% data for power flow problem
n = 12; % total number of nodes
m = 18; % number of edges (transmission lines)
k = 4; % number of generators
rand('state',0);
Pmax = 1+4*rand(m,1); % transmission line capacities
Gmax = [3; 2; 4; 7];  % maximum generator power
c    = [4; 8; 5; 3];  % supply generator costs
d    = 1+1.5*rand(n-k,1); % network power demands
% graph incidence matrix
A = [ -1 -1  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 ;
       0  0 -1 -1  0  0  0  0  0  0  0  0  0  0  0  0  0  0 ;
       0  0  0  0  0  0  0  0  0 -1 -1  0  0  0  0  0  0 -1 ;
       0  0  0  0  0  0 -1  0  0  0  0  0  0  0 -1  0 -1  0 ;
       1  0  0  0  1 -1  0  0  0  0  0  0  0  0  0  0  0  0 ;
       0  1  1  0 -1  0  1 -1  0  0  0  0  0  0  0  0  0  0 ;
       0  0  0  1  0  0  0  0 -1  1  0  0  0  0  0  0  0  0 ;
       0  0  0  0  0  0  0  1  1  0  0  0 -1  0  1  0  0  1 ;
       0  0  0  0  0  0  0  0  0  0  1 -1  0  0  0  0  0  0 ;
       0  0  0  0  0  0  0  0  0  0  0  1  1 -1  0  0  0  0 ;
       0  0  0  0  0  0  0  0  0  0  0  0  0  1  0  1  0  0 ;
       0  0  0  0  0  1  0  0  0  0  0  0  0  0  0 -1  1  0 ];

% the code below is not data for the problem
% it is used only to generate the network graph

% x-y coordinates
XY = [ ... % node x-y coordinates
 1.5 5.2;   % node 1
 4.9 5;     % node 2
 6.9 3.5;   % node 3
 1.9 3.5;   % node 4
 0.2 4.4;   % node 5
 3.2 4.8;   % node 6
 5.9 4.5;   % node 7
 3.9 3.6;   % node 8
 5.9 2.5;   % node 9
 3.9 3;     % node 10
 1.4 2.5;   % node 11
 0 3];      % node 12

% node adjacency matrix
Ad = -A*A';
Ad = Ad - diag(diag(Ad));

epsx = 0.05; epsy = 0.15; % text placing offset 

figure; 
% connect edges
gplot(Ad,XY,'-k'); hold on;

% label generator nodes
for j = 1:k
    plot(XY(j,1),XY(j,2),'rs',...
        'MarkerFaceColor','r',...
        'MarkerSize',12);
    text(XY(j,1)-eps,XY(j,2)+epsy,int2str(j),'FontSize',10);      
end

% label regular nodes 
for j = k+1:n
    plot(XY(j,1),XY(j,2),'.k',...
    'MarkerSize',15);
end
axis off; hold off;
% print('-depsc','pwr_net.eps');