## 2 Characterization and Modeling of the Fault Ride-Through Process in Doubly Fed Wind Turbines
### Structured Model of Electromechanical Transient of Doubly Fed Wind Turbine
#### 2.2.1 Mechanical Side Control and FM Inertia Control Modules  
1. Mechanical side control module;  
The mechanical side control module is the key component in completing the maximum wind energy tracking function. Its internal components usually consist of the wind turbine model, shaft system model, and pitch angle control model, all of which work together. The wind turbine model embodies the efficiency of converting wind energy into mechanical energy. The wind turbine model mathematical model is as follows:  
\[\left\{ \begin{array}{l}P_{\text{m}}=\frac{1}{2}\rho\pi C_{\text{p}}(\lambda, \beta)V_{wind}^{3}R^{2}\\ \omega_{\text{m}}=\frac{P_{\text{m}}}{\omega_{\text{m}}}=\frac{1}{2}\rho\pi C _{\text{p}}(\lambda,\beta)v_{wind}^{2}R^{3}\\ C_{p}(\lambda,\beta)=c_{1}\big{(}\frac{c_{2}}{\lambda_{1}}-c_{3}\beta-c_{4} \big{)}e^{\frac{c_{\text{p}}}{\lambda_{1}}}+c_{6}\lambda\\ \frac{1}{\lambda_{1}}=\frac{1}{\lambda+0.08\beta}-\frac{0.035}{\beta^{3}+1} \end{array} \right. \tag{1}\]  
where \(P_{m}\) is the output power of the prime mover (wind turbine), \(T_{m}\) is the output torque of the wind turbine, \(\rho\) is the air density, \(V_{wind}\) is the actual wind speed, \(R\) is the radius of the wind turbine impeller, \(\omega_{m}\) is the angular velocity of the wind turbine machinery, \(C_{p}(\lambda,\beta)\) is the power coefficient of the wind turbine, \(\lambda\) is the optimal tip speed ratio of the wind turbine, and \(\beta\) is the pitch angle of the paddle. \(c_{1}\)-\(c_{6}\) are, respectively, 0.5176, 116, 0.4, 5, 21, and 0.0068. The shaft system model simulates the equations of motion of the drive shaft rotor, which mainly includes two parts, the low-speed shaft and the high-speed shaft, and is generally simulated by two mass-block models (the wind turbine and the generator as two mass-blocks), and ignores the damping coefficients of the wind turbine and the generator itself, so the complete two-mass-block dynamic mathematical model of the shaft system is as follows:  
\[\left\{ \begin{array}{l}2H_{\text{W}}\frac{d\omega_{\text{m}}}{dt}=T_{\text{ m}}-K_{\text{s}}\theta_{mg}-D_{\text{s}}\big{(}\omega_{\text{m}}-\omega_{gen} \big{)}\\ 2H_{\text{C}}\frac{d\omega_{\text{em}}}{dt}=T_{gen}+K_{\text{s}}\theta_{mg}+D_ {\text{s}}\big{(}\omega_{\text{m}}-\omega_{gen}\big{)}\\ \frac{d\theta_{mg}}{dt}=\omega_{base}\big{(}\omega_{\text{m}}-\omega_{gen} \big{)}\end{array} \right. \tag{2}\]  
where \(H_{\text{W}}\) and \(H_{\text{G}}\) are the inertia time constants of the wind turbine and generator rotor, respectively; \(T_{\text{gen}}\) is the generator rotor torque; \(\omega_{\text{gen}}\) is the generator rotor angular velocity; \(K_{\text{s}}\) is the stiffness coefficient of the shaft system; \(D_{\text{s}}\) is the damping coefficient between the wind turbine and the generator; \(\theta_{mg}\) is the torsion angle of the wind turbine concerning the rotor of the generator; and \(\omega_{\text{base}}\) is the rated rotational speed of the generator. The pitch angle control model embodies the wind turbine's control of the aerodynamic characteristics of the blades and the output power of the wind turbine, which can change the angle between the blade and the rotating plane according to the command value, thus achieving the effect of controlling the wind power absorbed by the wind turbine, and its control model is shown in Figure 4. It mainly plays two roles: when the wind speed is too large, the absorbed wind power is reduced by increasing the pitch angle; when the system encounters faults such as a three-phase short-circuit, in order to avoid rotor overload caused by the mechanical power being more significant than the electromagnetic power, the pitch angle also needs to be adjusted.