on under a strict zero-voltage condition(Ideal situation). The inductor current passes through the channels of Q1 and Q4, and begins to rise linearly .
  Figure 2-7 DAB converter operating stage during Interval 2
• Interval 3 ( $t_1$ to $t_2$ - Current Reversal, as shown in Figure 2-8): At $t_1$ , the inductor current crosses zero and switches its direction to positive, continuing its linear progression driven by the voltage difference across the transformer.
  Figure 2-8 DAB Converter Operating Stage During Interval 3
• Interval 4 ( $t_2$ to $t_2^{\text{'}}$ - Secondary Side ZVS Realization, as shown in Figure 2-9): At $t_2$ , the secondary side switches Q5 and Q8 are turned off . To enable ZVS for the secondary bridge, the inductor current at this moment must be positive ( $I_L\left(t_2\right)>0$ ). This positive transformer current successfully discharges the output capacitances of Q5 and Q8 while charging Q6 and Q7 during the secondary side dead time.
  Figure 2-9 DAB Converter Operating Stage During Interval 4
• Interval 5 ( $t_2^{\text{'}}$ to $t_3$ ) - Full Commutation, as shown in Figure 2-9): At $t_2^{\text{'}}$ , Q5 and Q8 achieve soft turn-on. The current flows naturally through the secondary bridge channels, completing the primary-to-secondary power commutation phase until the next half-cycle repeats the identical process for the remaining FETs from $t_3$ to $t_6$ .
  Figure 2-10 DAB Converter Operating Stage During Interval 5