Patent ID: 11923685
Assignee: TSINGHUA UNIVERSITY
Field: Electrical machinery, apparatus, energy (Electrical engineering)
Classification: CPC H  G  Y | IPC G  H

Claim 0:
1. A reactive power-voltage control method, performed by a power system, comprising:
establishing a reactive power-voltage control model for the power system consisting of a transmission network and a plurality of distribution networks, wherein the plurality of distribution networks are radial in nature, the reactive power-voltage control model comprises an objective function and a plurality of constraints, the objective function is established for minimizing a sum of active power outputs of generators at a slack bus in the transmission network, and the plurality of constraints include a plurality of transmission network constraints, a plurality of distribution network constraints and a plurality of transmission-distribution network boundary constraints;
performing a second order cone relaxation on a non-convex constraint of the plurality of distribution network constraints to obtain a convex-relaxed reactive power-voltage control model;
solving the convex-relaxed reactive power-voltage control model to acquire control variables of the transmission network and control variables of each distribution network; and
performing coordinated reactive power-voltage control on the transmission network and each distribution network based on the control variables of the transmission network and the control variables of the distribution network,
wherein the objective function is represented as:, min
  ⁢
  
   
    ∑
    
     i
     ∈
     
      G
      PCC
      T
     
    
   
   
    P
    i
    G
   
  
 

where GPCCT presents a set of indexes of the generators at the slack bus in the transmission network, and PiG represents an active power output of an ith generator in GPCCT,
wherein the plurality of transmission network constraints comprise a first power flow constraint, a first power input equilibrium constraint, a first voltage limit constraint, a first power output constraint, and a first line capacity constraint;
wherein the first power flow constraint is represented as:, P
        ij
      
      =
      
        
          
            1
            
              τ
              ij
              2
            
          
          ⁢
          
            g
            ij
            ɛ
          
          ⁢
          
            V
            i
            2
          
        
        -
        
          
            1
            
              τ
              ij
            
          
          ⁢
          
            V
            i
          
          ⁢
          
            
              V
              j
            
            ⁡
            
              [
              
                
                  
                    g
                    ij
                    ɛ
                  
                  ⁢
                  
                    cos
                    ⁡
                    
                      (
                      
                        
                          θ
                          i
                        
                        -
                        
                          θ
                          j
                        
                        -
                        
                          ϕ
                          ij
                        
                      
                      )
                    
                  
                
                +
                
                  
                    b
                    ij
                    ɛ
                  
                  ⁢
                  
                    sin
                    ⁡
                    
                      (
                      
                        
                          θ
                          i
                        
                        -
                        
                          θ
                          j
                        
                        -
                        
                          ϕ
                          ij
                        
                      
                      )
                    
                  
                
              
              ]
            
          
        
      
    
    ,
    
      ∀
      
        ij
        ∈
        
          IL
          T
        
      
    
  

  
    
      
        P
        ji
      
      =
      
        
          
            g
            ij
            ɛ
          
          ⁢
          
            V
            j
            2
          
        
        -
        
          
            1
            
              τ
              ij
            
          
          ⁢
          
            V
            i
          
          ⁢
          
            
              V
              j
            
            ⁡
            
              [
              
                
                  
                    g
                    ij
                    ɛ
                  
                  ⁢
                  
                    cos
                    ⁡
                    
                      (
                      
                        
                          θ
                          j
                        
                        -
                        
                          θ
                          i
                        
                        +
                        
                          ϕ
                          ij
                        
                      
                      )
                    
                  
                
                +
                
                  
                    b
                    ij
                    ɛ
                  
                  ⁢
                  
                    sin
                    ⁡
                    
                      (
                      
                        
                          θ
                          j
                        
                        -
                        
                          θ
                          i
                        
                        +
                        
                          ϕ
                          ij
                        
                      
                      )
                    
                  
                
              
              ]
            
          
        
      
    
    ,
    
      ∀
      
        ij
        ∈
        
          IL
          T
        
      
    
  

  
    
      
        Q
        ij
      
      =
      
        
          
            -
            
              1
              
                τ
                ij
                2
              
            
          
          ⁢
          
            (
            
              
                b
                ij
                ɛ
              
              ⁢
              
                
                  b
                  ij
                  C
                
                2
              
            
            )
          
          ⁢
          
            V
            i
            2
          
        
        -
        
          
            1
            
              τ
              ij
            
          
          ⁢
          
            V
            i
          
          ⁢
          
            
              V
              j
            
            ⁡
            
              [
              
                
                  
                    g
                    ij
                    ɛ
                  
                  ⁢
                  
                    sin
                    ⁡
                    
                      (
                      
                        
                          θ
                          i
                        
                        -
                        
                          θ
                          j
                        
                        -
                        
                          ϕ
                          ij
                        
                      
                      )
                    
                  
                
                -
                
                  
                    b
                    ij
                    ɛ
                  
                  ⁢
                  
                    cos
                    ⁡
                    
                      (
                      
                        
                          θ
                          i
                        
                        -
                        
                          θ
                          j
                        
                        -
                        
                          ϕ
                          ij
                        
                      
                      )
                    
                  
                
              
              ]
            
          
        
      
    
    ,
    
      ∀
      
        ij
        ∈
        
          IL
          T
        
      
    
  

  
    
      
        Q
        ji
      
      =
      
        
          
