Abstract:
A method is disclosed for controlling a wind turbine by optimizing its production while minimizing the mechanical impact on the transmission. The wind turbine comprises a nacelle provided with a rotor on which blades are fastened, and an electrical machine linked to the rotor by a transmission, in which an pitch angle of the blades is controlled, comprising: An aerodynamic torque setpoint and an electrical machine torque setpoint making possible maximizing the recovered power are determined, from measurements of wind speed, of rotor speed and of electric machine speed. At least one of the setpoints is modified by subtracting from it a term proportional to a difference between the measured speed of the rotor and the measured speed of the electric machine. A pitch angle of the blades making possible production of the aerodynamic torque setpoint is determined. The blades are oriented according to the angle of inclination.

Description:
BACKGROUND OF THE INVENTION 
       [0001]    1. Field of the Invention 
         [0002]    The present invention relates to the field of renewable energies and more particularly to the control of wind turbines. 
         [0003]    2. Description of the Prior Art 
         [0004]    A wind turbine makes possible transformation of the kinetic energy of the wind into electrical or mechanical energy. The wind turbine has the following elements: 
         [0005]    A mast used to place the rotor at a sufficient height to allow for its movement (necessary for the wind turbines with a horizontal axis) or to place the rotor at a height that allows it to be driven by a wind that is stronger and more regular than at ground level. The mast generally houses some of the electrical and electronic components (modulator, control, multiplying year, generator, etc.). 
         [0006]    A nacelle mounted at the top of the mast, housing the mechanical and pneumatic components, and some of the electrical and electronic components, necessary to the operation of the machine. The nacelle can rotate to orient the machine in the right direction. 
         [0007]    A rotor, having blades (generally three) and the nose of the wind turbine fastened to the nacelle. The rotor is driven by the energy of the wind and is linked by a mechanical shaft directly or indirectly (via a mechanical gearbox and shaft system) to the electrical machine (electrical generator, etc) which converts the energy collected into electrical energy. 
         [0008]    A transmission, with two axes (mechanical shaft of the rotor and mechanical shaft of the electrical machine) linked by a gearbox. 
         [0009]    In the case of offshore wind, a distinction is made between the case where the wind turbine is placed on the seabed (fixed or established wind turbine), and the case where the wind turbine is supported by a platform which floats on the sea and which is anchored to the seabed (floating wind turbine). 
         [0010]    Since the beginning of the 1990s, there has been an upsurge of interest in wind energy, in particular in the European Union where the annual growth rate is approximately 20%. This growth is attributed to the production of electricity without carbon emissions. In order to sustain this growth, the efficiency of the wind turbines has to continue to be improved. Wind turbines are designed to produce electricity at a price that is as low as possible. Consequently, the wind turbines are generally constructed to achieve maximum performance at approximately 15 m/s. It is in fact pointless to design wind turbines which maximize their efficiency at even higher wind speeds, since such speeds are infrequent. In the case of wind speeds greater than 15 m/s, it is necessary to lose a portion of the additional energy contained in the wind in order to avoid any damage to the wind turbine. All the wind turbines are therefore designed with a power regulation system. 
         [0011]    Increasing wind energy production requires developing effective production tools and sophisticated control tools to enhance the performance levels of the machines. Consequently, the wind turbines are generally constructed to achieve their maximum performance at approximately 15 m/s. 
         [0012]    Linear controllers have been widely used for the power regulation by controlling the pitch angle of the blades (orientation of the blades). Techniques that use PI and PID controllers, LQ and LQG control techniques and strategies based on robust linear controls are known. 
         [0013]    However, the performance levels of these linear controllers are limited by the greatly non-linear characteristics of the wind turbine. First strategies based on non-linear controls were used in: Boukhezzar B., Lupu L., Siguerdidjane H., Hand M. “ Multivariable Control Strategy for Variable Speed, Variable Pitch Wind Turbines ” Renewable Energy, 32(2007) 1273-1287. 
         [0014]    However, none of these controllers makes it possible to take account for the mechanical impact (fatigue and extreme moment) on the transmission. Most wind turbine failures are due to breakages or damage affecting the transmission. From data recovered on an offshore application, breakages of the transmission, of the gearbox or of the electrical machine represent nearly 39% of the time when the wind turbine is not producing. 
       SUMMARY OF THE INVENTION 
       [0015]    The invention relates to a method for optimizing the electrical energy production of a wind turbine, by implementing a non-linear control of the orientation of the blades that accounts for the dynamics of the system, while minimizing the mechanical impact on the transmission. The impact is minimized by reducing the torsion speed variations of the transmission by accounting for the drift of the torsion angle of the transmission. 
         [0016]    Generally, the invention relates to a method for optimizing the electrical energy production of a wind turbine comprising a nacelle provided with a rotor on which blades are fastened, and an electrical machine linked to the rotor by a transmission, in which a pitch angle of the blades is controlled. The method comprises: 
         [0017]    a) determining an aerodynamic torque setpoint and an electric machine torque setpoint which maximizes the recovered power, from measurements of wind speed, of rotor speed and of the electrical machine speed; 
         [0018]    b) at least one of the setpoints is modified by subtracting from it a term proportional to a difference between the measured speed of the rotor and the measured speed of the electrical machine; 
         [0019]    c) determining a pitch angle of the blades that produces aerodynamic torque setpoint; and 
         [0020]    d) orienting the blades according to the angle of inclination. 
         [0021]    According to the invention, at least one of the setpoints is modified by carrying out the following steps: 
         [0022]    i) a torque  T   res  on the transmission resulting from the aerodynamic torque and electric machine torque setpoints is determined; 
         [0023]    ii) a resultant torque setpoint T res   sp  is determined by subtracting from the resultant torque  T   res  a term proportional to the difference between the measured speed of the rotor and the measured speed of the electric machine; 
         [0024]    iii) the aerodynamic torque setpoint is modified by dividing up the resultant torque setpoint into an aerodynamic torque and an electric machine torque. According to the invention, the resultant torque setpoint T res   sp  can be expressed as follows: 
         [0000]    
       
