Regarding optimization in MATLAB

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Ayesha
Ayesha on 3 Dec 2024 at 14:45
Commented: Torsten about 8 hours ago
Ran in:
Hi, I am student and using a linearized volt/var algorithm for maintaining grid stability and integrating ESS with PV in linearized model. I am only facing an issue in equation balance and I need to introduce a slack variable to manage export and import power to the grid. Please will anyone assist me regarding the MATLAB code, why there is ned of slack variables?
close all
clc
%input data from excel 13 bus system
line_data = xlsread('data.xlsx', 'Sheet4', 'A2:F13');
bus_data = xlsread('data.xlsx', 'Sheet2', 'A2:C14');
Pd=bus_data(:,2);
Qd=bus_data(:,3);
baseMVA = 1.5; % Using 1.5 MVA
%Pd=xlsread('C:\Users\user\Desktop\13_bus_Updated\data.xlsx', 'Sheet5', 'B2:E14')
%Qd=xlsread('C:\Users\user\Desktop\13_bus_Updated\data.xlsx', 'Sheet5', 'F2:I14')
% Branch data
fb = line_data(:,1); % From bus number...
tb = line_data(:,2); % To bus number...
r = line_data(:,3); % resistance pu...
x = line_data(:,4) ; % Reactance, X pu...
Bline = (line_data(:,5));%susceptance
Line_Rating=line_data(:,6)/baseMVA; % maximum line rating in MVA
h=4;
% Voltage data for buses
bv = xlsread('data.xlsx', 'Sheet3', 'A2:B14');
bv_4= repmat(bv(:, 2), 1, h);% for 24 hours
% system parameters
nbus = max(max(fb),max(tb)); % no. of buses...
nbranch = length(fb); % no. of branches..
slack = 1; % slack choice
VS = 1; % default value for slack voltage in pu
h = 4; % Number of hours (time steps)
baseMVA = 1.5; % Using 1.5 MVA
% lines and transformers selection
lines = [];
trafos = [];
% Loop over each branch
for ii = 1:nbranch
% Check if the buses connected by this branch have the same voltage
if bv(fb(ii), 2) == bv(tb(ii), 2) % Compare the voltage at the 'from' and 'to' buses
lines = vertcat(lines, ii); % If voltages are the same, it's a line
else
trafos = vertcat(trafos, ii); % If voltages differ, it's a transformer
end
end
%PV data
pv_max_gen = [0; 0; 0; 0.1264/baseMVA; 0.6232/baseMVA; 0.68268/baseMVA; 0; 0; 0.4296/baseMVA; 0.2610/baseMVA; 0.1432/baseMVA; 0; 0]; % Maximum PV generation at Buses in MW
P_import_max = [inf; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0];
P_Export_Max = [inf; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0];
% BESS Parameters
SOCmax = [0; 0; 0; 0; 0; 0; 0; 4.98/baseMVA; 0; 0; 0; 0; 0]; % Maximum SOC in MWh
SOC0 = 0.2 * SOCmax; % Initial SOC (20% of SOCmax)
charge_eff = 0.95; % Charging efficiency
discharge_eff = 0.9; % Discharging efficiency
P_ch_max = 0.2 * SOCmax; % 20% of SOCmax
P_dis_max = 0.2 * SOCmax; % 20% of SOCmax
Pb_AC_Array=max(P_ch_max,P_dis_max);
%battery inverter
% Define Qb_max as the maximum of P_ch_max and P_dis_max for each bus
Qb_max = max(P_ch_max(:), P_dis_max(:));
% Calculate linearized apparent power for each bus
Apparent_Power = [(P_ch_max(:)) + (Qb_max)];
Qb_min=-Qb_max;
% Expand parameters for each time step
Array_pv_max_gen = repmat(pv_max_gen, 1, h);
Array_P_Export_Max = repmat(P_Export_Max, 1, h);
Array_P_import_max = repmat(P_import_max, 1, h);
Array_Line_Rating = repmat(Line_Rating, 1, h);
Array_P_ch_max = repmat(P_ch_max, 1, h);
Array_P_dis_max = repmat(P_dis_max, 1, h);
Array_SOCmax = repmat(SOCmax, 1, h);
Array_Qb_max = repmat(Qb_max, 1, h);
S_max=repmat(Apparent_Power, 1, h);
Array_Qb_min = repmat(Qb_min, 1, h);
Array_Pd = repmat(Pd, 1, h); % Replicate active power demand for all hours
Array_Qd = repmat(Qd, 1, h); % Replicate reactive power demand for all hours
Array_Pb_AC = repmat(Pb_AC_Array, 1, h);
% Cost coefficients
cost_import_grid= 60; % Cost of importing from the grid per MW
cost_export_grid= 10; % Compensation for exporting to the grid per MW
LC_COST = 500;
QLC_COST=600;
PV_Curtailed_Cost = 50;
inverter_efficiency=0.95;
% Number of buses and branches
lines = [fb, tb];
%Create the branch matrix for load flow function
branch = [fb, tb, r, x, Bline];
% Create the bus matrix with time dimension (bus number, active load (Pd), reactive load (Qd))
bus = zeros(nbus, 3, h); % Initialize bus matrix with time dimension
for t = 1:h
bus(:, 1, t) = (1:nbus)'; % Bus numbers (remains the same for all time steps)
bus(:, 2, t) = Array_Pd(:, t); % Active power demand (Pd) for each hour
