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function [Aeq_grid,beq_grid]=LinearEqualityConstraintsForBFS_SOCP_powerbalance(Line,Kday,N_batt,Sinj_bus,BusOfBattery)
% Note: the root bus need to be defined as 1
LD=zeros(size(Line,1),5);
LD(:,1)=1:size(Line,1);
LD(:,2)=Line(:,1);
LD(:,3)=Line(:,2);
LD(:,4)=Line(:,3);
LD(:,5)=Line(:,4);
Nbranch = size(LD,1);
Nbus = max(max(LD(:,2:3)));
% index of the decision variable, which is the column index of Aeq
idx_P = 1:Nbranch;
idx_l = Nbranch+1:2*Nbranch;
idx_v = 2*Nbranch+1:3*Nbranch;
Aeq = zeros(2*Nbranch, 3*Nbranch);
beq = zeros(2*Nbranch,1);
offset = 2*Kday*N_batt + 2*Kday;
totalVars=3*Nbranch;
Aeq_grid=[];
beq_grid=[];
for step=1:Kday
for e = 1:Nbranch
INbus = LD(e,2);
OUTbus = LD(e,3);
r_e = LD(e,4);
% --- row number
row_pow = 2*e-1; % power balance equation
row_vlt = 2*e; % voltage equation
% ----------（1）power balance equation----------
Aeq(row_pow, idx_P(e)) = 1; % branch power at the current branch
% downstream branch start at OUTbus
child_branch = find(LD(:,2)==OUTbus);
for k = child_branch(:)'
Aeq(row_pow, idx_P(k)) = -1;
end
Aeq(row_pow, idx_l(e)) = -r_e;
% if there is node injection power at the right side (ejection side),
% and them here with "-".
beq(row_pow) = -real(Sinj_bus(OUTbus,step)); % node injection power
% ----------（2）voltage drop equation-----------
% save all downstream voltage 2~Nbus at the last Nbranch colcumn
Aeq(row_vlt, idx_v(OUTbus-1)) = 1;
if INbus==1
% root voltage is given at 1pu, and move into the right side
% coefficient vector
beq(row_vlt) = 1;
else
Aeq(row_vlt, idx_v(INbus-1)) = -1;
end
Aeq(row_vlt, idx_l(e)) = -r_e^2;
Aeq(row_vlt, idx_P(e)) = 2*r_e;
end
Aeq_extd = zeros(size(Aeq,1), offset+totalVars*Kday);
Aeq_extd(:,offset+1+(step-1)*totalVars:offset+step*totalVars)=Aeq;
Nbatt = length(BusOfBattery);
for bat_idx = 1:Nbatt
ii = BusOfBattery(bat_idx); % battery node number
base = 2*Kday*(bat_idx-1); % start location of the battery variable sequence
col_Pdis = base + step;
col_Pch = base + Kday + step;
branchNum = find(Line(:,2)==ii,1); % battery branch (battery node is the downstream node, branch number is the row number of that branch in the Line matrix)
Aeq_extd(2*branchNum-1, col_Pdis) = 1;
Aeq_extd(2*branchNum-1, col_Pch) = -1;
end
Aeq_grid=[Aeq_grid;Aeq_extd];
beq_grid=[beq_grid;beq];
end
end |