Patent ID: 11906556
Assignee: NORTH CHINA ELECTRIC POWER UNIVERSITY
Field: Measurement (Instruments)
Classification: CPC G  Y | IPC G

Claim 0:
1. A method for estimating area-level inertia in a power system, comprising:
partitioning the power system as a multi-area system, wherein:
a phasor measurement unit (“PMU”) is placed at a bus in at least one area of the multi-area system; and
for an N-th area which contains only one generator and one bus, the PMU placement must be placed at the multi-area system;

measuring bus frequencies, power flow related data including amplitude and phase angle of bus voltage by the PMUs or SCADA/EMS as follows:, Measurable Variables

fB,i ( ∀i ∈ N )
from PMU

ECOI,i(ss), δCOI,i(ss), and 
from power flow calculation

δCOI,i(0) ( ∀i ∈ N )
by SCADA/EMS

Ui(ss) and θi(ss)
from PMU or SCADA/EMS

( ∀i ∈ N )

fCOI,i(0) ( ∀i ∈ N )
from PMU or SCADA/EMS

specifying data window for inertia estimation during small disturbance situations;
preparing measured frequencies within the data window, wherein:
for the power flow data, variables at a linearization point correspond to a head of the data window, and variables at a system steady-state are utilized; and
determining an internal reactance or an inertia of the N-th area according to an identifiability analysis;

estimating the area-level inertia by:, min
       
        Ψ
        ^
       
      
      (
      
       
        ∫
        
         t
         0
        
        
         
          t
          0
         
         +
         T
        
       
       
        
         ∑
         
          i
          ∈
          N
         
        
        
         
          
           (
           
            
             
              
               f
               ^
              
              
               B
               ,
               i
              
             
             (
             
              Ψ
              ^
             
             )
            
            -
            
             f
             
              B
              ,
              i
             
            
           
           )
          
          2
         
         ⁢
         dt
        
       
      
      )
     
     ,
    
   
   
    
     (
     
      11
      ⁢
      a
     
     )
    
   
  
 

 
  
   
    
     
      
       Ψ
       ^
      
      =
      
       {
       
        
         
          H
          ^
         
         
          A
          ,
          i
         
        
        ,
        
         
          X
          ^
         
         
          A
          ,
          i
         
        
        ,
        
         
          X
          ^
         
         
          L
          ,
          ij
         
        
       
       }
      
     
     ,
    
   
   
    
     (
     
      11
      ⁢
      b
     
     )
    
   
  
 

 
  
   
    
     
      
       
        f
        ^
       
       
        B
        ,
        i
       
      
      =
      
       g
       ⁡
       (
       
        
         Ψ
         ^
        
        
         ,
         
          COI
          ,
          i
         
         
          (
          0
          )
         
        
        ,
        
         δ
         
          COI
          ,
          i
         
         
          (
          0
          )
         
        
        ,
        
         E
         
          COI
          ,
          i
         
         
          (
          ss
          )
         
        
        ,
        
         δ
         
          COI
          ,
          i
         
         
          (
          ss
          )
         
        
        ,
        
         U
         i
         
          (
          ss
          )
         
        
        ,
        
         θ
         i
         
          (
          ss
          )
         
        
       
       )
      
     
     ,
    
   
   
    
     (
     
      11
      ⁢
      c
     
     ), wherein t0 is a moment corresponding to a linearization point; T is a data window length; a vector {circumflex over (Ψ)} consisting of parameters to be estimated in (11b); based on {circumflex over (Ψ)} and power flow related variables, bus frequency dynamics are estimated in (11c);
wherein g(⋅) denotes:, 2
       ⁢
       
        H
        
         A
         ,
         i
        
       
       ⁢
       
        
         d
         ⁢
         Δ
         ⁢
         
          f
          
           COI
           ,
           i
          
         
        
        
         d
         ⁢
         t
        
       
      
      =
      
       
        -
        Δ
       
       ⁢
       
        P
        
         A
         ,
         i
        
        E
       
      
     
