## 3 Theory and Modeling  
### Principal and Modeling of Electret Transducer Component  
After polarization, the permanently polarized charges distributed on the surface of the electret serve as a source of electrostatic field, inducing surface charges on the metal plates. Relative motion causes changes in the equivalent capacitance of the electrostatic structure and the induced charge on the plates. This charge will be released into the external circuit, resulting in current output. In this structure, the electret transducer component consists of 16 plates arranged in pairs, equivalent to eight pairs of electrodes in parallel, enhancing the absolute output  
Figure 4: Mechanism of coupled structural rotational transmission and energy conversion. Figure 3: Schematic diagram of the rotational structure of the wind-energy-harvesting device. magnitude of the component. Due to the highly symmetric structure, a single pair of plates is analyzed. The working principle of the electret electrostatic component is based on the phenomenon of electrostatic induction with the electret acting as the field source. The ideal model can be derived from the charge induction and inter-electrode charge transfer theory of a parallel plate capacitor [12]. The theoretical model is based on the near-field assumption, which posits that under the condition where the distance between the plates is very small relative to the area of the plates, the electric field strength within the gap between the plates is uniformly distributed and perpendicular to the surface of the metal plate electrode. Furthermore, this model could only consider the interaction between the plates and the portion of the electret directly opposite them, because of the hypothesis that both the electret and the air are linear and uniform dielectrics, with a constant dielectric constant and a uniformly distributed internal electric field in the direction perpendicular to the upper and lower surfaces. Let the surface potential and charge of the upper side of the unipolar electret film be 0, while the lower side carries uniform unipolar surface charge. The electric field on both sides of the electret surface is discontinuous. Furthermore, the electret achieves fixed charges through high-voltage polarization; thus, its polarization effect could be neglected in the conditions of this model. Then, the induced charge on the upper surface of the metal plates could be calculated. When a unipolar electret moves from above plate 2 to above plate 1, the principle of electrostatic induction is illustrated in Figure 5 and then obtains Equation (2). On a unipolar electret, the surface charge and electric potential on the upper surface are zero, while the charge density \(\delta\) on the lower surface is fixed. As the electret moves, varying induced charges are generated in the region directly opposite the electrode plates, forming electric fields \(E_{r}\) and \(E_{1}\) within the electret and between the plates, as well as surface potentials \(V_{1}\) and \(V_{2}\). As the assumption mentioned earlier, neglecting the gap between electrodes and assuming a very small separation between the electret and the electrode plate, Equation (2) describes the electrostatic induction at the region of the electret directly opposite the plates:  
\[\left\{ \begin{array}{l}\varepsilon_{0}\varepsilon_{r}E_{r}-\varepsilon_{0} \varepsilon E_{1}=\delta\\ E_{r}h-E_{1}d=V_{2}\\ V_{2}=\frac{Q}{2\zeta}=\frac{\delta_{1}S}{2\zeta}\\ \frac{1}{\zeta}=\frac{h}{\varepsilon_{0}\varepsilon_{r}S}+\frac{d}{\varepsilon _{0}\varepsilon S}\\ \delta_{1}=\varepsilon_{0}\varepsilon E_{1}\end{array} \right. \tag{2}\]  
where \(d\) represents the distance between the electret and the plates, \(h\) is the thickness of the electret, \(\varepsilon_{r}\) and \(\varepsilon\) are the dielectric constants of the electret and air, respectively, \(S\) is the area  
Figure 5: Principle of induced charge on plates excited by electret during shaft rotation at speed of \(\omega_{r}\).