      
       T 
       res 
       sp 
       =  T   
       res 
       −ký 
       tr  
      
     
         [0000]    k is being strictly positive calibration parameters, and ý tr  is the speed of the torsion of the transmission, equal to a difference in speed of the rotor Ω r , and of the electrical machine Ω g  related to the same axis: 
         [0000]    
       
         
           
             
               
                 
                   γ 
                   . 
                 
                 tr 
               
               = 
               
                 
                   Ω 
                   r 
                 
                 - 
                 
                   
                     1 
                     N 
                   
                    
                   
                     Ω 
                     g 
                   
                 
               
             
             , 
           
         
       
     
         [0000]    where N is a gear ratio between the axis of the rotor and the axis of the electrical machine. 
         [0025]    The pitch angle of the blades can be determined by inverting an aerodynamic torque model and by using the wind speed and rotor speed measurements. 
         [0026]    Finally, the proportional term can be determined by using a model of the dynamics of the transmission. 
         [0027]    Other features and advantages of the method according to the invention will become apparent on reading the following description of non-limiting exemplary embodiments, by referring to the appended drawings described hereinbelow. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0028]      FIG. 1  represents the sequencing of the steps of the method according to the invention. 
           [0029]      FIG. 2  illustrates an exemplary mapping of the parameter c q . 
       
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
       [0030]    In the description, the following notations are used: 
         [0031]    Controlled variables:
   θ is the pitch angle of the blades in degrees, which is also called “pitch” and which corresponds to the angle of attack to the wind of each of the blades.   T g  is the torque of the electric machine in Nm; and   T aero  is the aerodynamic torque (rotational force applied to the rotor under the effect of the wind).   
 
         [0035]    Measured variables, denoted MEAS(-):
   V W  is the speed of the wind in m/s which is derived from a measurement from an anemometer or derived from an estimation;   Ω r  is the speed of the rotor in rad/s; and   Ω g  the speed of the electric machine in rad/s.   
 