bus(:, 3, t) = Array_Qd(:, t); % Reactive power demand (Qd) for each hour
end
% AC linear model: Compute A,B,C matrices
[Model] = Linear_Load_Flow_Matrixx(branch, bus, baseMVA, VS, slack);
Ybus Matrix at t = 1 1.0e+03 * Columns 1 through 9 0.0000 - 0.0088i 0.0000 + 0.0028i 0.0000 + 0.0060i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0028i 0.0000 - 0.0028i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0060i 0.0000 + 0.0000i 0.0251 - 0.0069i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i -0.0251 + 0.0018i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0050 - 0.0002i 0.0000 + 0.0000i 0.0000 + 0.0000i -0.0050 + 0.0004i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0016 - 0.0000i 0.0000 + 0.0000i -0.0016 + 0.0001i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0006 - 0.0000i -0.0006 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i -0.0251 + 0.0018i -0.0050 + 0.0004i -0.0016 + 0.0001i -0.0006 + 0.0000i 0.0329 - 0.0011i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0013 - 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0152 - 0.0070i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i -0.0006 + 0.0000i -0.0013 + 0.0000i -0.0152 + 0.0140i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i Columns 10 through 13 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i -0.0006 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i -0.0013 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i -0.0152 + 0.0140i 0.0000 + 0.0000i 0.3171 - 0.0460i 0.0000 + 0.0000i -0.3171 + 0.0953i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0902 - 0.0422i -0.0902 + 0.0844i 0.0000 + 0.0000i -0.3171 + 0.0953i -0.0902 + 0.0844i 2.1079 - 0.3764i -1.6835 + 0.5612i 0.0000 + 0.0000i 0.0000 + 0.0000i -1.6835 + 0.5612i 1.6835 - 0.2812i SP (Constant Power Loads) at t = 1 0.0000 + 0.0000i -0.0500 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i -1.2544 - 0.3659i Non-Slack Bus Indices: 2 3 4 5 6 7 8 9 10 11 12 13 YNS: 0.0000 + 2.7778i 0.0000 + 6.0241i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i YNN 1.0e+03 * Columns 1 through 9 0.0000 - 0.0028i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0251 - 0.0069i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i -0.0251 + 0.0018i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0050 - 0.0002i 0.0000 + 0.0000i 0.0000 + 0.0000i -0.0050 + 0.0004i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0016 - 0.0000i 0.0000 + 0.0000i -0.0016 + 0.0001i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0006 - 0.0000i -0.0006 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i -0.0251 + 0.0018i -0.0050 + 0.0004i -0.0016 + 0.0001i -0.0006 + 0.0000i 0.0329 - 0.0011i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0013 - 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0152 - 0.0070i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.3171 - 0.0460i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i -0.0006 + 0.0000i -0.0013 + 0.0000i -0.0152 + 0.0140i -0.3171 + 0.0953i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i Columns 10 through 12 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i -0.0006 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i -0.0013 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i -0.0152 + 0.0140i 0.0000 + 0.0000i 0.0000 + 0.0000i -0.3171 + 0.0953i 0.0000 + 0.0000i 0.0902 - 0.0422i -0.0902 + 0.0844i 0.0000 + 0.0000i -0.0902 + 0.0844i 2.1079 - 0.3764i -1.6835 + 0.5612i 0.0000 + 0.0000i -1.6835 + 0.5612i 1.6835 - 0.2812i Br Matrix at t = 1 -0.0500 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1.2544 Ybus Matrix at t = 2 1.0e+03 * Columns 1 through 9 0.0000 - 0.0088i 0.0000 + 0.0028i 0.0000 + 0.0060i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0028i 0.0000 - 0.0028i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0060i 0.0000 + 0.0000i 0.0251 - 0.0069i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i -0.0251 + 0.0018i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0050 - 0.0002i 0.0000 + 0.0000i 0.0000 + 0.0000i -0.0050 + 0.0004i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0016 - 0.0000i 0.0000 + 0.0000i -0.0016 + 0.0001i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0006 - 