Patent ID: 11870254
Assignee: TIANJIN UNIVERSITY
Field: Electrical machinery, apparatus, energy (Electrical engineering)
Classification: CPC H | IPC H

Claim 2:
3. The multi-terminal differential protection setting method for a distributed generator T-connected distribution network according to claim 1, wherein step S4 of establishing non-convex constraint space according to the overall maximum error of superimposed multi-terminal current errors comprises:
according to Δİ*1, Δİ*2, . . . , Δİ*n-1, Δİ*n, establishing a sector shadow area, wherein the phasors of Δİ*1, Δİ*2, . . . , Δİ*n-1, Δİ*n end on the boundaries of the respective sector shadow area;
if the position relationship between Δİ*1+Δİ*2+ . . . +Δİ*n-1 and Δİ*n in a complex plane is that Δİ*1+Δİ*2+ . . . +Δİ*n-1 and Δİ*n are at an angle of θ*n;
wherein θ*n is the phase difference between phasors Δİ*1+Δİ*2+ . . . +Δİ*n-1 and Δİ*n, and θ*n∈[0, 2π);
according to the Law of Cosines, ΔIΣ.max2 is:, Δ
      ⁢
      
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        .
        max
       
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         ·
         
          
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         ·
         
          
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            Δ
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              .
             
             1
             *
            
           
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            ⁢
            
             
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              .
             
             2
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           +
           …
           +
           
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              .
             
             
              n
              -
              1
             
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        ⁢
        
         cos
         ⁡
         (
         
          π
          -
          
           θ
           n
           *
          
         
         )
        
       
      
     
    
   
   
    
     (
     14
     )
    
   
  
 

denoting Δİn having the phase difference of θ*n from Δİ*1+Δİ*2+ . . . +Δİ*n-1 as Δİnθn*, and denoting Δİnθn* ending on the boundaries of the shadow area as Δİnθn*, max;
since Δİ*1, Δİ*2, . . . , Δİ*n-1, Δİnθn* are independent of each other, the derivative of ΔIΣ2 with respect to |Δİnθn*| is:, d
       ⁡
       (
       
        Δ
        ⁢
        
         I
         Σ
         2
        
       
       )
      
      
       d
       ⁡
       (
       
        
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          n
          
           θ
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     =
     
      
       2
       ⁢
       
        
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         Δ
         ⁢
         
          
           I
           .
          
          n
          
           θ
           n
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      -
      
       2
       ·
       
        cos
        ⁡
        (
        
         π
         -
         
          θ
          n
          *
         
        
        )
       
       ·
       
        
         ❘
         "\[LeftBracketingBar]"
        
        
         
          Δ
          ⁢
          
           
            I
            .
           
           1
           *
          
         
         +
         
          Δ
          ⁢
          
           
            I
            .
           
           2
           *
          
         
         +
         …
         +
         
          Δ
          ⁢
          
           
            I
            .
           
           
            n
            -
            1
           
           *
          
         
        
        
         ❘
         "\[RightBracketingBar]"
        
       
      
     
    
   
   
    
     (
     15
     )
    
   
  
 

the second derivative of ΔIΣ2 with respect to |Δİnθn*| is:, d
        2
       
       (
       
        Δ
        ⁢
        
         I
         Σ
         2
        
       
       )
      
      
       
        d
        ⁡
        (
        
         
          ❘
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          Δ
          ⁢
          
           
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           n
           
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        )
       
       2
      
     
     =
     
      2
      >
      0
     
    
   
   
    
     (
     16
     )
    
   
  
 

according to formula (14) to formula (16), since the quadratic term coefficients of the second derivative and the first derivative are both larger than 0, as |İnθn*| changes from 0 to |Δİnθn*,max|, ΔIΣ has at most one extreme point which is a minimum point;
ΔIΣ is maximum when Δİnθn*=0 or Δİnθn*=Δİnθn*,max;
at least one Δİξn inevitably exists in the sector shadow area so that:

|Δİ*1+Δİ*2+ . . . +Δİ*n-1+Δİnξ|>|Δİ*1+Δİ*2+ . . . +Δİ*n-1+0|  (17)

when the overall error of superimposed multi-terminal current errors is maximum, Δİ*n=Δİnθn*,max;
numbering four boundaries of the sector shadow area corresponding to Δİn,
the boundaries 1 and 2 are straight boundaries, and the boundaries 3 and 4 are arc boundaries;
wherein ΔİI ending on the boundary 1 can be decomposed into:

Δİn=Δİ*n,x+Δİn,y  (18)

wherein Δİ*n,x is the projection of Δİn on the vertical line of the boundary 1, and Δİn,y is the projection of Δİn on the boundary 1;
when Δİ*n,y ends near the A1 side, ΔIΣ.max2 is:, Δ
      ⁢
      
       I
       
        Σ
        .
        max
       
       2
      
     
     =
     
      
       
        
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          Δ
          ⁢
          
           
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           *
          
         
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         …
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          ⁢
          
           
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            .
           