         [0039]    The method according to the invention maximizes the energy production of an onshore or offshore wind turbine while limiting the extreme moments and the fatigue of the transmission. To do this, a rotor speed setpoint and an electrical machine torque setpoint are determined first to maximize the recovered power. These two setpoints are obtained by mappings which are a function of the wind speed. This type of mapping is well known. 
         [0040]    To control the mechanical structure, the aerodynamic torque applied to the hub is driven by actuating the orientation of the blades. To do this, models are used of this average aerodynamic torque as a function of the pitch, of the wind speed and of the speed of the rotor. Then, the position setpoint of the pitch and of the torque of the electric machine is modified in order to limit the mechanical impact of the wind variations. Thus, to model driving the system, the steps illustrated in  FIG. 1  are carried out: 
         [0041]    E1. Determination of the pitch making possible optimizing the recovered power
       i. Generation of an electrical torque setpoint T g   sp      ii. Generation of an aerodynamic torque setpoint T aero   sp      iii. Determination of a pitch position  θ         
 
         [0045]    E2. Determination of the resultant torque of the torque setpoint T g   sp  and T aero   sp    
         [0046]    E3. Generation of a resultant torque setpoint (T res   sp ) which reduces the fatigue and the extreme moments of the transmission 
         [0047]    E4. Dividing up of the resultant torque setpoint (T res   sp ) between the aerodynamic and electrical torques 
         [0048]    E5. Determination of a pitch position which makes it possible to produce this aerodynamic torque 
         [0049]    E6. Orientation of the blades according to the determined pitch 
       1. Determination of the Pitch Making it Possible to Optimize the Recovered Power 
       [0050]    One aspect of the method according to the invention is to maximize the energy production of a wind turbine with a horizontal axis (propeller at right angles to the wind), installed onshore or offshore, while limiting the extreme moments and the fatigue of the mechanical structure. 
         [0051]    To maximize the energy production of a wind turbine, the pitch angle of the blades, called “pitch” and denoted  θ , that makes it possible to maximize the recovered power P aero  as a function of the wind speed V W , is sought. The orientation of the blades is the angle between the blades and a reference such as the ground (horizontal plane, at right angles to the mast of the wind turbine). 
         [0052]    According to one embodiment, to define this angle, a model of the recoverable power is used. This power P aero  can be expressed: 
         [0000]        P   aero   =T   aero *Ω r  
 
         [0000]    with:
       T aero  being the aerodynamic torque (rotational force applied to the rotor under the effect of the wind);   Ω r  being the speed of the rotor in rad/s.       
 
         [0055]    The angle  θ  which makes it possible to maximize P aero  is therefore sought. To do this, the following steps are carried out:
       i.—Generation of a torque setpoint of the electric machine T g   sp      ii.—Generation of an aerodynamic torque setpoint T aero   sp      iii.—Determination of a pitch position  θ 
 
i—Generation of a Torque Setpoint of the Electric Machine T g   sp  
       
 
         [0059]    A torque setpoint of the electric machine T g   sp  is first determined. This setpoint is obtained mapping as a function of the speed of the electric machine. 
         [0060]    According to the invention, the aerodynamic torque T aero  is modeled by a model describing the power of the wind contained in a cylinder, multiplied by a factor describing the fact that a wind turbine allows only a portion of this power to be recovered. The aerodynamic torque is thus modeled as a function of the speed of the wind V W , of the pitch θ and of the speed of the rotor Ω r . Such a model can thus be expressed, in steady state operation: 
         [0000]    
       
         
           
             
               
                 
                   
                     T 
                     aero 
                   
                   = 
                   
                     0.5 
                      
                     
                         
                     
                      
                     ρ 
                      
                     
                         
                     
                      
                     Π 
                      
                     
                         
                     
                      
                     
                       R 
                       b 
                       3 
                     
                      
                     
                       
                         c 
                         q 
                       
                        
                       
                         ( 
                         
                           θ 
                           , 
                           
                             
                               
                                 R 
                                 b 
                               
                                
                               
                                 Ω 
                                 r 
                               
                             
                             
                               V 
                               w 
                             
                           
                         
                         ) 
                       
                     
                      
                     
                       V 
                       w 
                       2 
                     
                   
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
           
         
       
     
       With: 
       [0000]    
       
         
           
             R b : the radius of the rotor; 
             ρ: the density of the air; 
             c q : the mapping to be calibrated. 
           
