## 4 Design of a Contactless Coupler for Inductive-Power-Transfer-Based Wind Power Systems  
The contactless coupler utilized in the small wind power system based on inductive power transfer (IPT) was engineered with a PM11 material circular core (R/r/H: 100 mm/5 mm/4 mm) and a spiral winding technique, applied to both the primary and secondary pads of equivalent area. To address core saturation, the core thickness was chosen as 4 mm, and a minimal air gap of 10 mm was maintained between the primary and secondary sides of the coupler. To protect against stray magnetic fields in the actual nacelle environment, aluminum shielding plates (R'/H': 140 mm/4 mm) were installed above and below the circular core to mitigate the stray flux on the primary and secondary sides of the coupler [16]. While the ferrite core enhances the effective inductance by reducing magnetic reluctance within the flux path, the aluminum shielding plates contribute to increased magnetic reluctance and decreased effective inductance due to eddy currents generated when exposed to the magnetic field. To minimize eddy current losses in the aluminum shielding plates, a 0.3 mm gap was introduced between the ferrite core  
Figure 5: Simulated DC link voltage (V\({}_{\text{Link}}\)) characteristics of a 3-phase single-stage AC-DC converter due to boost inductance (L\({}_{\text{B}}\): 40 \(\mu\)H, 50 \(\mu\)H, 60 \(\mu\)H) under full load conditions (400 V\({}_{\text{DC}}\), 1 kW). and the aluminum shielding. The design of the ferrite core and aluminum shielding plates is illustrated in Figure 6.  
To minimize reactive power and maximize power transfer, the number of turns on the primary and secondary sides needed to determine the primary-side magnetizing inductance (L\({}_{\text{m}}\)) of the contactless coupler can be calculated when the resonant frequency (f\({}_{\text{r}}\)) and the switching frequency (f\({}_{\text{s}}\)) are identical, with the input and output voltage gains being constant in the series-series compensation circuit, regardless of the AC equivalent resistance (R\({}_{\text{ac}}\)). As shown in Figures 7 and 8, when the contactless coupler has a single turn on both the primary and secondary sides, the magnetizing inductance from the perspective of the secondary side (L\({}_{\text{m}0}\)) and the mutual inductance (M\({}_{\text{0}}\)) for a single turn are equivalent. Therefore, the mutual inductance (M\({}_{\text{0}}\)) for a single turn, which is used to determine the number of turns for the contactless coupler, was extracted using Maxwell 3D (Ansys Electronics Desktop 2021 R2) electromagnetic field analysis based on the determined coupler geometry (R/r/H: 100 mm/5 mm/4 mm) and the air gap (10 mm), resulting in a mutual inductance (M\({}_{\text{0}}\)) of 375.75 nH, as shown in Figure 7. Based on this, with a fixed output voltage (V\({}_{\text{o}}\): 400 V\({}_{\text{DC}}\)) and a rated output load of 1 kW, the number of turns on the primary side (N\({}_{\text{1}}\)) and secondary side (N\({}_{\text{2}}\)) of the contactless coupler was determined to be N\({}_{\text{1}}\) = 13 turns and N\({}_{\text{2}}\) = 19 turns, respectively (refer to [17] for more detail). Accordingly, the contactless coupler was fabricated as shown in Figure 9. Additionally, for wireless power transfer, international standards specify the frequency ranges for high-power devices (200 W to 2.4 kW). The WPC Qi standard designates an inductive power transfer frequency band of 87 kHz to 205 kHz. According to the wireless power transfer standard SAE-J2954 for electric vehicles, the standard power transfer system operates within a frequency range of 79 to 90 kHz, with a nominal power transfer frequency of 85 kHz [16]. In this study, as discussed in Section 5 (refer to Figure 11b), the resonant frequency (f\({}_{\text{r}}\)) was designed to be 80 kHz, maintaining consistent voltage gain characteristics regardless of the AC equivalent resistance (R\({}_{\text{ac}}\)) in the series-series compensation circuit.