Patent ID: 11876381
Assignee: NORTH CHINA ELECTRIC POWER UNIVERSITY
Field: Electrical machinery, apparatus, energy (Electrical engineering)
Classification: CPC H | IPC H

Claim 0:
1. A method for avoiding blackouts caused by an RoCoF-based relay tripping in a power system by limiting a post-disturbance node maximum rate of change of frequency (“RoCoF”) by optimizing UC decisions, the method comprising:
determining post-disturbance node initial rate of change of frequency (“RoCoF”) by:
determining a load disturbance power ΔPgG,0 picked up by a g-th generator, where Sg,nDD is a synchronizing power coefficient (SPC) between a disturbed load and a generator based on, Δ
      ⁢
      
       P
       g
       
        G
        ,
        0
       
      
     
     =
     
      
       S
       
        g
        ,
        
         n
         D
        
       
       D
      
      ⁢
      Δ
      ⁢
      
       P
       
        n
        D
       
       D
      
     
    
   
   
    
     (
     
      3
      ⁢
      a
     
     )
    
   
  
 

 
  
   
    
     
      s
      
       g
       ,
       
        n
        D
       
      
      D
     
     =
     
      
       
        E
        g
       
       ⁢
       
        U
        
         n
         D
        
       
       ⁢
       
        y
        
         g
         ,
         
          n
          D
         
        
        
         G
         ⁢
         D
        
       
       ⁢
       
        sin
        ⁡
        (
        
         
          δ
          g
         
         -
         
          θ
          
           n
           D
          
         
         -
         
          γ
          
           g
           ,
           
            n
            D
           
          
          
           G
           ⁢
           D
          
         
        
        )
       
      
      
       
        
         ∑
          
        
        
         g
         B
        
       
       ⁢
       
        E
        
         g
         B
        
       
       ⁢
       
        U
        
         n
         D
        
       
       ⁢
       
        Y
        
         
          g
          B
         
         ,
         
          n
          D
         
        
        
         G
         ⁢
         D
        
       
       ⁢
       
        sin
        ⁡
        (
        
         
          -
          
           (
           
            
             δ
             
              g
              B
             
            
            -
            
             θ
             
              n
              D
             
            
           
           )
          
         
         -
         
          γ
          
           
            g
            B
           
           ,
           
            n
            D
           
          
          
           G
           ⁢
           D
          
         
        
        )
       
      
     
    
   
   
    
     (
     
      3
      ⁢
      b
     
     )
    
   
  
 

wherein Egejδg is the g-th element of Ė, a generator EMF of the g-th generator; and
Yg,nDGDejγg,nDGD is g-th element of {dot over (Y)}nDGD, a equivalent admittance between the g-th generator and nD-th node; and
wherein, [
       
        
         
          
           
            I
            .
           
           G
          
         
        
        
         
          
           
            I
            .
           
           
            n
            D
           
           D
          
         
        
       
       ]
      
      =
      
       
        [
        
         
          
           
            
             Y
             ˙
            
            
             G
             ⁢
             G
            
           
          
          
           
            
             Y
             ˙
            
            
             n
             D
            
            
             G
             ⁢
             D
            
           
          
         
         
          
           
            
             Y
             ˙
            
            
             n
             D
            
            
             D
             ⁢
             G
            
           
          
          
           
            
             Y
             .
            
            
             
              n
              D
             
             ,
             
              n
              D
             
            
            
             D
             ⁢
             D
            
           
          
         
        
        ]
       
       [
       
        
         
          
           E
           ˙
          
         
        
        
         
          
           
            U
            .
           
           
            n
            D
           
          
         
        
       
       ]
      
     
     ,
    
   
   
    
     (
     2
     )
    
   
  
 

where İnDD is an injected current phasor from the nD-th node, {dot over (U)}nD is a voltage phasor of the node, {dot over (Y)} is derived from {dot over (Y)}0;
determining a line switching disturbance power picked up by the g-th generator based on:, Δ
      ⁢
      
       P
       g
       
        G
        ,
        0
       
      
     
     =
     
      
       S
       
        g
        ,
        
         l
         L
        
       
       L
      
      ⁢
      Δ
      ⁢
      
       P
       
        l
        L
       
       L
      
     
    
   
   
    
     (
     
      7
      ⁢
      a
     
     )
    
   
  
 

 
  
   
    
     
      S
      
       g
       ,
       
        l
        L
       
      
      L
     
     =
     
      
       (
       
        
         
          
           
            
             L
             
              g
              ,
              
               n
               s
              
             
             
