Patent ID: 11923685
Assignee: TSINGHUA UNIVERSITY
Field: Electrical machinery, apparatus, energy (Electrical engineering)
Classification: CPC H  G  Y | IPC G  H

Claim 11:
12. The apparatus according to claim 11, wherein the processor is further configured to:
a) letting m=1, ŷkm=0, η=0.999, αm=1, and dkm=0, setting a residual parameter um, the positive penalty factor ρ, a time margin Tthr, an upper limit τ of the number of occurrences that the kth distribution network encounters consecutive asynchronism and a convergence threshold, and assigning an initial value of {circumflex over (x)}Dk,B1 which represents a variant of the fourth column vector in the first iterative step, where m represents a number of iterative steps, ŷkm represents a variant of the fifth column vector in an mth iterative step, η represents a parameter indicating decrement of residual, αm represents an initial parameter in the mth iterative step, and dkm represents a variable indicating the number of occurrences that the kth distribution network encounters consecutive asynchronism during the mth iterative step, um represents the residual parameter in the mth iterative step;
b) during the mth iterative step, solve by a control center of the transmission network the reactive power-voltage control model in a following form to obtain an optimal solution xTm+1:, min
        
          x
          T
        
      
      ⁢
      
        
      
      ⁢
      
        
          C
          T
        
        ⁡
        
          (
          
            x
            T
          
          )
        
      
    
    +
    
      
        ∑
        
          k
          ∈
          ID
        
      
      ⁢
      
        {
        
          
            
              
                (
                
                  
                    y
                    ^
                  
                  m
                  k
                
                )
              
              T
            
            ⁡
            
              [
              
                
                  x
                  
                    
                      T
                      k
                    
                    ,
                    B
                  
                
                -
                
                  
                    x
                    ^
                  
                  
                    
                      D
                      k
                    
                    ,
                    B
                  
                  m
                
              
              ]
            
          
          +
          
            
              ρ
              2
            
            ⁢
            
              
                
                
                  
                    x
                    
                      
                        T
                        k
                      
                      ,
                      B
                    
                  
                  -
                  
                    
                      x
                      ^
                    
                    
                      
                        D
                        k
                      
                      ,
                      B
                    
                    m
                  
                
                
              
              2
              2
            
          
        
        }
      
    
  

  
    satisfying
    ⁢
    
      :
    
  

  
    
      
        F
        T
      
      ⁡
      
        (
        
          x
          T
        
        )
      
    
    ≤
    0
  

where ŷkm represents a variant of the fifth column vector in the mth iterative step, and {circumflex over (x)}Dk,Bm represents a variant of the fourth column vector in the mth iterative step;
c) transmitting by the control center of the transmission network the third column vector xTk,Bm+1 orresponding to the kth distribution network in the optimal solution xTm+1 to the kth distribution network;
d) during the mth iterative step, receiving the third column vector xTk,Bm+1 from the transmission network by the kth distribution network and solving the reactive power-voltage control model in a following form to obtain an optimal solution xDkm+1:, min
        
          x
          
            D
            k
          
        
      
      ⁢
      
        
      
      ⁢
      
        
          
            (
            
              
                y
                ^
              
              k
              m
            
            )
          
          T
        
        ⁡
        
          [
          
            
              x
              
                
                  T
                  k
                
                ,
                B
              
              
                m
                +
                1
              
            
            -
            
              x
              
                
                  D
                  k
                
                ,
                B
              
            
          
          ]
        
      
    
    +
    
      
        ρ
        2
      
      ⁢
      
        
          
          
            
              x
              
                
                  T
                  k
                
                ,
                B
              
              
                m
                +
                1
              
            
            -
            
              x
              
                
                  D
                  k
                
                ,
                B
              
            
          
          
        
        2
        2
      
    
  

  
    satisfying
    ⁢
    
      :
    
  

  
    
      
        F
        
          D
          k
        
      
      ⁡
      
        (
        
          x
          
            D
            k
          
        
        )
      
    
    ≤
    0
  

e) transmitting by a control center of the kth distribution network the fourth column vector xDk,Bm+1 corresponding to the kth distribution network in the optimal solution xDkm+1 to the transmission network;
f) determine by the control center of the transmission network whether the number of occurrences exceeds the upper limit τ for each distribution network;
g) when the number of occurrences does not exceed the upper limit τ for each distribution network, obtaining by the control center of the transmission network the fourth column vector xDk,Bm+1 from each distribution network within the time margin Tthr which is counted from the time when the control center of the transmission network transmits the third column vector to the respective distribution network as follows:, x
    
      
        D
        k
      
      ,
      B
    
    
      m
      +
      1
    
  
  =
  
    {
    
      
        
          
            
              
                x
                
                  
                    D
                    k
                  
                  ,
                  B
                
                
                  m
                  +
                  1
                
              
              ,
              
                ∀
                
                  k
                  ∈
                  
                    H
                    m
                  
                
              
            
            ⁢
            
              
            
          
        
      
      
        
          
            
              x
              
                
                  D
                  k
                
                ,
                B
              
              
                LV
                ,
                m
              
            
            ,
            
              ∀
              
                k
                ∈
                
                  (
                  
                    ID
                    -
                    
                      H
                      m
                    
                  
                  )
                
