## 2 Methods  
The research of dynamic simulation of wind turbine under typhoon mainly includes three parts: simulation of typhoon fluctuating wind, modeling of wind turbine and aeroelastic response analysis. The whole framework is shown in Figure 2. Combined with the inverse Fourier transform method, the fluctuating wind is simulated by the power spectrum to record from the measured data of typhoon. A 6 MW wind turbine is modeled, the aerodynamic loads and aeroelastic are calculated by the blade element momentum and multibody dynamics. The aeroelastic responses and ultimate loads of the wind turbine at different inflow angles of typhoon are studied. According to the recorded data of the typhoon \"Hagupit\" [36], the wind speed in different regions of typhoons changes notably. From the typhoon gale region to the eye wall region and then to the typhoon center, the wind speed increases first and later decreases, respectively. After the typhoon center, the wind direction changes up to 180 degrees, so as to form a circular structure. The wind speed of the whole typhoon presents the distribution like the letter \"M\". Different researchers have fitted the typhoon measured data, of which the most suitable results are selected in relation with the characteristics of the eye wall region. The index of wind profile is 0.158, which is substituted in the index model listed as Equation (1):  
\[v=v_{0}(\frac{h}{h_{0}})^{\alpha}. \tag{1}\]  
The simulation of the typhoon needs a combined mean and fluctuating wind speed, and the spectral method is usually the general method to simulate the fluctuating wind distribution. Wind power spectral density (PSD) is the important parameter for describing and simulating in this part, which characterizes the energy distribution of the turbulence in different frequency ranges. At present, most of the studies taking into account these factors in wind energy usually adopt the Kaimal spectrum or Von Karman spectrum recommended in various standards [37], which are not combined with the measured data under the real typhoon environment. Obviously, the fluctuation characteristics of typhoon are quite different from that of the normal strong wind, so the spectral function in the specification is not applicable. In order to ensure the accuracy of the simulated fluctuating wind to represent the typhoon, the determination of the parameters in the fluctuating power spectrum should be based on the measured data from the strong typhoon as described above. Referring to the records and analysis of the fluctuating data of typhoon \"Hagupit\" from earlier reports [38; 39], the eyewall  
Figure 2: Block diagram structure of the analysis of wind turbine in typhoons. region of typhoon \"Hagupit\" is obtained based on the framework of the Moning-Obukhov similarity theory and the homogeneous isotropic turbulence theory. The power spectrum functions in three directions are shown in Equation (2):  
\[\left\{ \begin{array}{l}\frac{nS_{u}(n)}{u_{x}^{2}}=\frac{0.647f}{0.029+1.808f^{ 5/3}}\\ \frac{nS_{v}(n)}{u_{x}^{2}}=\frac{0.258f}{0.019+1.8f^{5/3}}\\ \frac{nS_{v}(n)}{u_{x}^{2}}=\frac{0.224}{0.148+2.869f^{5/3}}\end{array} \right.. \tag{2}\]  
In order to obtain the inflow conditions of typhoon for subsequent dynamic calculation, it is essential to convert the fitted power spectral density function to the frequency domain to simulate the fluctuating wind speed during the whole period according to the stationary Gauss process. Since the measured power spectrum of the typhoon has been fixed above in this paper, the inverse Fourier transform method [40] is chosen to realize the situation. This method can simulate the ideal wind field similar to the measured data with a high accuracy.