**3. Modeling of Three-Phase Interleaved Parallel Bidirectional Converter**

The main circuit topology of the three-phase interleaved parallel bidirectional half bridge DC-DC converter is shown in Figure 5, consisting of three bidirectional Bucks–Boosts in parallel. In the same switching cycle, only one switch tube is on the upper and lower bridge arms of the half-bridge switch tube. According to the conduction state of the switch tube, there are two states: Boost and Buck. When the energy storage capacitor releases the stored energy to the load end, the input end of the converter can be approximated as a constant voltage source, and the energy flows from the input end to the load end, where the converter is in a Boost state. When the load side needs to store energy, it operates in Buck mode, and the load-side power flows to the input side to charge the energy storage capacitor. The topology parameters of the three-phase interleaved parallel converter are shown in Table 1.

**Figure 5.** Topology structure of three-phase interleaved parallel bidirectional DC/DC main circuit.


**Table 1.** Topology diagram parameters of three-phase interleaved parallel converter.

The advantages of adopting an interleaved parallel structure in bidirectional DC/DC circuits are, on the one hand, under a certain power output, the voltage and current stress of the inductor are reduced, allowing for the selection of smaller inductors, thereby reducing the volume and weight of the converter; and, on the other hand, the difference between the PWM driving waveforms of each phase is 120◦, further reducing the input current ripple, reducing the inductance, while also reducing the output voltage ripple and reducing the capacitor voltage and current stress, thus ensuring that the bidirectional DC/DC converter has a higher power density. For the convenience of analysis, if the switching frequency is set to fs and the influence of voltage dead band is ignored, then ws = 2 πfs. Ts = 1/fs. Figure 6 shows the main waveforms of the three-phase interleaved parallel boost converter under different duty ratios, d.

Assuming that the duty cycle, d, of each switch tube is equal and each phase is 120◦ different in sequence, there are eight switching modes of the converter. Use "1" and "0" to represent the "on" and "off" of the switch tubes, respectively. The switch states of switch tubes Q1, Q2, and Q3 can be represented as corresponding binary numbers: 001 (Mode I), 010 (Mode II), 011 (Mode III), 100 (Mode IV), 101 (Mode V), 110 (Mode VI), 111 (Mode VII), and 000 (Mode VIII). Figure 7 shows the equivalent circuits with 0, 1, 2, and 3 switch tubes on, respectively.

**Figure 6.** The main waveforms of the three-phase interleaved parallel converter during steady-state operation: (**a**) the main waveform of 0 < d < 1/3, (**b**) the main waveform of 1/3 < d < 2/3, and (**c**) the main waveform of 2/3<d< 1/3.

**Figure 7.** Equivalent topology diagram of three-phase interleaved converter at different working stages: (I) Switch tubes Q1 and Q2 are turned off, and switch tube Q3 is on. (II) Switch tubes Q1 and Q3 are turned off, and switch tube Q2 is on. (III) Switch tube Q1 is off, switch tubes Q2 and Q3 are on. (IV) Switch tube Q1 is on, switch tubes Q2 and Q3 are off. (V) Switch tubes Q1 and Q3 are on, while switch tube Q2 is off. (VI) Switch tubes Q1 and Q2 are on, while switch tube Q3 is off. (VII) The switch tubes Q1, Q2, and Q3 are conducting. (VIII) The switch tubes Q1, Q2, and Q3 are turned off.

For the convenience of description, this article takes one of the situations as an example for analysis, while other situations can be analogized. When the duty cycle is 0 < d < 1/3, the converter can be divided into six working modes based on the power switch on/off situation. The driving signal and inductance current waveform of the corresponding switch in the system under these six working modes are shown in Figure 6a.

Process 1: (Corresponding Mode IV) The switch Q1 is in a conductive state, and the current of inductor L1 continues to increase. The vin end charges the inductor L1, Q2 and Q3 are in the off state, and the current of inductors L2 and L3 continues to decrease. Inductors L2 and L3 discharge towards the vo terminal.

Process 2: (Corresponding Mode VIII) Switch tubes Q1, Q2, and Q3 are in the off state, and the current of inductors L1, L2, and L3 continues to decrease. Inductors L1, L2, and L3 discharge towards the vo terminal.

Process 3: (Corresponding Mode II) The switch tube Q2 is in a conductive state, and the current of inductor L2 continues to increase. The vin end charges the inductor L2, Switch tubes Q1 and Q3 are in the off state, and the current of inductors L1 and L3 continuously decreases. Inductors L1 and L3 discharge towards the vo terminal.

Process 4: (Corresponding Mode VIII) Switch tubes Q1, Q2, and Q3 are in the off state, and the current of inductors L1, L2, and L3 is continuously decreasing. Inductors L1, L2, and L3 discharge towards the vo terminal.

Process 5: (Corresponding Mode I) The switch Q3 is in a conductive state, and the current of inductor L3 continues to increase. The vin end charges the inductor L3. The switch tubes Q1 and Q2 are in a conductive state, and the current of inductors L1 and L2 continues to decrease. Inductors L1 and L2 discharge towards the vo terminal.

Process 6: (Corresponding Mode VIII) Switch tubes Q1, Q2, and Q3 are in the off state, and the current of inductors L1, L2, and L3 continues to decrease. Inductors L1, L2, and L3 discharge towards the vo terminal.
