## 2 Three-Phase Single-Stage AC-DC Converter in Inductive-Power-Transfer-Based Wind Power Systems
### Operation Modes of Inductive-Power-Transfer-Based Three-Phase Single-Stage AC-DC Converter  
The operation modes of the IPT-based three-phase single-stage AC-DC converter are illustrated in Figure 3, corresponding to the time periods (t\({}_{\rm 0}\)-t\({}_{\rm 9}\)) shown in Figure 2b. The operation modes for each period are as follows. **Mode 1 (t\({}_{\rm 0}\)-t\({}_{\rm 1}\))/MODE 2 (t\({}_{\rm 1}\)-t\({}_{\rm 2}\)):** The primary resonant current (I\({}_{\rm P}\)) flows due to the previously negative resonant current through the path of the anti-parallel diode of switching device Q\({}_{\rm 2}\)\(\rightarrow\) voltage divider capacitor (C\({}_{\rm B1}\)) \(\rightarrow\) primary winding of the contactless coupler (N\({}_{\rm P}\)) \(\rightarrow\) resonant capacitor (C\({}_{\rm r1}\)) \(\rightarrow\) anti-parallel diode of switching device Q\({}_{\rm 2}\), and simultaneously through the path of the anti-parallel diode of switching device Q\({}_{\rm 2}\)\(\rightarrow\) flying capacitor (C\({}_{\rm B}\)) \(\rightarrow\) voltage divider capacitor (C\({}_{\rm B2}\)) \(\rightarrow\) primary winding of the contactless coupler (N\({}_{\rm P}\)) \(\rightarrow\) resonant capacitor (C\({}_{\rm r1}\)) \(\rightarrow\) anti-parallel diode of switching device Q\({}_{2}\). At this time, at t\({}_{0}\), Q\({}_{2}\) turns on with zero-voltage switching (ZVS). In the t\({}_{0}\)-t\({}_{1}\) period of MODE 1, the filter capacitor voltages of the a-phase and c-phase (V\({}_{\text{CFA}}\), V\({}_{\text{CFC}}\)) are applied to the boost inductors L\({}_{\text{B1}}\) and L\({}_{\text{B3}}\), respectively. The boost inductor currents (I\({}_{\text{B1}}\), I\({}_{\text{B3}}\)) flow through the path of filter capacitors (C\({}_{\text{FA}}\), C\({}_{\text{FC}}\)) \(\rightarrow\) boost inductors (L\({}_{\text{B1}}\), L\({}_{\text{B3}}\)) \(\rightarrow\) input rectifier diode \(\rightarrow\) switching devices (Q\({}_{1}\), Q\({}_{2}\)) \(\rightarrow\) filter capacitors (C\({}_{\text{FA}}\), C\({}_{\text{FC}}\)) \(\rightarrow\) boost inductors (L\({}_{\text{B1}}\), L\({}_{\text{B3}}\)), and begin to store energy in the boost inductors (L\({}_{\text{B1}}\), L\({}_{\text{B3}}\)). Simultaneously, the energy stored in the boost inductor (L\({}_{\text{B2}}\)) is reduced through the path of boost inductor (L\({}_{\text{B2}}\)) \(\rightarrow\) filter capacitor (C\({}_{\text{FB}}\)) \(\rightarrow\) anti-parallel diode of switching device Q\({}_{2}\)\(\rightarrow\) flying capacitor (C\({}_{\text{B}}\)) \(\rightarrow\) circulating diode (D\({}_{2}\)) \(\rightarrow\) voltage divider link capacitor (C\({}_{2}\)) \(\rightarrow\) input rectifier diode \(\rightarrow\) boost inductor (L\({}_{\text{B2}}\)), and is completely reset at t\({}_{1}\). Since switching devices Q\({}_{1}\) and Q\({}_{2}\) remain turned on, a quarter of the link voltage (V\({}_{\text{Link}}\)) is applied to the primary resonant circuit, allowing the primary and secondary resonant currents (I\({}_{\text{P}}\), I\({}_{\text{S}}\)) to flow. In the t\({}_{1}\)-t\({}_{2}\) period of MODE 2, the primary resonant current (I\({}_{\text{P}}\)) flows through the path of voltage divider capacitor (C\({}_{\text{B1}}\)) \(\rightarrow\) switching device (Q\({}_{2}\)) \(\rightarrow\) resonant capacitor (C\({}_{\text{r1}}\)) \(\rightarrow\) primary winding of the contactless coupler (N\({}_{\text{P}}\)) \(\rightarrow\) voltage divider capacitor (C\({}_{\text{B1}}\)), and simultaneously through the path of link capacitor (C\({}_{\text{1}}\)) \(\rightarrow\) switching devices (Q\({}_{1}\), Q\({}_{2}\)) \(\rightarrow\) resonant capacitor (C\({}_{\text{r1}}\)) \(\rightarrow\) primary winding of the contactless coupler (N\({}_{\text{P}}\)) \(\rightarrow\) voltage divider capacitor (C\({}_{\text{B2}}\)) \(\rightarrow\) circulating diode (D\({}_{2}\)) \(\rightarrow\) link capacitor (C\({}_{\text{1}}\)).