Patent ID: 11888432
Assignee: NORTH CHINA ELECTRIC POWER UNIVERSITY
Field: Electrical machinery, apparatus, energy (Electrical engineering)
Classification: CPC H  F  G | IPC F  G  H

Claim 0:
1. A method of power system frequency dynamics analysis implemented in a power grid including a doubly-fed induction generator (DFIG) wind turbine, wherein the DFIG wind turbine includes a doubly-fed induction machine (DFIM), a wind turbine, and proportional-integral (PI) controllers configured for a maximum power point tracking (MPPT) control module, a phase-locked loop (PLL) module, an active power control loop module, and an reactive power control loop module, the method comprising:
facilitating the DFIG wind turbine to be operated in a MPPT mode;
generating a simplified transient model of the DFIG wind turbine, wherein the simplified transient model of the DFIG wind turbine includes
an equivalent circuit model,, E
        
         e
         ⁢
         q
        
       
       ⁢
       
        e
        
         j
         ⁢
         
          δ
          
           e
           ⁢
           q
          
         
        
       
      
      =
      
       
        
         U
         .
        
        s
       
       +
       
        
         (
         
          
           R
           
            e
            ⁢
            q
           
          
          +
          
           jX
           
            e
            ⁢
            q
           
          
         
         )
        
        ⁢
        
         
          I
          .
         
         s
        
       
      
     
     ,
    
   
   
    
     (
     9
     )
    
   
  
 

 
  
   
    
     
      
       R
       
        e
        ⁢
        q
       
      
      =
      
       
        R
        s
       
       -
       
        
         
          ω
          s
         
         ⁢
         
          X
          m
         
         ⁢
         
          k
          
           p
           ⁢
           1
          
         
         ⁢
         
          U
          s
          *
         
         ⁢
         
          ω
          m
          2
         
         ⁢
         
          P
          e
         
         ⁢
         
          Q
          e
         
        
        
         
          P
          e
          2
         
         +
         
          
           ω
           m
           2
          
          ⁢
          
           Q
           e
           2
          
         
        
       
      
     
     ,
    
   
   
    
     (
     
      10
      ⁢
         
      a
     
     )
    
   
  
 

 
  
   
    
     
      
       X
       
        e
        ⁢
        q
       
      
      =
      
       
        
         ω
         s
        
        ⁢
        
         X
         s
        
       
       +
       
        
         
          ω
          s
         
         ⁢
         
          X
          m
         
         ⁢
         
          k
          
           p
           ⁢
           1
          
         
         ⁢
         
          U
          s
          *
         
         ⁢
         
          ω
          m
         
         ⁢
         
          P
          e
          2
         
        
        
         
          P
          e
          2
         
         +
         
          
           ω
           m
           2
          
          ⁢
          
           Q
           e
           2
          
         
        
       
      
     
     ,
    
   
   
    
     (
     
      10
      ⁢
         
      b
     
     )
    
   
  
 

 
  
   
    
     
      
       E
       
        e
        ⁢
        q
       
      
      =
      
       
        ω
        s
       
       ⁢
       
        X
        m
       
       ⁢
       
        
         
          
           (
           
            
             
              ξ
              M
             
             ⁢
             
              k
              
               p
               ⁢
               1
              
             
             ⁢
             
              ω
              m
              3
             
            
            +
            
             
              k
              
               i
               ⁢
               1
              
             
             ⁢
             
              x
              1
             
            
           
           )
          
          2
         
         +
         
          i
          rq0
          
           P
           2
          
         
        
       
      
     
     ,
    
   
   
    
     (
     
      10
      ⁢
         
      c
     
     )
    
   
  
 

 
  
   
    
     
      δ
      
       e
       ⁢
       q
      
     
     =
     
      
       θ
       
        P
        ⁢
        L
        ⁢
        L
       
      
      -
      
       
        
         tan
         
          -
          1
         
        
        (
        
         
          
           
            ξ
            M
           
           ⁢
           
            k
            
             p
             ⁢
             1
            
           
           ⁢
           
            ω
            m
            3
           
          
          +
          
           
            k
            
             i
             ⁢
             1
            
           
           ⁢
           
            x
            1
           
          
         
         
          i
          
           r
           ⁢
           q
           ⁢
           0
          
          P
         
        
        )
       
       .
      
