Patent ID: 11916423
Assignee: GUIZHOU UNIVERSITY
Field: Electrical machinery, apparatus, energy (Electrical engineering)
Classification: CPC H  G  Y | IPC G  H

Claim 8:
9. The method according to claim 7, further comprising:
obtaining the introduced variable rij(k), comprising:
adjusting a constraint range by:
defining Δiu(k) as a distance between the state xi(k) and the upper limit xi and defining Δil (k) as a distance between the state xi(k) and the lower limit xi, wherein Δiu(k) and Δil(k) are respectively expressed as follows:, {
     
      
       
        
         
          
           
            Δ
            i
            u
           
           (
           k
           )
          
          =
          
           
            ❘
            "\[LeftBracketingBar]"
           
           
            
             
              x
              i
             
             (
             k
             )
            
            -
            
             
              x
              _
             
             i
            
           
           
            ❘
            "\[RightBracketingBar]"
           
          
         
        
       
       
        
         
          
           
            Δ
            i
            l
           
           (
           k
           )
          
          =
          
           
            ❘
            "\[LeftBracketingBar]"
           
           
            
             
              x
              i
             
             (
             k
             )
            
            -
            
             
              x
              _
             
             i
            
           
           
            ❘
            "\[RightBracketingBar]"
           
          
         
        
       
      
      ,
     
    
   
   
    
     (
     4
     )
    
   
  
 

adjusting the upper limit and the lower limit during iterating as per a formula (5) and a formula (6) in order to make a state outside of the constraint range be transferred to be within the constraint range in a process of iterating, wherein the formula (5) and the formula (6) are respectively expressed as follows:, x
       _
      
      i
      ′
     
     =
     
      {
      
       
        
         
          
           
            
             x
             _
            
            i
           
           -
           
            τ
            ⁢
            
             
              Δ
              i
              u
             
             (
             k
             )
            
           
          
         
         
          
           
            
             x
             i
            
            (
            k
            )
           
           >
           
            
             x
             _
            
            i
           
          
         
        
        
         
          
           
            x
            _
           
           i
          
         
         
          
           
            
             x
             i
            
            (
            k
            )
           
           ≤
           
            
             x
             _
            
            i
           
          
         
        
       
       ,
      
     
    
   
   
    
     (
     5
     )
    
   
  
 

 
  
   
    
     
      
       x
       _
      
      i
      ′
     
     =
     
      {
      
       
        
         
          
           
            
             x
             _
            
            i
           
           +
           
            τ
            ⁢
            
             
              Δ
              i
              l
             
             (
             k
             )
            
           
          
         
         
          
           
            
             x
             i
            
            (
            k
            )
           
           <
           
            
             x
             _
            
            i
           
          
         
        
        
         
          
           
            x
            _
           
           i
          
         
         
          
           
            
             x
             i
            
            (
            k
            )
           
           ≥
           
            
             x
             _
            
            i
           
          
         
        
       
       ,
      
     
    
   
   
    
     (
     6
     )
    
   
  
 

wherein the formula (5) and the formula (6) each represent that a constraint boundary is adjusted according to a distance between a current state and the constraint boundary, so that the state outside the constraint range is transferred to be within the state constraint in the process of iterating, and a value range of τ is:, 0
   <
   τ
   <
   
    min
    ⁡
    (
    
     
      
       
        ❘
        "\[LeftBracketingBar]"
       
       
        
         x
         _
        
        i
       
       
        ❘
        "\[RightBracketingBar]"
       
      
      
       
        Δ
        i
        u
       
       (
       k
       )
      
     
     ,
     
      
       
        ❘
        "\[LeftBracketingBar]"
       
       
        
         x
         _
        
        i
       
       
        ❘
        "\[RightBracketingBar]"
       
      
      
       
        Δ
        i
        l
       
       (
       k
       )
      
     
    
    )
   
  
  ;
 

calculating intermediate variables as per a formula (7) expressed as follows:, {
     
      
       
        
         
          
           Δ
           ⁢
           
            
             
              x
              _
             
             i
            
            (
            k
            )
           
          
          =
          
           
            ❘
            "\[LeftBracketingBar]"
           
           
            
             
              x
              i
             
             (
             k
             )
            
            -
            
             
              x
              _
             
             i
             ′
            
           
           
            ❘
            "\[RightBracketingBar]"
           
          
         
        
       
       
        
         
          
           Δ
           ⁢
           
            
             
              x
              _
             
             i
            
            (
            k
            )
           
          
          =
          
           
            ❘
            "\[LeftBracketingBar]"
           
           
            
             
              x
              i
             
             (
             k
             )
            
            -
            
             
              x
              _
             
             i
             ′
            
           
           
            ❘
            "\[RightBracketingBar]"
           
          
         
        
       
      
      ;
     
    
   
   
    
     (
     7
     )
    
   
  
 

calculating the variable rij(k), comprising:
sending, by the i-th node, the intermediate variables (Δxi(k), Δxi(k)) and the state xi(k) to adjacent nodes, and receiving intermediate variables and a state of adjacent j-th node for calculating the variable rij (k) as per a formula (8) expressed as follows:, r
       ij
      
      (
      k
      )
     
     =
     
      {
      
       
        
         
          min
          ⁢
          
           {
           
            1
            ,
            
             
              Δ
              ⁢
              
               
                
                 x
                 _
                
                i
               
               (
               k
               )
              
             
             
              
               ❘
               "\[LeftBracketingBar]"
              
              
               
                σ
                ij
               
               (
               k
               )
              
              
               ❘
               "\[RightBracketingBar]"
              
             
            
            ,
            
             
              Δ
              ⁢
              
               
                
                 x
                 _
                
                j
               
               (
               k
               )
              
             
             
              
               ❘
               "\[LeftBracketingBar]"
              
              
               
                σ
                ij
               
               (
               k
               )
              
              
               ❘
               "\[RightBracketingBar]"
              
             
            
           
           }
          
         
        
        
         
          
           
            σ
            ij
           
           (
           k
           )
          
          >
          0
         
        
       
       
        
         
          min
          ⁢
          
           {
           
            1
            ,
            
             
              Δ
              ⁢
              
               
                
                 x
                 _
                
                j
               
               (
               k
               )
              
             
             
              
               ❘
               "\[LeftBracketingBar]"
              
              
               
                σ
                ij
               
               (
               k
               )
              
              
               ❘
               "\[RightBracketingBar]"
              
             
            
            ,
            
             
              Δ
              ⁢
              
               
                
                 x
                 _
                
                i
               
               (
               k
               )
              
             
             
              
               ❘
               "\[LeftBracketingBar]"
              
              
               
                σ
                ij
               
               (
               k
               )
              
              
               ❘
               "\[RightBracketingBar]"
              
             
            
           
           }
          
         
        
        
         
          
           
            σ
            ij
           
           (
           k
           )
          
          <
          0
         
        
       
       
        
         1
        
        
         
          
           
            σ
            ij
           
           (
           k
           )
          
          =
          0
         
        
       
      
     
    
   
   
    
     (
     8
     )
    
   
  
 

where σij(k)=xj(k)−xi(k), j∈Ni(k); rij(k) is configured to prevent xi(k) from exceeding the constraint boundaries in the process of iterating when transferring along a direction approaching the constraint boundaries to thereby ensure that a convergence result meets the state constraint.