            -
            
              (
              
                
                  b
                  ij
                  ɛ
                
                ⁢
                
                  
                    b
                    ij
                    C
                  
                  2
                
              
              )
            
          
          ⁢
          
            V
            j
            2
          
        
        -
        
          
            1
            
              τ
              ij
            
          
          ⁢
          
            V
            i
          
          ⁢
          
            
              V
              j
            
            ⁡
            
              [
              
                
                  
                    g
                    ij
                    ɛ
                  
                  ⁢
                  
                    sin
                    ⁡
                    
                      (
                      
                        
                          θ
                          j
                        
                        -
                        
                          θ
                          i
                        
                        +
                        
                          ϕ
                          ij
                        
                      
                      )
                    
                  
                
                -
                
                  
                    b
                    ij
                    ɛ
                  
                  ⁢
                  
                    cos
                    ⁡
                    
                      (
                      
                        
                          θ
                          j
                        
                        -
                        
                          θ
                          i
                        
                        +
                        
                          ϕ
                          ij
                        
                      
                      )
                    
                  
                
              
              ]
            
          
        
      
    
    ,
    
      ∀
      
        ij
        ∈
        
          IL
          T
        
      
    
  

where Pij represents an active power flowing from an ith bus to a jth bus in the transmission network, τij represents a transformer ratio of an (ij)th branch in the transmission network, gijε represents an electric conductance of the (ij)th branch in the transmission network, Vi represents a voltage magnitude of the ith bus in the transmission network, Vj represents a voltage magnitude of the jth bus in the transmission network, θi represents a voltage phase-angle of the ith bus in the transmission network, θj represents a voltage phase-angle of the jth bus in the transmission network, ϕij represents a transformer phase shifting angle of the (ij)th branch in the transmission network, bijε represents a susceptance of the(ij)th branch in the transmission network, the (ij)th branch represents a branch from the ith bus to the jth bus, ILT represents a set of indexes of branches in the transmission network, Pji represents an active power flowing from the jth bus to the ith bus in the transmission network, Qji represents a reactive power flowing from the ith bus to the jth bus in the transmission network, bijC represents a charging susceptance of the (ij)th branch in the transmission network, Qji represents a reactive power flowing from the jth bus to the ith bus in the transmission network;
wherein the first power input equilibrium constraint is represented as:, ∑
            
              j
              ∈
              
                IG
                Ti
              
            
          
          ⁢
          
            P
            j
            G
          
        
        -
        
          
            ∑
            
              
                j
                ⁢
                
                  :
                
                ⁢
                ji
              
              ∈
              
                IL
                T
              
            
          
          ⁢
          
            P
            ij
          
        
        -
        
          
            ∑
            
              
                j
                ⁢
                
                  :
                
                ⁢
                ij
              
              ∈
              
                IL
                T
              
            
          
          ⁢
          
            P
            ij
          
        
        -
        
          P
          i
          D
        
        -
        
          
            V
            i
            2
          
          ⁢
          
            g
            i
            s
          
        
      
      =
      0
    
    ,
    
      ∀
      
        i
        ∈
        
          IB
          T
        
      
    
  

  
    
      
        
          
            ∑
            
              j
              ∈
              
                IG
                Ti
              
            
          
          ⁢
          
            Q
            j
            G
          
        
        -
        
          
            ∑
            
              
                j
                ⁢
                
                  :
                
                ⁢
                ji
              
              ∈
              
                IL
                T
              
            
          
          ⁢
          
            Q
            ij
          
        
        -
        
          
            ∑
            
              
                j
                ⁢
                
                  :
                
                ⁢
                ij
              
              ∈
              
                IL
                T
              
            
          
          ⁢
          
            Q
            ij
          
        
        -
        
          Q
          i
          D
        
        +
        
          
            V
            i
            2
          
          ⁢
          
            b
            i
            s
          
        
      
      =
      0
    
    ,
    
      ∀
      
        i
        ∈
        
          IB
          T
        
      
    
  

where IGTi represents a set of indexes of generators connected to the ith bus in the transmission network, PjG represents an active power output of a jth generator, PiD represents an active load of the ith bus in the transmission network, giS represents a parallel conductance of the ith bus in the transmission network, IBT represents a set of indexes of buses in the transmission network, QjG represents a reactive power output of the jth generator, QiD represents a reactive load of the ith bus in the transmission network, biS represents a parallel susceptance of the ith bus in the transmission network;
wherein the first voltage limit constraint is represented as:

Vi≤Vi≤Vi,∀i∈IBT 

where Vi represents a lower limit of the voltage magnitude of the ith bus in the transmission network, and Vi represents an upper limit of the voltage magnitude of the ith bus in the transmission network;
wherein the first power output constraint is represented as:

PiG≤PiG≤PiG,QiG≤QiG≤QiG,∀i∈IGT 

where IGT represents a set of indexes of generators in the transmission network, PiG represents a lower limit of an active power of an ith generator, and PiG represents an upper limit of the active power of the ith generator, QiG represents a lower limit of a reactive power of an ith generator, and QiG represents an upper limit of the reactive power of the ith generator;
wherein the first line capacity constraint is represented as:

Pij2+Qij2≤Sij2,Pji2+Qji2≤Sij2,∀ij∈ILT 

where Sij  represents an apparent power capacity of the (ij)th branch in the transmission network.