[Electrical dielectric number] electrical dielectric number and calculation considering HVDC and facts components

1. Software version

matlab2013b

2. System Overview

1. Calculation of Branch Electrical dielectric number

Access Rd m-n The formula for calculating the electrical dielectric number of is as follows ：

 2. Calculation of node electrical dielectric

node k The formula for calculating the electrical dielectric number of is as follows ：

 

  among ,F(k) For and nodes k Set of connected edges .

It is necessary to obtain the calculated value and distribution of the electrical dielectric number of branches and nodes for the test system .

Refer to the attached literature 《 contain HVDC and FACTS Calculation of electrical dielectric number of components Part 1 》、《 contain HVDC and FACTS Calculation of electrical dielectric number of components Part II 》 computing method . The DC power flow model is adopted as the power flow model .

HVDC、FACTS（ contain TCSC and UPFC） The three simplified models are embodied in the calculation of electrical dielectric number in the form of ： For test system , The above three simplified models can be selected on any number and location of lines in the system . After considering the three models, the calculated value and distribution of the electrical dielectric number of branches and nodes in the system are obtained .

        According to the calculation flow of electrical dielectric number provided in the paper ：

Step one ： Simplify the network , Obtain the power grid topology model ;

Step two ： Connectivity analysis , The whole network is divided into different regions by using the connectivity analysis algorithm in graph theory ;

Step three ： Calculate the admittance matrix of each different region ;

Step four ： Select a pair of generation load nodes in the same area , And inject active power , Then calculate the power flow , And ensure that all generation load stages are selected ;

Step five ： Calculate the electrical dielectric number of lines and nodes ;

Step six ： Calculate the corresponding cumulative difference ;

3. Part of the source code

clc;
clear;
close all;
warning off;
addpath 'func\'
RandStream.setDefaultStream(RandStream('mt19937ar','seed',1));
mpc   = case118;
% Initialization of the number of nodes 
BUS                            = mpc.bus;
GEN                            = mpc.gen;
BRANCH                         = mpc.branch;   
[r,c]                          = size(mpc.bus);   %r Is the number of nodes   
Bus_Num                        = r;
[r,c]                          = size(mpc.branch);%r Is the number of branches 
F_Num                          = r;
% step 1： Display network topology 
[Connect,Cmatrix] = func_topology(BRANCH,BUS(end,1),0);
% step 2： Connectivity analysis , The whole network is divided into different regions by using the connectivity analysis algorithm in graph theory 
[S,Q]             = func_Adjacent_matrix(Cmatrix);
% step 3： Calculate the admittance matrix of each different region 
Ak                = func_Admittance_matrix_different_area(BUS,BRANCH,S,Q); 
% step 4： Select a pair of generation load nodes in the same area , And inject active power , Then calculate the power flow , And ensure that all generation load stages are selected ;
Fo                = func_Lb_flow(Ak,BUS,GEN,Bus_Num,Connect,S,Q);
% step 5： Calculate the electrical dielectric number of the line 
disp(' Electrical dielectric number of the line ：');
func_Line_JS(mpc,Fo,BRANCH,BUS,GEN,S,Bus_Num);
title(' Electrical dielectric number of the line ');
% step 6： Calculate the electrical dielectric number of nodes 
disp(' Node electrical dielectric number ：');
func_Node_JS(mpc,Fo,BRANCH,BUS,GEN,S,Bus_Num);
title(' Node electrical dielectric number ');
% step 7： Calculate the degree of the node 
disp(' The degree of the node ：');
func_Node_degree(BUS,BRANCH);

function Ak = func_Admittance_matrix(bus,line);

[nb,mb] = size(bus);
[nl,ml] = size(line);
% Assign an initial value to the admittance matrix 0 
Ak      = zeros(nl,nb);         

for k=1:nl
    I  = line(k,1);                     
    J  = line(k,2);
    Zt = line(k,3)+j*line(k,4);
    Yt = 1/Zt;
    Ym = line(k,5)+j*line(k,10);
    K  = line(k,9);
    
    % Common lines 
    if (K==0)  & (J~=0)
       Ak(I,I) = Ak(I,I) + Yt + Ym;
       Ak(J,J) = Ak(J,J) + Yt + Ym;
       Ak(I,J) = Ak(I,J) - Yt;
       Ak(J,I) = Ak(I,J);
    end
    
    % To ground branch 
    if (K==0)&(J==0)               
       Ak(I,I) = Ak(I,I) + Ym;
    end
    
    % Transformer line 
    if K > 0                        
       Ak(I,I) = Ak(I,I) + Yt + Ym;
       Ak(J,J) = Ak(J,J) + Yt / K / K;
       Ak(I,J) = Ak(I,J) - Yt / K;
       Ak(J,I) = Ak(I,J);
    end
    
    % Transformer line 
    if K < 0                      
       Ak(I,I) = Ak(I,I) + Yt + Ym;
       Ak(J,J) = Ak(J,J) + K*K*Yt;
       Ak(I,J) = Ak(I,J) + K*Yt;
       Ak(J,I) = Ak(I,J);
    end
end

a = [nb+1:nl];
T = length([nb+1:nl]);
for ii = 1:T
    Ak(nb+ii,:) = Ak(line(a(ii),1),:);
end

[rr,cc] = size(Ak);

for ii = 1:rr
    for jj = 1:cc
        if abs(Ak(ii,jj)) > 100000
           Ak(ii,jj) = 0;
        end
    end
end

4. Simulation conclusion

       here , The topology of the system is as follows ：

Finally, the simulation results of the node degree, node intermediate number and edge intermediate number calculated by us are as follows ：

  Line dielectric ：

  The heterogeneity value is ：0.739.

Node intermediate number ：

The heterogeneity value is ：0.7796

Degrees ：

         Here is a brief introduction to HVDC Explanation , According to the description in our doctoral thesis ：

        HVDC Model , Mainly in simulation , We need to choose a starting point in the original system m And the end n, And then, respectively m and n Injection power pacr and paci. And then do the following calculation .

Line dielectric ：

 

  The heterogeneity value is ：0.7133.

Node intermediate number ：

  The heterogeneity value is ：0.7797

Degrees ：

 

       TCSC The main difference , Is to select two buses l and p, And then inject Pip and Ppl power , among , stay l and m Between , Nodes need to be added P, Then participate in the following calculation .

Line dielectric ：

  The heterogeneity value is ：0. 7390.

Node intermediate number ：

  The heterogeneity value is ：0. 7796

Degrees ：

 

      UPFC The main difference , Is to select two buses l and p, And then inject Pip and Ppl power , He and TCSC The biggest difference is , stay l and m Between , There is no need to add nodes P, Then participate in the following calculation , Other calculations are similar .

Line dielectric ：

 

The heterogeneity value is ：0.7390

Node intermediate number ：

  The heterogeneity value is ：0.7796

Degrees ：

 A02-22