         
       
     
         [0064]    An exemplary mapping of the parameter c q  is presented in  FIG. 2 . This mapping indicates the value of the parameter c q  as a function of the ratio 
         [0000]    
       
         
           
             
               
                 R 
                 b 
               
                
               
                 Ω 
                 r 
               
             
             
               V 
               w 
             
           
         
       
     
         [0000]    for different pitches (one curve for each θ). This type of mapping is well known to the experts. The ratio 
         [0000]    
       
         
           
             
               
                 R 
                 b 
               
                
               
                 Ω 
                 r 
               
             
             
               V 
               w 
             
           
         
       
     
         [0000]    is denoted TSR in  FIG. 2 . 
         [0065]    Thus, to determine the torque setpoint of the electric machine as a function of the speed of the electric machine, the recovered aerodynamic power is optimized for each wind speed. 
         [0000]    
       
         
           
             
               T 
               g 
               sp 
             
             = 
             
               arg 
                
               
                 ( 
                 
                   
                     max 
                     
                       θ 
                       , 
                       
                         V 
                         w 
                       
                     
                   
                    
                   
                     
                       0.5 
                       N 
                     
                      
                     ρ 
                      
                     
                         
                     
                      
                     Π 
                      
                     
                         
                     
                      
                     
                       R 
                       b 
                       3 
                     
                      
                     
                       
                         c 
                         q 
                       
                        
                       
                         ( 
                         
                           θ 
                           , 
                           
                             
                               
                                 R 
                                 b 
                               
                                
                               
                                 Ω 
                                 g 
                               
                             
                             
                               NV 
                               w 
                             
                           
                         
                         ) 
                       
                     
                      
                     
                       V 
                       w 
                       2 
                     
                   
                 
                 ) 
               
             
           
         
       
     
         [0066]    This gives us the setpoint torque Tg which depends on the speed of the electric machine: T g   sp =f(Ω g ) 
         [0067]    However, compared to this reference curve, two limitations are applied:
       a zero torque for the low speeds of the electrical machine to be able to increase the speed of the wind turbine;   a maximum torque to limit the power of the electrical machine.       
 
         [0070]    Thus, there are three regions on the curve T g   sp =f(Ω g ):
       Region 1: zero torque;   Region 2: optimum torque;   Region 3: torque limited by the maximum power.
 
ii—Generation of an Aerodynamic Torque Setpoint T aero   sp  
       
 
         [0074]    The objective is to generate an aerodynamic torque setpoint T aero   sp  which makes it possible to produce the setpoint rotor speed Ω g   sp . For this, a model of the dynamics of the rotor is used. 
         [0000]    
       
         
           
             
               
                 J 
                 r 
               
                
               
                 
                    
                   
                     Ω 
                     r 
                   
                 
                 
                    
                   t 
                 
               
             
             = 
             
               
                 T 
                 aero 
               
               - 
               
                 
                   T 
                   l 
                 
                  
                 
                   ( 
                   
                     Ω 
                     r 
                   
                   ) 
                 
               
               - 
               
                 
                   NT 
                   g 
                 
                  
                 
                   ( 
                   
                     Ω 
                     g 
                   
                   ) 
                 
               
             
           
         
       
     
         [0000]    with:
       J r  being inertia of the rotor;   T I (Ω r ) being friction and load torque on the rotor (a second order polynomial is conventionally used);   N being a gear ratio between the axis of the rotor and the axis of the electric machine.       
 