              G
              ⁢
              D
             
            
            ⁢
            
             L
             
              
               n
               s
              
              ,
              
               n
               E
              
             
             
              D
              ⁢
              D
             
            
           
           +
           
            
             L
             
              g
              ,
              
               n
               s
              
             
             
              G
              ⁢
              D
             
            
            ⁢
            
             L
             
              
               n
               E
              
              ,
              
               n
               E
              
             
             
              D
              ⁢
              D
             
            
           
          
         
        
        
         
          
           
            
             -
             
              L
              
               
                n
                s
               
               ,
               
                n
                s
               
              
              
               D
               ⁢
               D
              
             
            
            ⁢
            
             L
             
              g
              ,
              
               n
               E
              
             
             
              G
              ⁢
              D
             
            
           
           -
           
            
             L
             
              
               n
               E
              
              ,
              
               n
               s
              
             
             D
            
            ⁢
            
             L
             
              g
              ,
              
               n
               E
              
             
             
              G
              ⁢
              D
             
            
           
          
         
        
       
       )
      
      
       
        
         L
         
          
           n
           s
          
          ,
          
           n
           E
          
         
         
          D
          ⁢
          D
         
        
        ⁢
        
         L
         
          
           n
           E
          
          ,
          
           n
           s
          
         
         DD
        
       
       -
       
        
         L
         
          
           n
           s
          
          ,
          
           n
           s
          
         
         
          D
          ⁢
          D
         
        
        ⁢
        
         L
         
          
           n
           E
          
          ,
          
           n
           E
          
         
         
          D
          ⁢
          D
         
        
       
      
     
    
   
   
    
     (
     
      7
      ⁢
      b
     
     )
    
   
  
 

wherein Sg,lLL is an extended SPC of the line switching disturbance; and
wherein, [
       
        
         
          
           Δ
           ⁢
           
            P
            G
           
          
         
        
        
         
          
           Δ
           ⁢
           
            P
            
             n
             S
            
            L
           
          
         
        
        
         
          
           Δ
           ⁢
           
            P
            
             n
             E
            
            L
           
          
         
        
       
       ]
      
      =
      
       
        [
        
         
          
           
            L
            
             G
             ⁢
             G
            
           
          
          
           
            L
            
             n
             S
            
            
             G
             ⁢
             D
            
           
          
          
           
            L
            
             n
             E
            
            
             G
             ⁢
             D
            
           
          
         
         
          
           
            L
            
             n
             S
            
            
             D
             ⁢
             G
            
           
          
          
           
            L
            
             
              n
              S
             
             ,
             
              n
              S
             
            
            
             D
             ⁢
             D
            
           
          
          
           
            L
            
             
              n
              S
             
             ,
             
              n
              E
             
            
            
             D
             ⁢
             D
            
           
          
         
         
          
           
            L
            
             n
             E
            
            
             D
             ⁢
             G
            
           
          
          
           
            L
            
             
              n
              E
             
             ,
             
              n
              S
             
            
            
             D
             ⁢
             D
            
           
          
          
           
            L
            
             
              n
              E
             
             ,
             
              n
              E
             
            
            
             D
             ⁢
             D
            
           
          
         
        
        ]
       
       [
       
        
         
          
           Δ
           ⁢
           δ
          
         
        
        
         
          
           Δ
           ⁢
           
            θ
            
             n
             S
            
           
          
         
        
        
         
          
           Δ
           ⁢
           
            θ
            
             n
             E
            
           
          
         
        
       
       ]
      
     
     ,
    
   
   
    
     (
     5
     )
    
   
  
 

where ΔPG∈NG×1, PnSL, and PnEL are active power injected from a generator EMF and the two terminals of disturbed line, Δδ=NG×1, θnS, and θnE are a phase angle of Ė, {dot over (U)}nS, and {dot over (U)}nE, respectively, and parameters characterized by L are linearization coefficients between an active power and a phase angle;
determining a generator turbine disturbance SPC Sg,gTT based on:, Δ
      ⁢
      
       P
       g
       
        G
        ,
        0
       
      
     
     =
     
      
       S
       
        g
        ,
        
         g
         T
        
       
       T
      
      ⁢
      Δ
      ⁢
      
       P
       
        g
        T
       
       T
      
     
    
   
   
    
     (
     
      9
      ⁢
      a
     
     )
    
   
  
 

 
  
   
    
     
      S
      
       g
       ,
       
        g
        T
       
      
      T
     
     =
     
      {
      
       
        