              
            
          
        
      
    
  

where, Hm represents a set of indexes of distribution networks from which the fourth column vector is received within the time margin Tthr; xDk,BLV,m represents the fourth column vector received from the kth distribution network during the (m−1)th iterative step;
(h) when the number of occurrences exceeds the upper limit τ for any distribution network, obtaining by the control center of the transmission network the fourth column vector xDk,Bm+1 from each distribution network, and if a plurality of fourth column vectors are received from the kth distribution network during the mth iterative step, using the latest received fourth column vector;
(i) update by the control center of the transmission network the number of occurrences as follows:, d
    k
    
      m
      +
      1
    
  
  =
  
    {
    
      
        
          
            
              0
              ,
            
            ⁢
            
              
            
          
        
        
          
            
              ∀
              
                k
                ∈
                
                  H
                  m
                
              
            
            ⁢
            
              
            
          
        
      
      
        
          
            
              
                d
                k
                m
              
              +
              1
            
            ,
          
        
        
          
            ∀
            
              k
              ∈
              
                (
                
                  ID
                  -
                  
                    H
                    m
                  
                
                )
              
            
          
        
      
    
  

where dkm+1 represents the number of occurrences for the kth distribution network after the mth iterative step;
(j) updating by the control center of the transmission network the Lagrange multiplier corresponding to the kth distribution network as follows:

ykm+1=ŷkm+ρ(xTk,Bm+1−xDk,Bm+1)

where ykm+1 represents the Lagrange multiplier corresponding to the kth distribution network obtained in the mth iterative step;
(k) determining by the control center of the transmission network a primal residual and a dual residual after the mth iterative step as follows:

pm+1=∥xT,Bm+1−xD,Bm+1∥∞

dm+1=∥xT,Bm+1−xT,Bm∥∞

where pm+1 represents the primal residual of the reactive power-voltage control model after the mth iterative step, dm+1 represents the dual residual of the reactive power-voltage control model after the mth iterative step, xT,Bm+1 represents a set containing all the third column vector xTk,Bm+1, xD,Bm+1 represents a set containing all the fourth column vector xDk,Bm+1, ∥·∥∞ represents a ∞-Norm of a vector;
(l) determining by the control center of the transmission network whether a convergence condition, 
      
        
          
            
              p
              
                m
                +
                1
              
            
          
        
        
          
            
              d
              
                m
                +
                1
              
            
          
        
      
      
    
    ∞
  
  <
  ɛ, is met, if yes, configuring the optimum solution xTm+1 obtained in the mth iterative step as the control variables of the transmission network and configuring the optimum solution xDkm+1 obtained in the mth iterative step as the control variables of the k distribution network; if no, executing step (m);
(m) updating the residual parameter as follows:

um+1=ρ−1∥ym+1−ŷm∥22+ρ∥xD,Bm+1−{circumflex over (x)}D,Bm∥22 

where um+1 represents the residual parameter after the mth iterative step, ym+1 represents a set containing all the Lagrange multipliers ykm+1, ŷm represents a set containing all the variants ŷkm of the fifth column vectors, {circumflex over (x)}D,Bm represents a set containing all the variants {circumflex over (x)}Dk,Bm of the fourth column vectors;
(n) determining whether a condition um+1<ηum is met,
if yes, updating the initial parameter, the variant of the fourth column vector, and the variant of the fifth column vector as follows:, α
     
      m
      +
      1
     
    
    =
    
     
      1
      +
      
       
        1
        +
        
         4
         ⁢
         
          
           (
           
            α
            m
           
           )
          
          2
         
        
       
      
     
     2
    
   
   

   

  
  ⁢
  

  
   
    
     
      x
      ˆ
     
     
      
       D
       k
      
      ,
      B
     
     
      m
      +
      1
     
    
    =
    
     
      x
      
       
        D
        k
       
       ,
       B
      
      
       m
       +
       1
      
     
     +
     
      
       
        
         α
         m
        
        -
        1
       
       
        α
        
         m
         +
         1
        
       
      
      ⁢
      
       (
       
        
         x
         
          
           D
           k
          
          ,
          B
         
         
          m
          +
          1
         
        
        -
        
         x
         
          
           D
           k
          
          ,
          B
         
         m
        
       
       )
      
     
    
   
   

   

  
  ⁢
  

  
   
    
     y
     ˆ
    
    k
    
     m
     +
     1
    
   
   =
   
    
     y
     k
     
      m
      +
      1
     
    
    +
    
     
      
       
        α
        m
       
       -
       1
      
      
       α
       
        m
        +
        1
       
      
     
     ⁢
     
      (
      
       
        y
        k
        
         m
         +
         1
        
       
       -
       
        y
        k
        m
       
      
      )
     
    
   
  
 

where αm+1 represents the initial parameter after the mth iterative step;
if no, updating the initial parameter, the variant of the fourth column vector, and the variant of the fifth column vector as follows:

αm+1=1,um+1=η−1um,{circumflex over (x)}Dk,Bm+1=xDk,Bm−1,ŷkm+1=ykm−1 

(o) transmitting the updated variant ŷkm+1 of the fifth column vector to the kth distribution network and executing step (p);
(p) letting m=m+1 and returning to step (b).