     ,
    
   
   
    
     (
     
      7
      ⁢
      a
     
     )
    
   
  
 

 
  
   
    
     
      
       
        d
        ⁢
        Δ
        ⁢
        
         δ
         
          COI
          ,
          i
         
        
       
       
        d
        ⁢
        t
       
      
      =
      
       
        f
        N
       
       ⁢
       Δ
       ⁢
       
        f
        
         C
         ⁢
         O
         ⁢
         
          I
          i
         
        
       
      
     
     ,
    
   
   
    
     (
     
      7
      ⁢
      b
     
     )
    
   
  
 

 
  
   
    
     
      
       Δ
       ⁢
       
        P
        
         A
         ,
         i
        
        E
       
      
      =
      
       
        K
        
         A
         ,
         i
        
       
       (
       
        
         Δδ
         
          COI
          ,
          i
         
        
        -
        
         Δθ
         i
        
       
       )
      
     
     ,
    
   
   
    
     (
     
      7
      ⁢
      c
     
     )
    
   
  
 

 
  
   
    
     
      K
      
       A
       ,
       i
      
     
     =
     
      
       
        
         E
         
          COI
          ,
          i
         
         
          (
          ss
          )
         
        
        ⁢
        
         U
         i
         
          (
          
           s
           ⁢
           s
          
          )
         
        
        ⁢
        S
        ⁢
        S
       
       
        X
        
         A
         ,
         i
        
       
      
      ⁢
      
       cos
       ⁡
       (
       
        
         5
         
          COI
          ,
          i
         
         
          (
          ss
          )
         
        
        -
        
         θ
         i
         
          (
          
           s
           ⁢
           s
          
          )
         
        
       
       )
      
     
    
   
   
    
     (
     
      7
      ⁢
      d
     
     )
    
   
  
 

 
  
   
    
     
      
       d
       ⁢
       Δ
       ⁢
       
        θ
        i
       
      
      
       d
       ⁢
       t
      
     
     =
     
      
       f
       N
      
      ⁢
      Δ
      ⁢
      
       
        f
        
         B
         ,
         i
        
       
       .
      
     
    
   
   
    
     (
     8
     )
    
   
  
 

 
  
   
    
     
      
       Δ
       ⁢
       
        P
        
         A
         ,
         i
        
        E
       
      
      =
      
       
        ∑
        
         
          j
          ∈
          N
         
         ,
         
          j
          ≠
          i
         
        
       
       
        
         K
         
          L
          ,
          ij
         
        
        (
        
         
          Δθ
          i
         
         -
         
          Δθ
          j
         
        
        )
       
      
     
     ,
    
   
   
    
     (
     
      9
      ⁢
      a
     
     )
    
   
  
 

 
  
   
    
     
      
       K
       
        L
        ,
        ij
       
      
      =
      
       
        
         
          U
          i
          
           (
           
            s
            ⁢
            s
           
           )
          
         
         ⁢
         
          U
          j
          
           (
           
            s
            ⁢
            s
           
           )
          
         
        
        
         X
         ij
        
       
       ⁢
       
        cos
        ⁡
        (
        
         
          θ
          i
          
           (
           
            s
            ⁢
            s
           
           )
          
         
         -
         
          θ
          j
          
           (
           
            s
            ⁢
            s
           
           )
          
         
        
        )
       
      
     
     ,
    
   
   
    
     (
     
      9
      ⁢
      b
     
     ), where KA,i is a linearization coefficient of a generator active power; the superscript {⋅}(ss) denotes a steady-state value; and where KA,i is a linearization coefficient of an inter-area active power;
obtaining an area equivalent internal reactance and an equivalent inter-area line reactance;
determining a real-time frequency stability level and a real-time degree of frequency spatial distribution based on the area equivalent internal reactance and the equivalent inter-area line reactance;
issuing an alarm in the event of a determined frequency instability;
when an online inertia level is low, allocating optimal inertia from battery storage and unit commitment optimization of synchronous generators.