     
    
   
   
    
     (
     
      10
      ⁢
         
      d
     
     )
    
   
  
 

and
an equivalent rotor motion model, ω
      
       e
       ⁢
       q
      
     
     =
     
      
       
        
         1
         
          ω
          N
         
        
        ⁢
        
         
          d
          ⁢
          
           δ
           
            e
            ⁢
            q
           
          
         
         dt
        
       
       +
       1
      
      =
      
       
        
         
          1
          
           ω
           N
          
         
         ⁢
         
          (
          
           
            
             
              ∂
               
              
               δ
               
                e
                ⁢
                q
               
              
             
             
              ∂
              
               θ
               
                P
                ⁢
                L
                ⁢
                L
               
              
             
            
            ⁢
            
             
              d
              ⁢
              
               θ
               
                P
                ⁢
                L
                ⁢
                L
               
              
             
             dt
            
           
           +
           
            
             
              ∂
               
              
               
                δ
                 
               
               
                e
                ⁢
                q
               
              
             
             
              ∂
              
               ω
               m
              
             
            
            ⁢
            
             
              d
              ⁢
              
               ω
               m
              
             
             dt
            
           
           +
           
            
             
              ∂
              
               δ
               
                e
                ⁢
                q
               
              
             
             
              ∂
              
               x
               1
              
             
            
            ⁢
            
             
              dx
              1
             
             dr
            
           
          
          )
         
        
        +
        1
       
       =
       
        
         ω
         
          P
          ⁢
          L
          ⁢
          L
         
        
        -
        
         
          
           3
           ⁢
           
            ξ
            M
           
           ⁢
           
            k
            
             p
             ⁢
             1
            
           
           ⁢
           
            ω
            m
            2
           
          
          
           
            ω
            N
           
           (
           
            
             i
             
              rq
              ⁢
              0
             
             P
            
            +
            
             
              
               (
               
                
                 
                  ξ
                  M
                 
                 ⁢
                 
                  k
                  
                   p
                   ⁢
                   1
                  
                 
                 ⁢
                 
                  ω
                  m
                  3
                 
                
                +
                
                 
                  k
                  
                   i
                   ⁢
                   1
                  
                 
                 ⁢
                 
                  x
                  1
                 
                
               
               )
              
              2
             
             
              i
              
               rq
               ⁢
               0
              
              P
             
            
           
           )
          
         
         ⁢
         
          
           d
           ⁢
           
            ω
            m
           
          
          dt
         
        
        -
        
         
          
           k
           
            i
            ⁢
            1
           
          
          
           
            ω
            N
           
           (
           
            
             i
             
              rq
              ⁢
              0
             
             P
            
            +
            
             
              
               (
               
                
                 
                  ξ
                  M
                 
                 ⁢
                 
                  k
                  
                   p
                   ⁢
                   1
                  
                 
                 ⁢
                 
                  ω
                  m
                  3
                 
                
                +
                
                 
                  k
                  
                   i
                   ⁢
                   1
                  
                 
                 ⁢
                 
                  x
                  1
                 
                
               
               )
              
              2
             
             
              i
              
               rq
               ⁢
               0
              
              P
             
            
           
           )
          
         
         ⁢
         
          
           
            dx
            1
           
           dt
          
          .
         
        
       
      
     
    
   
   
    
     (
     12
     )
    
   
  
 

 the equivalent rotor motion model (12) being in a nonlinear form;
linearizing the equivalent rotor motion model (12) to be an equivalent rotor motion model (16) in a linear form with respect to a steady-state operating point of the DFIG wind turbine, Δ
       ⁢
       
        ω
        
         e
         ⁢
         q
        
       
      
      =
      
       
        
         
          ∂
          
           ω
           
            e
            ⁢
            q
           
          
         
         
          ∂
          
           ω
           
            P
            ⁢
            L
            ⁢
            L
           
          
         
        
        
         |
         0
        
        
         
          Δ
          ⁢
          
           ω
           
            P
            ⁢
            L
            ⁢
            L
           
          
         
         +
         
          
           ∂
           
            ω
            
             e
             ⁢
             q
            
           
          
          
           ∂
           
            ω
            m
           
          
         
        
        
         |
         0
        
        
         
          Δ
          ⁢
          
           ω
           m
          
         
         +
         
          ∂
          
           ∂
           
            
             d
             ⁢
             
              ω
              m
             
            
            dt
           
          
         
        
        
         |
         0
        
        
         
          
           d
           ⁢
           Δ
           ⁢
           
            ω
            m
           
          
          dt
         
         +
          
         
          
           ∂
           
            ω
            
             e
             ⁢
             q
            
           
          
          
           ∂
           
            x
            1
           
          
         
        
        
         |
         0
        
        
         
          Δ
          ⁢
          
           x
           1
          
         
         +
         
          
           ∂
            
           
            ω
            eq
           
          
          
           ∂
           
            
             dx
             1
            
            dt
           
          
         
        
        
         |
         0
        
        
         
          d
          ⁢
          Δ
          ⁢
          
           x
           1
          
         
         dt
        
       
       =
       
        
         Δω
         
          P
          ⁢
          L
          ⁢
          L
         
        
        +
        
         
          h
          
           D
           ⁢
           ω
          
         
         ⁢
         
          
           d
           ⁢
           Δ
           ⁢
           
            ω
            m
           
          
          dt
         
        
        +
        
         
          h
          
           D
           ⁢
           x
          
         
         ⁢
         
          
           d
           ⁢
           Δ
           ⁢
           
            x
            1
           
          
          dt
         
        
       
      
     
     ,
    
   
   
    
     (
     16
     )
    