         
          1
          ,
         
        
        
         
          g
          =
          
           g
           T
          
         
        
       
       
        
         
          0
          ,
         
        
        
         
          g
          ≠
          
           g
           T
          
         
        
       
      
     
    
   
   
    
     (
     
      9
      ⁢
      b
     
     )
    
   
  
 

wherein a disturbance power of a gT-th disturbed generator is ΔPgTD, and the SPC is made up of constant values and equal to 1 only a disturbed generator is concerned;

determining node frequency ΔfnRD as follows:, Δ
       ⁢
       
        f
        
         n
         R
        
        D
       
      
      =
      
       
        ∑
        g
       
       
        
         F
         
          
           n
           R
          
          ,
          g
         
        
        ⁢
        Δ
        ⁢
        
         f
         g
         G
        
       
      
     
     ,
    
   
   
    
     (
     
      18
      ⁢
      a
     
     )
    
   
  
 

 
  
   
    
     
      
       F
       
        
         n
         R
        
        ,
        g
       
      
      =
      
       
        
         E
         g
        
        
         U
         
          n
          R
         
        
       
       ⁢
       
        B
        
         
          n
          R
         
         ,
         g
        
       
       ⁢
       
        cos
        ⁡
        (
        
         
          δ
          g
         
         -
         
          θ
          
           n
           R
          
         
         +
         
          β
          
           
            n
            R
           
           ,
           g
          
         
        
        )
       
      
     
     ,
    
   
   
    
     (
     
      18
      ⁢
      b
     
     )
    
   
  
 

wherein FnR,g is named as frequency formation coefficient (FFC) for g-th generator; and
wherein, p
       ⁢
       
        U
        
         n
         R
        
       
      
      +
      
       j
       ⁢
       
        U
        
         n
         R
        
       
       ⁢
       
        f
        N
       
       ⁢
       Δ
       ⁢
       
        f
        
         n
         R
        
        D
       
      
     
     =
     
      
       ∑
       g
      
      
       
        B
        
         
          n
          R
         
         ,
         g
        
       
       ⁢
       j
       ⁢
       
        E
        g
       
       ⁢
       
        e
        
         j
         ⁡
         (
         
          
           δ
           g
          
          -
          
           θ
           
            n
            ⁢
            R
           
          
          +
          
           
            β
            
             n
             ,
            
           
           ⁢
           g
          
         
         )
        
       
       ⁢
       
        f
        N
       
       ⁢
       Δ
       ⁢
       
        
         f
         g
         G
        
        .
       
      
     
    
   
   
    
     (
     17
     )
    
   
  
 

determining impacts of UC decision variables on the FFC and the SPC;
approximating node initial RoCoF and the UC decision variables by approximating linear fitting coefficients agC and a0:, A
      
       {
       ·
       }
      
      
       
        {
        ·
        }
       
       ,
       Fit
      
     
     =
     
      
       
        ∑
        
         
          g
          c
         
         ∈
         
          𝒢
          c
         
        
       
       
        
         a
         
          g
          c
         
        
        ⁢
        
         u
         
          g
          c
         
        
       
      
      +
      
       a
       0
      
     
    
   
   
    
     (
     
      25
      ⁢
      a
     
     )
    
   
  
 

 
  
   
    
     
      a
      
       g
       c
      
     
     =
     
      
       Γ
       
        g
        c
       
      
      [
      
       
        u
        
         g
         s
        
       
       (
       
        ∀
        
         
          g
          S
         
         ∈
         
          𝒢
          S
         
        
       
       )
      
      ]
     
    
   
   
    
     (
     
      25
      ⁢
      b
     
     )
    
   
  
 

 
  
   
    
     
      a
      0
     
     =
     
      
       Γ
       0
      
      [
      
       
        u
        
         g
         s
        
       
       (
       
        ∀
        
         
          g
          S
         
         ∈
         
          𝒢
          S
         
        
       
       )
      
      ]
     
    
   
   
    
     (
     
      25
      ⁢
      c
     
     )
    
   
  
 

wherein ΓgC[⋅] and Γ0[⋅] represent a if-then logic; and
wherein

A{⋅}{⋅}=γ[ug(∀g∈)],  (23)

approximating a maximum RoCoF of any node as:

RoCoFnR,tMax=max{RoCoFnR,td,0,RoCoFCOI,td,Max,∀d},  (26)

wherein COI maximum RoCoF constraints are as follows:, Δ
       ⁢
       
        P
        
         n
         D
        
        D
       
      
      ≤
      
       2
       ⁢
       
        
         ∑
         g
        
        
         
