Simulation and Analysis of Direct-driven Wind Turbine

— Direct-driven wind turbine has become one of the mainstream technologies in wind power generation. Studying the system structure and the control technology of direct-driven wind turbine is the basis for optimization operation of direct-driven wind turbine. The system structure of direct-driven wind turbines is analyzed and the main subsystem mathematical model of direct-driven wind turbine are established, including wind speed model, aerodynamic model, generator model, and grid side converter model. The overall model of direct-driven wind turbine is established by integration of each subsystem mathematical model. The overall model of the direct-driven wind turbine is modeled and analyzed, and the simulation results show that the direct-driven wind turbine model can accurately reflect the dynamic characteristics of the direct-driven wind turbine operation process.


INTRODUCTION
With the gradual development of wind power technology, especially the development of large power converter technology, full power converter wind turbines have gradually become the mainstream model of wind power. Direct-driven wind turbine as a full power converter wind turbines have been obtained the widespread application. Therefore, studying the system structure and the operation principle of direct-driven wind turbine, is one of the main ways to improve the operating efficiency of direct -driven wind turbine.
Rolan et al. [1] analyzed the advantages of the directdriven wind turbine , established the wind speed model, the aerodynamic model and the generator model. These model were simulated and analyzed, the results show that these model can reflect the operating characteristics of the direct-driven wind turbine in a certain extent. Kim et al. [2] analyzed and simulated the direct-driven wind turbine control system and presented a direct-driven wind turbine reactive power control algorithm, so as to provide reactive power support for grid. The converter is an important component of the direct-driven wind turbine, therefore, research on the control algorithm of the full power converter is the basis for the stable operation of the direct-driven wind turbines [3][4]. Tiwari et al. [5][6] modeled and analyzed the direct-driven wind turbine using MATLAB/SIMULINK toolbox, which further promotes the study of the direct-driven wind turbine technology. Jayalakshmi et al. [7][8] analyzed the running characteristics of the grid type direct-driven wind turbines, and established the corresponding simulation model ,which provides support for the grid control technology research of the direct-driven wind turbines. Janani et al. [9] analyzed and modeled the small directdriven wind turbine running principle, which Provides the foundation for the application of the small direct-driven wind turbine. Large direct-driven wind turbines are the development direction of the direct-driven wind turbine. Studying the large direct-driven wind turbine operating principle and control scheme are to provide support for the application of the direct-driven wind turbine [10].
Based on the existing direct-driven wind turbine research, the system of the direct-driven wind turbine are analyzed. The mathematical model of the direct-driven wind turbine main subsystems are established, including wind speed model, aerodynamic model, generator model, the grid side converter model. The whole model of the direct-driven wind turbine is established by integrating each subsystem mathematical model. The dynamic characteristics of the direct-driven wind turbine are studied and analyzed.

II. WIND SPEED MODEL
Before the system mathematical model of the directdriven wind turbine is established, the overall structure of the direct-driven wind turbine is analyzed firstly. The overall structure of the direct-driven wind turbine is shown as Figure 1.
The direct-driven wind turbine includes the rotor, the direct-driven permanent magnet synchronous generator (PMSG), the converter (including machine side converter and grid side converter), the direct-driven wind turbine control system, the power grid and other parts. The rotor is to convert the wind energy into the mechanical energy. For the direct-driven wind turbine, the rotor is directly connected to the direct-driven permanent magnet synchronous generator, so the gear box is no longer needed. The PMSG converts the mechanical energy into the electrical energy. However, because of the frequency and the amplitude of the PMSG output voltage do not match, the PMSG can not be directly connected to the grid, the PMSG is connected to the power system through a converter. The direct-driven wind turbine control system is responsible for the wind turbine maximum wind energy capture, as well as the amplitude control and the phase control of the converter output voltage. The coordinated operation between the direct-driven wind turbine and the power grid is achieved. Wind speed is the power source of the wind turbine and the wind speed PAPER SIMULATION AND ANALYSIS OF DIRECT-DRIVEN WIND TURBINE model is the basis for the research of the wind turbine. Wind speed model is studied and analyzed firstly in this paper.
The natural wind speed has random characteristics, and the natural wind speed can be described through the Vander Hoven wind speed spectrum model, As shown in Figure 2.  Figure 2 shows that the Vander Hoven wind speed spectrum model is composed of the mid-long term wind speed and the short-time wind speed (the part of the dotted line in Figure 2, the wind speed spectrum curve from the beginning of 10min to the right). The short-time wind speed is the main factor influencing the dynamic characteristics of the wind turbine and the wind energy capture efficiency. Therefore, The wind speed model established in the paper is the short-term wind speed model.
The short-time wind speed can be composed of the average wind speed (the average wind speed between the 10 min to 1 h) and the turbulence. The turbulence obeys the gauss normal distribution and the average value of the gauss normal distribution is zero, and the standard of the gauss normal distribution deviation depends on the size of the average wind speed. The calculation formula can be shown as equation (1) . where, Where, ( ) t v S w represents power spectral density and its value is constant, ( ) t H jw !represents the transfer function of the shaping filter. Von Karman gave the shaping filter transfer function expression, which is shown as equation (3).
Where,  ( ) Where, S T represents the sampling time of the white noise, which can be configured. ( ) , B x y represents the beta function. The non integer order filter in the Von Karman filter is used in equation (3), the calculation process of the non integer order filter is difficult. Therefore, this article uses the improved Von Karman filter and the improved Von Karman filter has the integer order transfer function. The improved von Karman filter transfer function has the same efficiency with the non integer order filter, but the calculation process becomes simple. The improved filter transfer function expression formula is shown as equation (6).
Based on the above knowledge, the calculation process of the turbulence can be shown as Figure 3. When the average wind speed is 14m/s, the standard deviation ! is greater than the standard deviation of the average speed 7m/s. The above simulation results prove the correctness of the established turbulence model.