   
  
 

where ∂ωeq/∂ωm|0 and ∂ωeq/∂x1|0 equal to 0 considering dωm/dt and dx1/dt equal to 0 in a steady state;
determining a first contribution of the DFIG wind turbines to a post-disturbance frequency of the power grid, in a center of inertia (COI) frequency frame by incorporating the simplified transient model of the DFIG wind turbine into a frequency dynamics analysis through, Δ
       ⁢
       
        ω
        COI
       
      
      =
      
       
        
         
          
           ∑
            
          
          
           ∀
           g
          
         
         ⁢
         
          H
          
           G
           ,
           g
          
         
         ⁢
         
          S
          
           N
           ,
           g
          
         
         ⁢
         Δ
         ⁢
         
          ω
          
           G
           ,
           g
          
         
        
        +
        
         
          
           ∑
            
          
          
           ∀
           w
          
         
         ⁢
         
          H
          
           eq
           ,
           w
          
          tol
         
         ⁢
         
          S
          
           N
           ,
           w
          
         
         ⁢
         
          Δω
          
           eq
           ,
           w
          
         
        
       
       
        
         
          
           ∑
            
          
          
           ∀
           g
          
         
         ⁢
         
          H
          
           G
           ,
           g
          
         
         ⁢
         
          S
          
           N
           ,
           g
          
         
        
        +
        
         
          
           ∑
            
          
          
           ∀
           w
          
         
         ⁢
         
          H
          
           eq
           ,
           w
          
          tol
         
         ⁢
         
          S
          
           N
           ,
           w
          
         
        
       
      
     
     ,
    
   
   
    
     (
     
      21
      ⁢
      a
     
     )
    
   
  
 

 
  
   
    
     
      
       H
       COI
      
      =
      
       
        
         
          
           ∑
            
          
          
           ∀
           g
          
         
         ⁢
         
          H
          
           G
           ,
           g
          
         
         ⁢
         
          S
          
           N
           ,
           g
          
         
        
        +
        
         
          
           ∑
            
          
          
           ∀
           w
          
         
         ⁢
         
          H
          
           eq
           ,
           w
          
          tol
         
         ⁢
         
          S
          
           N
           ,
           w
          
         
        
       
       
        
         
          
           ∑
            
          
          
           ∀
           g
          
         
         ⁢
         
          S
          
           N
           ,
           g
          
         
        
        +
        
         
          
           ∑
            
          
          
           ∀
           w
          
         
         ⁢
         
          S
          
           N
           ,
           w
          
         
        
       
      
     
     ,
    
   
   
    
     (
     
      21
      ⁢
      b
     
     )
    
   
  
 

determining a second contribution of the DFIG wind turbines to the post-disturbance frequency of the power grid, in a frequency spatial variation frame by incorporating the simplified transient model of the DFIG wind turbine into the frequency dynamics analysis through;, SPC
       
        w
        ,
        
         d
         ⁢
         i
         ⁢
         s
         ⁢
         t
        
       
      
      =
      
       
        
         
          E
          
           
            e
            ⁢
            q
            ⁢
            0
           
           ,
           w
          
         
         ⁢
         
          U
          
           0
           ,
           dist
          
         
        
        
         X
         
          w
          ,
          dist
         
        
       
       ⁢
       
        cos
        ⁡
        (
        
         
          δ
          
           
            e
            ⁢
            q
            ⁢
            0
           
           ,
           w
          
         
         -
         
          θ
          
           0
           ,
           
            d
            ⁢
            i
            ⁢
            s
            ⁢
            t
           
          
         
        
        )
       
      
     
     ,
    
   
   
    
     (
     
      25
      ⁢
      a
     
     )
    
   
  
 

 
  
   
    
     
      
       Δ
       ⁢
       
        P
        
         s
         ,
         w
        
       
      
      =
      
       
        
         S
         ⁢
         P
         ⁢
         
          C
          
           w
           ,
           
            d
            ⁢
            i
            ⁢
            s
            ⁢
            t
           
          
         
        
        
         
          
           
            ∑
             
           
           
            ∀
            g
           
          
          ⁢
          S
          ⁢
          P
          ⁢
          
           C
           
            g
            ,
            
             d
             ⁢
             i
             ⁢
             s
             ⁢
             t
            
           
          
         
         +
         
          
           
            ∑
             
           
           
            ∀
            w
           
          
          ⁢
          S
          ⁢
          P
          ⁢
          
           C
           
            w
            ,
            
             d
             ⁢
             i
             ⁢
             s
             ⁢
             t
            
           
          
         
        
       
       ⁢
       Δ
       ⁢
       
        P
        dist
       
      
     
     ,
    
   
   
    
     (
     
      25
      ⁢
      b
     
     )
    
   
  
 

and
based on the first contribution and the second contribution, adjusting operating point of the DFIG wind turbines through the PI controllers, to stabilize frequency of the power grid, wherein the operating point includes active power, reactive power, terminal voltage, and wind speed.