         [0078]    Thus, the control strategy used is a dynamic control strategy which anticipates the setpoint variation and which corrects with two terms, a proportional term and an integral term. The strategy is expressed: 
         [0000]    
       
         
           
             
               T 
               aero 
               sp 
             
             = 
             
               
                 
                   T 
                   l 
                 
                  
                 
                   ( 
                   
                     Ω 
                     r 
                   
                   ) 
                 
               
               + 
               
                 
                   nT 
                   e 
                 
                  
                 
                   ( 
                   
                     Ω 
                     r 
                   
                   ) 
                 
               
               + 
               
                 
                   J 
                   r 
                 
                  
                 
                   
                      
                     
                       Ω 
                       r 
                       sp 
                     
                   
                   
                      
                     t 
                   
                 
               
               - 
               
                 
                   k 
                   p 
                 
                  
                 
                   ( 
                   
                     
                       Ω 
                       r 
                     
                     - 
                     
                       Ω 
                       r 
                       sp 
                     
                   
                   ) 
                 
               
               - 
               
                 
                   k 
                   i 
                 
                  
                 
                   ∫ 
                   
                     ( 
                     
                       
                         Ω 
                         r 
                       
                       - 
                       
                         Ω 
                         r 
                         sp 
                       
                     
                     ) 
                   
                 
               
             
           
         
       
     
         [0079]    where kp and ki are two real parameters to be calibrated to guarantee the convergence of the speed toward its setpoint. 
         [0000]    iii—Determination of a Pitch Position  θ   
         [0080]    From this aerodynamic torque setpoint T aero   sp , a pitch angle  θ  of the blades is determined which satisfies this aerodynamic torque demand T aero   sp . For this, the aerodynamic torque model (equation 1) is used, with the measurement of the speed of the wind V W , the measurement of the speed of the rotor Ω r   sp , and the setpoint torque T aero   sp . By inverting the model (by a Newton algorithm for example), a pitch setpoint  θ  is obtained: 
         [0000]    
       
         
           
             
               θ 
               _ 
             
             = 
             
               arg 
                
               
                 ( 
                 
                   
                     min 
                     θ 
                   
                    
                   
                     
                       ( 
                       
                         
                           T 
                           aero 
                           sp 
                         
                         - 
                         
                           0.5 
                            
                           
                               
                           
                            
                           ρ 
                            
                           
                               
                           
                            
                           Π 
                            
                           
                               
                           
                            
                           
                             R 
                             b 
                             3 
                           
                            
                           
                             
                               c 
                               q 
                             
                              
                             
                               ( 
                               
                                 θ 
                                 , 
                                 
                                   
                                     
                                       R 
                                       b 
                                     
                                      
                                     
                                       Ω 
                                       r 
                                     
                                   
                                   
                                     V 
                                     w 
                                   
                                 
                               
                               ) 
                             
                           
                            
                           
                             V 
                             w 
                             2 
                           
                         
                       
                       ) 
                     
                     2 
                   
                 
                 ) 
               
             
           
         
       
     
         [0081]    Thus, with this control law, the convergence toward the reference rotor speed is guaranteed which makes it possible to maximize the recovered power. 
       2—Determination of the Resultant Torque of the Torque Setpoints T g   sp  and T aero   sp    
       [0082]    From the setpoints T g   sp  and T aero   sp , the torque  T   res  resulting from these two torques and which will bear on the transmission is determined. For this, this torque is modelled by the following formula: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       T 
                       _ 
                     
                     res 
                   
                   = 
                   
                     
                       
                         
                           J 
                           g 
                         
                         
                           
                             J 
                             r 
                           
                           + 
                           
                             J 
                             g 
                           
                         
                       
                        
                       
                         ( 
                         
                           
                             T 
                             aero 
                             sp 
                           
                           - 
                           
                             T 
                             l 
                           
                         
                         ) 
                       
                     
                     + 
                     
                       
                         
                           J 
                           r 
                         
                         
                           
                             J 
                             r 
                           
                           + 
                           
                             J 
                             g 
                           
                         
                       
                        
                       
                         NT 
                         g 
                         sp 
                       
                     
                   
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
           
         
       