          H
          g
         
         ⁢
         
          u
          
           g
           ,
           t
          
         
         ⁢
         R
         ⁢
         o
         ⁢
         C
         ⁢
         o
         ⁢
         
          F
          
           n
           R
          
          
           L
           ⁢
           i
           ⁢
           m
          
         
        
       
      
     
     ,
     
      ∀
      
       n
       R
      
     
     ,
     
      ∀
      
       n
       D
      
     
     ,
     
      ∀
      t
     
    
   
   
    
     (
     
      30
      ⁢
      a
     
     )
    
   
  
 

 
  
   
    
     
      
       Δ
       ⁢
       
        P
        
         g
         T
        
        T
       
      
      ≤
      
       2
       ⁢
       
        
         ∑
         g
        
        
         
          H
          g
         
         ⁢
         
          u
          
           g
           ,
           t
          
         
         ⁢
         R
         ⁢
         o
         ⁢
         C
         ⁢
         o
         ⁢
         
          F
          
           n
           R
          
          
           L
           ⁢
           i
           ⁢
           m
          
         
        
       
      
     
     ,
     
      ∀
      
       n
       R
      
     
     ,
     
      ∀
      
       g
       M
      
     
     ,
     
      ∀
      t
     
    
   
   
    
     (
     
      30
      ⁢
      b
     
     )
    
   
  
 

constructing an RoCof constrained UC model as follows:, min
      ⁢
      
       
        ∑
        t
       
       
        
         ∑
         g
        
        
         (
         
          
           
            C
            g
           
           ⁢
           
            (
            
             P
             
              g
              ,
              t
             
             G
            
            )
           
          
          +
          
           
            C
            g
            U
           
           ⁢
           
            z
            
             g
             ,
             t
            
            U
           
          
          +
          
           
            C
            g
            D
           
           ⁢
           
            z
            
             g
             ,
             t
            
            D
           
          
         
         )
        
       
      
     
     ,
    
   
  
  
   
    
     
      
       
        C
        g
       
       ⁢
       
        (
        
         P
         
          g
          ,
          t
         
         G
        
        )
       
      
      =
      
       
        
         C
         g
         
          R
          ⁢
          2
         
        
        ⁢
        
         P
         
          g
          ,
          t
         
         
          G
          2
         
        
       
       +
       
        
         C
         g
         
          R
          ⁢
          1
         
        
        ⁢
        
         P
         
          g
          ,
          t
         
         G
        
       
       +
       
        C
        g
        
         R
         ⁢
         0
        
       
      
     
     ;, and
wherein, min
         
          
           a
           p
           
            g
            C
           
          
          ,
          
           a
           p
           0
          
         
        
        
         
          (
          
           
            A
            
             
              {
              ·
              }
             
             ,
             p
            
            
             {
             ·
             }
            
           
           -
           
            A
            
             
              {
              ·
              }
             
             ,
             p
            
            
             
              {
              ·
              }
             
             ,
             Fit
            
           
          
          )
         
         2
        
       
      
     
     
      
       
        
         
          con
          .
             
          1
         
         ⁢
            
         
          A
          
           
            {
            ·
            }
           
           ,
           p
          
          
           {
           ·
           }
          
         
        
        =
        
         γ
         [
         
          
           u
           
            g
            c
           
          
          (
          
           ∀
           
            
             g
             c
            
            ∈
            
             𝒢
             c
            
           
          
          )
         
         ]
        
       
      
     
     
      
       
        
         
          con
          .
             
          2
         
         ⁢
            
         
          A
          
           
            {
            ·
            }
           
           ,
           p
          
          
           
            {
            ·
            }
           
           ,
           Fit
          
         
        
        =
        
         
          
           ∑
           
            
             g
             c
            
            ∈
            
             𝒢
             c
            
           
          
          
           
            a
            p
            
             g
             c
            
           
           ⁢
           
            u
            
             g
             c
            
           
          
         
         +
         
          a
          p
          0
         
        
       
      
     
    
   
   
    
     (
     24
     )
    
   
  
 

collecting future 24-hour operation data of the power system including a power system topology and parameters, forecasted load curves, node RoCoF limitations, and envisioned disturbances;
substituting the future 24-hour operation data into the UC model and solving the UC model by the optimization algorithm to obtain an operating status and a power output of synchronous generators for a future 24 hours;
avoiding the blackouts caused by a RoCoF-based relay tripping by operating the power system using a stable frequency such that the post-disturbance node RoCoF does not exceed a predetermined limitation.