           
            n
            -
            1
           
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           Δ
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           ⁢
           
            
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             n
             -
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          2
          ·
          
           
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             ⁢
             
              
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              1
              *
             
            
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             Δ
             ⁢
             
              
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               .
              
              2
              *
             
            
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            +
            
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               n
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              *
             
            
           
           
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         ⁢
         
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          ⁡
          (
          
           
            π
            2
           
           -
           
            δ
            n
            *
           
          
          )
         
        
       
      
     
    
   
   
    
     (
     19
     )
    
   
  
 

wherein δ*n is the phase difference between Δİ*1+Δİ*2+ . . . +Δİ*n-1 and Δİ*n,x, and δ*n∈[0, 2π);
since Δİ*1, Δİ*2, . . . , Δİ*n-1, Δİ*n,x, Δİn,y are independent of each other, the derivative of ΔIΣ2 with respect to |Δİn,y| is:, d
       ⁡
       (
       
        Δ
        ⁢
        
         I
         Σ
         2
        
       
       )
      
      
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     =
     
      
       2
       ⁢
       
        
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         Δ
         ⁢
         
          
           I
           .
          
          
           n
           ,
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      -
      
       2
       ⁢
       
        
         cos
         ⁡
         (
         
          
           π
           2
          
          -
          
           δ
           n
           *
          
         
         )
        
        ·
        
         
          ❘
          "\[LeftBracketingBar]"
         
         
          
           Δ
           ⁢
           
            
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            1
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           Δ
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            2
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          …
          +
          
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             n
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     (
     20
     )
    
   
  
 

the second derivative of ΔIΣ2 with respect to |Δİn,y| is:, d
        2
       
       (
       
        Δ
        ⁢
        
         I
         Σ
         2
        
       
       )
      
      
       
        d
        ⁡
        (
        
         
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            n
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        )
       
       2
      
     
     =
     
      2
      >
      0
     
    
   
   
    
     (
     21
     )
    
   
  
 

when Δİ*n,y ends near the A2 side, ΔIΣ.max2 is:, Δ
      ⁢
      
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        Σ
        .
        max
       
       2
      
     
     =
     
      
       
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         2
        
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         2
        
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          2
          ·
          
           
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            Δ
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              n
              ,
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            ❘
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          ·
          
           
            ❘
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             Δ
             ⁢
             
              
               I
               .
              
              1
              *
             
            
            +
            
             Δ
             ⁢
             
              
               I
               .
              
              2
              *
             
            
            +
            …
            +
            
             Δ
             ⁢
             
              
               I
               .
              
              
               n
               ,
               x
              
              *
             
            
           
           
            ❘
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         ⁢
         
          cos
          ⁡
          (
          
           
            
             3
             ⁢
             π
            
            2
           
           -
           
            δ
            n
            *
           
          
          )
         
        
       
      
     
    
   
   
    
     (
     22
     )
    
   
  
 

at this moment, the derivative of ΔIΣ2 with respect to |Δİn,y| is:, d
       ⁡
       (
       
        Δ
        ⁢
        
         I
         Σ
         2
        
       
       )
      
      
       d
       ⁡
       (
       
        
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           .
          
          
           n
           ,
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       )
      
     
     =
     
      
       2
       ⁢
       
        
         ❘
         "\[LeftBracketingBar]"
        
        
         Δ
         ⁢
         
          
           I
           .
          
          
           n
           ,
           y
          
         
        
        
         ❘
         "\[RightBracketingBar]"
        
       
      
      -
      
       2
       ⁢
       
        
         cos
         ⁡
         (
         
          
           
            3
            ⁢
            π
           
           2
          
          -
          
           δ
           n
           *
          
         
         )
        
        ·
        
         
          ❘
          "\[LeftBracketingBar]"
         
         
          
           Δ
           ⁢
           
            
             I
             .
            
            1
            *
           
          
          +
          
           Δ
           ⁢
           
            
             I
             .
            
            2
            *
           
          
          +
          …
          +
          
           Δ
           ⁢
           
            
             I
             .
            
            
             n
             -
             1
            
            *
           
          
          +
          
           Δ
           ⁢
           
            
             I
             .
            
            
             n
             ,
             x
            
            *
           
          
         
         
          ❘
          "\[RightBracketingBar]"
         
        
       
      
     
    
   
   
    
     (
     23
     )
    
   
  
 

when Δİ*n,y ends near the A2 side, the second derivative of ΔIΣ2 with respect to |Δİn,y| is the same as formula (21):
denoting Δİn,y ending at A1 as Δİn,yA1, and denoting Δİn,y ending at A2 as Δİn,yA2;
respectively denoting derivatives in formula (20) and formula (23) as fn,y1 and fn,y2.