     
         [0083]    wherein J r  and J g  are the inertias of the rotor and of the electric machine. 
       3—Generation of a Resultant Torque Setpoint (T res   sp ) Which Reduces the Fatigue and the Moments of the Transmission 
       [0084]    Efforts are made to modify this resultant torque  T   res  in order to minimize the impact on the transmission and therefore increase its life. For this, efforts are made to reduce the torsion speed variations of the transmission. Thus, efforts are made to compensate the torque with terms proportional to the difference between the speed of the rotor and of the electric machine. The dynamics of the mechanical structure (dynamics of the transmission) can be expressed in the form of two coupled second order systems. 
         [0000]    
       
         
           
             
               
                 
                   { 
                   
                     
                       
                         
                           
                             
                               
                                 
                                   J 
                                   r 
                                 
                                  
                                 
                                   J 
                                   g 
                                 
                               
                               
                                 
                                   J 
                                   r 
                                 
                                 + 
                                 
                                   J 
                                   g 
                                 
                               
                             
                              
                             
                               
                                 γ 
                                 ¨ 
                               
                               tr 
                             
                           
                           = 
                           
                             
                               
                                 - 
                                 
                                   c 
                                   d 
                                 
                               
                                
                               
                                 γ 
                                 tr 
                               
                             
                             - 
                             
                               
                                 k 
                                 d 
                               
                                
                               
                                 
                                   γ 
                                   . 
                                 
                                 tr 
                               
                             
                             + 
                             
                               
                                 
                                   J 
                                   g 
                                 
                                 
                                   
                                     J 
                                     r 
                                   
                                   + 
                                   
                                     J 
                                     g 
                                   
                                 
                               
                                
                               
                                 ( 
                                 
                                   
                                     T 
                                     aero 
                                   
                                   - 
                                   
                                     T 
                                     l 
                                   
                                 
                                 ) 
                               
                             
                             + 
                             
                               
                                 
                                   J 
                                   r 
                                 
                                 
                                   
                                     J 
                                     r 
                                   
                                   + 
                                   
                                     J 
                                     g 
                                   
                                 
                               
                                
                               
                                 NT 
                                 g 
                               
                             
                           
                         
                       
                     
                     
                       
                         
                           
                             
                               J 
                               g 
                             
                              
                             
                               
                                 Ω 
                                 . 
                               
                               g 
                             
                           
                           = 
                           
                             
                               
                                 c 
                                 d 
                               
                                
                               
                                 γ 
                                 tr 
                               
                             
                             + 
                             
                               
                                 k 
                                 d 
                               
                                
                               
                                 
                                   γ 
                                   . 
                                 
                                 tr 
                               
                             
                             + 
                             
                               
                                 N 
                                 gb 
                               
                                
                               
                                 T 
                                 g 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
           
         
       
     
         [0085]    where
       γ tr , {dot over (γ)} tr  and ÿ tr  are respectively the angle, the speed and the acceleration of the torsion of the shaft. It should be noted that the torsion speed of the transmission is the difference in speed of the rotor and of the generator related to the same axis, i.e.       
 
         [0000]    
       
         
           
             
               
                 
                   γ 
                   . 
                 
                 tr 
               
               = 
               
                 
                   Ω 
                   r 
                 
                 - 
                 
                   
                     1 
                     N 
                   
                    
                   
                     Ω 
                     g 
                   
                 
               
             
             ; 
           
         
       
       
         
           
             kd is the structural damping of the transmission; 
             cd is the stiffness of the transmission. 
           
