Patent ID: 11923688
Assignee: NORTH CHINA ELECTRIC POWER UNIVERSITY
Field: Electrical machinery, apparatus, energy (Electrical engineering)
Classification: CPC H | IPC H

Claim 0:
1. A method for maintaining power system stability comprising:
collecting system topology data, reactance values and resistance values of transmission lines from an SCADA/EMS system;
collecting frequency and active power samples from phaser measurement units (PMU) installed at point of interconnection (POI) buses;
calculating active power {circumflex over (P)}T at an POI-level aggregated generator terminal and the rotor speed {circumflex over (f)}G of the POI-level aggregated generator according to the following:, Δ
      ⁢
      
       
        f
        ˆ
       
       G
      
     
     =
     
      
       
        
         diag
         (
         
          b
          
           G
           ⁢
           B
          
         
         )
        
        
         -
         1
        
       
       ⁢
       
        
         
          
           B
           
            D
            ⁢
            B
           
          
          [
          
           
            
             E
            
           
           
            
             
              B
              
               D
               ⁢
               L
              
             
            
           
          
          ]
         
         +
        
        [
        
         
          
           
            Λ
            L
           
          
         
         
          
           
            0
            
             N
             ×
             L
            
           
          
         
        
        ]
       
       ⁢
       Δ
       ⁢
       
        f
        
         D
         ,
         
          m
          ⁢
          e
         
        
       
      
      =
      
       A
       ⁢
       Δ
       ⁢
       
        f
        
         D
         ,
         
          m
          ⁢
          e
         
        
       
      
     
    
   
   
    
     (
     19
     )
    
   
  
 

whereas f,min=ΔfD,me(1) ∩ . . . ∩ΔfD,me(i) ∩ . . . ∩ΔfD,me(M)=ΔfD,me(POI).,
whereas calculation of Δ{circumflex over (f)}D is the following weighted least squares problem:, min
      
       Δ
       ⁢
       
        
         f
         ˆ
        
        D
       
      
     
     
      e
      T
     
     ⁢
     We
    
   
   
    
     (
     
      20
      ⁢
      a
     
     )
    
   
  
 

 
  
   
    
     
      e
      =
      
       
        
         [
         
          
           
            
             Λ
             L
            
           
          
          
           
            
             0
             
              N
              ×
              L
             
            
           
          
         
         ]
        
        ⁢
        Δ
        ⁢
        
         f
         
          D
          ,
          
           m
           ⁢
           e
          
         
        
       
       +
       
        
         [
         
          
           
            
             -
             E
            
           
          
          
           
            
             B
             
              D
              ⁢
              L
             
            
           
          
         
         ]
        
        ⁢
        Δ
        ⁢
        
         
          f
          ˆ
         
         D
        
       
      
     
     ,
    
   
   
    
     (
     
      20
      ⁢
      b
     
     )
    
   
  
 

where W∈(L+N)×(L+N) denotes a diagonal matrix related to the measured frequency data quality at each measured point;
where A∈M×M is a linear correlation between rotor speeds and POI bus frequencies;

{circumflex over (P)}T=PB,me+diag(r)IB,me2,   (22)

where IB,me∈M×1 and PB,me∈M×1 are the current and active power of the incoming line measured by the POI-bus PMU, respectively, and diag(r)∈M×M is a diagonal matrix; and
where PMUs are placed at all POI buses for active power measurement such that, 𝒮
    P
   
   =
   
    P
    
     B
     ,
     me
    
    
     (
     POI
     )
    
   
  
  ,, and that fP,min=f,min∩P;
if the frequency of POI PMU is not available, adopting (19) under an adjusted PMU combination;
if the non-POI PMUs data are available, calculating the following and obtaining the weighted-least-squares solution {circumflex over (f)}G,W:, Δ
       ⁢
       
        
         f
         ˆ
        
        
         G
         ,
         W
        
       
      
      =
      
       
        
         
          diag
          (
          
           b
           
            G
            ⁢
            B
           
          
          )
         
         
          -
          1
         
        
        ⁢
        
         
          
           
            B
            
             D
             ⁢
             B
            
           
           [
           
            
             
              E
             
            
            
             
              
               B
               
                D
                ⁢
                L
               
              
             
            
           
           ]
          
          W
          +
         
         [
         
          
           
            
             Λ
             L
            
           
          
          
           
            
             0
             
              N
              ×
              L
             
            
           
          
         
         ]
        
        ⁢
        Δ
        ⁢
        
         f
         
          D
          ,
          
           m
           ⁢
           e
          
         
        
       
       =
       
        
         A
         W
        
        ⁢
        Δ
        ⁢
        
         f
         
          D
          ,
          me
         
        
       
      
     
     ,
    
   
   
    
     (
     21
     )
    
   
  
 

estimating POI-level aggregated inertia by solving the following for each POI bus:

2Ĥagpy(t)=Δ{circumflex over (P)}mu1(t)+u2(t),   (23a)

y={0, {circumflex over (f)}G(t2)−{circumflex over (f)}G(t1), {circumflex over (f)}3(t3) −{circumflex over (f)}G(t1), . . . , {circumflex over (f)}G(tK)−{circumflex over (f)}G(t1)},   (23b)

ū1={1,1,1, . . . , 1},   (23c)

ū2={0, −{circumflex over (P)}T(t2)+{circumflex over (P)}T(t1), −{circumflex over (P)}T(t3) +{circumflex over (P)}T(t1), . . . , −{circumflex over (P)}T(tK)+{circumflex over (P)}T(t1)}.   (23d)

in which {Ĥag, Δ{circumflex over (P)}m} is the parameter vector to be identified; y(t) and u2(t) are the values of rotor speed and active power deviation from the operating point, respectively; and u1 (t) represents the mechanical power and remains constant;

estimating the system-level inertia by:, H
        ^
       
       
        
         s
         ⁢
         y
         ⁢
         s
        
        ,
        t
       
      
      =
      
       
        
         
          ∑
           
         
         i
        
        ⁢
        
         
          H
          ^
         
         
          ag
          ,
          i
         
        
        ⁢
        
         S
         
          ag
          ,
          i
         
        
       
       
        
         
          ∑
           
         
         i
        
        ⁢
        
         S
         
          ag
          ,
          i
         
        
       
      
     
     ,
     
      ∀
      t
     
     ,
    
   
   
    
     (
     24
     )
    
   
  
 

where Ĥag,i and Sag,i are the POI-level aggregated inertia constant and rated capacity of generator i, respectively;

estimating frequency stability indexes including post-disturbance rate of change of frequency (RoCoF) and frequency nadir based on the system-level inertia;
determine whether the frequency stability indexes reach a predetermined limitation;
when the predetermined limitation is reached, activate at least one generator to increase system inertia.