III. MATHEMATICAL MODEL OF THE AERODYNAMIC
Rotor is the device to convert wind energy into mechanical energy. The conversion relation is shown as equation (7) . Where, WT P represents the mechanical power of the wind turbine; ! represents the air density; R !represents the rotor radius; v represents the wind speed; ! represents the pitch Angle; ! represents tip speed ratio; p C represents the wind energy use efficiency. The relationship among p C , ! and ! is shown as equation (8). Figure 6 illustrate the relationship among p C , ! and ! . This paper mainly studies the dynamic characteristics of the direct-driven wind turbine. In order to facilitate the analysis of the main problems, the directdriven wind turbine is running below the rated wind speed and the pitch angle is 0 degrees in the study process.! Under this assumption, the size of p C is associated with ! only.

SYSTEM
The voltage (a, b, c) three coordinate system can be transformed into (d, q) two coordinate system through the Park transform. The transformed coordinate system (d, q) is shown as equation (9).
Where R represents the stator resistance; d u and q u represent d axis and q axis stator voltage component respectively; d L and q L represent d axis and q axis inductance respectively; S ! represents the stator frequency; d ! and q ! represent d axis and q axis magnetic flux respectively; d ! and q ! can be calculated from equations (10) and (11).
In equation (10), m ! is determined by the permanent magnet constant flux.
The electromagnetic torque can be calculated by equation (13).
Where, p represents the number of pole pairs. If the permanent magnet is installed in the rotor surface , then d L = q L . The equation (13) can be simplified as equation (14).
When the generator connected to the grid, the equation (12) is turned into equation (15).
The simulation model of the generator control system is shown as figure 7.

V. MATHEMATICAL MODEL OF THE GRID SIDE CONVERTER
For direct-driven wind turbine, the grid side converter works in the inverter mode. The voltage and the current of the inverter complies with the requirements of the AC network. Figure 8 is a direct-driven wind turbine grid side threephase voltage source inverter structure diagram. g L represents grid side filter inductor parameters, g R represents grid side line resistance. For the grid side, the inductance equivalent impedance is far greater than the resistance value. In the control system design the impact of g R on the control system is negligible. The DC voltage source dc u is!on behalf of the grid side inverter DC bus voltage.! During the model building process, the three-phase grid voltage are assumed symmetrical and stable. The switch components in the circuit are the ideal switch. The DC bus voltage dc u maintains constant.! The grid side filter inductor g L !has a linear characteristic and without considering the saturation.  ' ' The state equation of equation (21) is shown as equation (22). According to the mathematical model of the aforementioned direct-driven wind turbine, the directdriven wind turbine control system structure is constructed, which is shown as Figure 9.
The control system is modeled and analyzed, the model parameters are shown in Table 1. The direct-driven wind turbine dynamic characteristic is simulated and analyzed using the constructed model. Figure 10 is the direct-driven wind turbine stator output voltage. In the simulation process, the grid voltage drops to 90KV from 120KV within 0.03-0.13 seconds, the system is back to normal at 0.13 seconds after. Figure 10 shows that the direct-driven wind turbine output voltage also reduces with the grid voltage dropping. When the  Figure 11 is the direct-driven wind turbine stator output current. Figure 11 shows that the generator stator output current increases within 0.03-0.13 seconds. The generator stator output current increases mainly because the direct-driven wind turbine in order to maintain the stability of the output voltage of the stator end in this period. The reactive power output is increased, resulting in the direct-driven wind turbine output current increases. In 0.13 seconds later, the grid voltage returns to normal, but the generator output current requires a response time to return to normal, this is because of the lag of the direct-driven wind turbine power output control system response time.  Figure 12 is the direct-driven wind turbine output active power. It is can be seen from Figure 12 that the direct-driven wind turbine output active power reduces within 0.03-0.13 seconds. In 0.13 second later, the grid voltage returns to normal, but the generator output active power requires a response time to return to normal, this is because of the lag of the direct-driven wind turbine active power output control system response time. Figure 13 is the DC bus voltage of the direct-driven wind turbine. It is can be seen from Figure 13 that the DC bus voltage increases mainly due to the increasing of the direct-driven wind turbines output reactive power within 0.03-0.13 seconds. In 0.13 seconds later, the grid voltage returns to normal, the DC bus voltage fluctuates a period time before to return to normal, this is because of the lag of the DC bus control system response time. The system structure of the direct-driven wind turbine was analyzed in the paper. The mathematical model of the direct-driven wind turbine all major subsystems, including wind speed model, aerodynamic model generator model, the grid-side converter model were established. Based on these subsystems, the whole model of the direct-driven wind turbine was established by integrating the various subsystem mathematical model.
The whole model of the direct-driven wind turbine was modeled and analyzed, the simulation results indicate that the direct-driven wind turbine model can accurately reflect the dynamic characteristics of the wind turbine operation process. The study of the paper provides support for studying the wind turbine operating principles and improving wind turbine operating efficiency.