         
       
     
         [0089]    Thus, the control strategy generates a resultant torque different from  T   res  to minimize the fatigue and the extreme moments of the transmission. Therefore, the relationship: 
         [0000]        T   res   sp =    T   res   − k {dot over (γ)} tr  
 
         [0090]    with k being strictly positive calibration parameters. These parameters can be determined by trial and error. It can be considered that all these parameters k are equal to 1 for example. 
       4—Dividing Up of the Resultant Setpoint Torque (T res   sp ) Between the Aerodynamic and Electrical Torques 
       [0091]    This resultant torque setpoint T res   sp  is then divided up between the aerodynamic torque T aero  and the torque of the electric machine T g . For this, the dividing up is done according to operational areas. In an area 2, where the aerodynamic torque is limiting, a reserve of torque is present. In this case, the torque modification influences the torque of the electrical machine and not the aerodynamic torque. Thus, in this case, the relationship: 
         [0000]    
       
         
           
             
               
                 
                   { 
                   
                     
                       
                         
                           
                             T 
                             aero 
                             strat 
                           
                           = 
                           
                             T 
                             aero 
                             sp 
                           
                         
                       
                     
                     
                       
                         
                           
                             T 
                             g 
                             strat 
                           
                           = 
                           
                             
                               T 
                               g 
                               sp 
                             
                             - 
                             
                               k 
                                
                               
                                 
                                   
                                     J 
                                     r 
                                   
                                   + 
                                   
                                     J 
                                     g 
                                   
                                 
                                 
                                   NJ 
                                   r 
                                 
                               
                                
                               
                                 
                                   γ 
                                   . 
                                 
                                 tr 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
           
         
       
     
         [0000]    Similarly, in an area 3, where the torque of the electrical machine is limiting, the torque modification influences the aerodynamic torque which gives the relationship: 
         [0000]    
       
         
           
             
               
                 
                   { 
                   
                     
                       
                         
                           
                             T 
                             aero 
                             strat 
                           
                           = 
                           
                             
                               T 
                               aero 
                               sp 
                             
                             - 
                             
                               k 
                                
                               
                                 
                                   
                                     J 
                                     r 
                                   
                                   + 
                                   
                                     J 
                                     g 
                                   
                                 
                                 
                                   J 
                                   g 
                                 
                               
                                
                               
                                 
                                   γ 
                                   . 
                                 
                                 tr 
                               
                             
                           
                         
                       
                     
                     
                       
                         
                           
                             T 
                             g 
                             strat 
                           
                           = 
                           
                             T 
                             g 
                             sp 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   5 
                   ) 
                 
               
             
           
         
       
     
       5—Determination of a Pitch Position Makes Possible Production Other Aerodynamic Torque 
       [0092]    From the aerodynamic torque setpoint T aero   strat , a pitch angle θ SP  of the blades is determined to satisfy this aerodynamic torque demand T aero   strat . For this, the aerodynamic torque model (equation 1) is used, with the measurement of the speed of the wind V W , the measurement of the speed of the rotor Ω r   sp , and the setpoint torque T aero   strat . By inverting the model (by a Newton algorithm for example), a pitch setpoint θ SP  is obtained: 
         [0000]    
       
         
           
             
               θ 
               SP 
             
             = 
             
               arg 
                
               
                 ( 
                 
                   
                     min 
                     θ 
                   
                    
                   
                     
                       ( 
                       
                         
                           T 
                           aero 
                           strat 
                         
                         - 
                         
                           0.5 
                            
                           
                               
                           
                            
                           ρ 
                            
                           
                               
                           
                            
                           Π 
                            
                           
                               
                           
                            
                           
                             R 
                             b 
                             3 
                           
                            
                           
                             
                               c 
                               q 
                             
                              
                             
                               ( 
                               
                                 θ 
                                 , 
                                 
                                   
                                     
                                       R 
                                       b 
                                     
                                      
                                     
                                       Ω 
                                       r 
                                     
                                   
                                   
                                     V 
                                     w 
                                   
                                 
                               
                               ) 
                             
                           
                            
                           
                             V 
                             w 
                             2 
                           
                         
                       
                       ) 
                     
                     2 
                   
                 
                 ) 
               
             
           
         
       
     
         [0093]    Thus, with this control law, the convergence toward the reference rotor speed is guaranteed, making it possible to maximize the recovered power, while minimizing the mechanical impact (fatigue and extreme moment) on the transmission. 
       6—Orientation of the Blades According to the Determined Pitch 
       [0094]    To optimize the electrical power recovered by the wind turbine, the blades are oriented according to the pitch angle calculated in the preceding step.