0.0000i -0.0006 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i -0.0251 + 0.0018i -0.0050 + 0.0004i -0.0016 + 0.0001i -0.0006 + 0.0000i 0.0329 - 0.0011i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0013 - 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0152 - 0.0070i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i -0.0006 + 0.0000i -0.0013 + 0.0000i -0.0152 + 0.0140i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i Columns 10 through 13 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i -0.0006 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i -0.0013 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i -0.0152 + 0.0140i 0.0000 + 0.0000i 0.3171 - 0.0460i 0.0000 + 0.0000i -0.3171 + 0.0953i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0902 - 0.0422i -0.0902 + 0.0844i 0.0000 + 0.0000i -0.3171 + 0.0953i -0.0902 + 0.0844i 2.1079 - 0.3764i -1.6835 + 0.5612i 0.0000 + 0.0000i 0.0000 + 0.0000i -1.6835 + 0.5612i 1.6835 - 0.2812i SP (Constant Power Loads) at t = 2 0.0000 + 0.0000i -0.0500 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i -1.2544 - 0.3659i Non-Slack Bus Indices: 2 3 4 5 6 7 8 9 10 11 12 13 YNS: 0.0000 + 2.7778i 0.0000 + 6.0241i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i YNN 1.0e+03 * Columns 1 through 9 0.0000 - 0.0028i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0251 - 0.0069i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i -0.0251 + 0.0018i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0050 - 0.0002i 0.0000 + 0.0000i 0.0000 + 0.0000i -0.0050 + 0.0004i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0016 - 0.0000i 0.0000 + 0.0000i -0.0016 + 0.0001i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0006 - 0.0000i -0.0006 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i -0.0251 + 0.0018i -0.0050 + 0.0004i -0.0016 + 0.0001i -0.0006 + 0.0000i 0.0329 - 0.0011i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0013 - 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0152 - 0.0070i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.3171 - 0.0460i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i -0.0006 + 0.0000i -0.0013 + 0.0000i -0.0152 + 0.0140i -0.3171 + 0.0953i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i Columns 10 through 12 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i -0.0006 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i -0.0013 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i -0.0152 + 0.0140i 0.0000 + 0.0000i 0.0000 + 0.0000i -0.3171 + 0.0953i 0.0000 + 0.0000i 0.0902 - 0.0422i -0.0902 + 0.0844i 0.0000 + 0.0000i -0.0902 + 0.0844i 2.1079 - 0.3764i -1.6835 + 0.5612i 0.0000 + 0.0000i -1.6835 + 0.5612i 1.6835 - 0.2812i Br Matrix at t = 2 -0.0500 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1.2544 Ybus Matrix at t = 3 1.0e+03 * Columns 1 through 9 0.0000 - 0.0088i 0.0000 + 0.0028i 0.0000 + 0.0060i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0028i 0.0000 - 0.0028i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0060i 0.0000 + 0.0000i 0.0251 - 0.0069i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i -0.0251 + 0.0018i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0050 - 0.0002i 0.0000 + 0.0000i 0.0000 + 0.0000i -0.0050 + 0.0004i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0016 - 0.0000i 0.0000 + 0.0000i -0.0016 + 0.0001i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0006 - 0.0000i -0.0006 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i -0.0251 + 0.0018i -0.0050 + 0.0004i -0.0016 + 0.0001i -0.0006 + 0.0000i 0.0329 - 0.0011i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0013 - 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0152 - 0.0070i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i -0.0006 + 0.0000i -0.0013 + 0.0000i -0.0152 + 0.0140i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i Columns 10 through 13 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i -0.0006 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i -0.0013 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i -0.0152 + 0.0140i 0.0000 + 0.0000i 0.3171 - 0.0460i 0.0000 + 0.0000i -0.3171 + 0.0953i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0902 - 0.0422i -0.0902 + 0.0844i 0.0000 + 0.0000i -0.3171 + 0.0953i -0.0902 + 0.0844i 2.1079 - 0.3764i -1.6835 + 0.5612i 0.0000 + 0.0000i 0.0000 + 0.0000i -1.6835 + 0.5612i 1.6835 - 0.2812i SP (Constant Power Loads) at t = 3 0.0000 + 0.0000i -0.0500 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i -1.2544 - 0.3659i Non-Slack Bus Indices: 2 3 4 5 6 7 8 9 10 11 12 13 YNS: 0.0000 + 2.7778i 0.0000 + 6.0241i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i YNN 1.0e+03 * Columns 1 through 9 0.0000 - 0.0028i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0251 - 0.0069i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i -0.0251 + 0.0018i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0050 - 0.0002i 0.0000 + 0.0000i 0.0000 + 0.0000i -0.0050 + 0.0004i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0016 - 0.0000i 0.0000 + 0.0000i -0.0016 + 0.0001i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0006 - 0.0000i -0.0006 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i -0.0251 + 0.0018i -0.0050 + 0.0004i -0.0016 + 0.0001i -0.0006 + 0.0000i 0.0329 - 0.0011i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0013 - 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0152 - 0.0070i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.3171 - 0.0460i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i -0.0006 + 0.0000i -0.0013 + 0.0000i -0.0152 + 0.0140i -0.3171 + 0.0953i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i Columns 10 through 12 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i -0.0006 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i -0.0013 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i -0.0152 + 0.0140i 0.0000 + 0.0000i 0.0000 + 0.0000i -0.3171 + 0.0953i 0.0000 + 0.0000i 0.0902 - 0.0422i -0.0902 + 0.0844i 0.0000 + 0.0000i -0.0902 + 0.0844i 2.1079 - 0.3764i -1.6835 + 0.5612i 0.0000 + 0.0000i -1.6835 + 0.5612i 1.6835 - 0.2812i Br Matrix at t = 3 -0.0500 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1.2544 Ybus Matrix at t = 4 1.0e+03 * Columns 1 through 9 0.0000 - 0.0088i 0.0000 + 0.0028i 0.0000 + 0.0060i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0028i 0.0000 - 0.0028i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0060i 0.0000 + 0.0000i 0.0251 - 0.0069i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i -0.0251 + 0.0018i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0050 - 0.0002i 0.0000 + 0.0000i 0.0000 + 0.0000i -0.0050 + 0.0004i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0016 - 0.0000i 0.0000 + 0.0000i -0.0016 + 0.0001i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0006 - 0.0000i -0.0006 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i -0.0251 + 0.0018i -0.0050 + 0.0004i -0.0016 + 0.0001i -0.0006 + 0.0000i 0.0329 - 0.0011i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0013 - 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0152 - 0.0070i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i -0.0006 + 0.0000i -0.0013 + 0.0000i -0.0152 + 0.0140i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i Columns 10 through 13 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i -0.0006 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i -0.0013 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i -0.0152 + 0.0140i 0.0000 + 0.0000i 0.3171 - 0.0460i 0.0000 + 0.0000i -0.3171 + 0.0953i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0902 - 0.0422i -0.0902 + 0.0844i 0.0000 + 0.0000i -0.3171 + 0.0953i -0.0902 + 0.0844i 2.1079 - 0.3764i -1.6835 + 0.5612i 0.0000 + 0.0000i 0.0000 + 0.0000i -1.6835 + 0.5612i 1.6835 - 0.2812i SP (Constant Power Loads) at t = 4 0.0000 + 0.0000i -0.0500 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i -1.2544 - 0.3659i Non-Slack Bus Indices: 2 3 4 5 6 7 8 9 10 11 12 13 YNS: 0.0000 + 2.7778i 0.0000 + 6.0241i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i YNN 1.0e+03 * Columns 1 through 9 0.0000 - 0.0028i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0251 - 0.0069i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i -0.0251 + 0.0018i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0050 - 0.0002i 0.0000 + 0.0000i 0.0000 + 0.0000i -0.0050 + 0.0004i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0016 - 0.0000i 0.0000 + 0.0000i -0.0016 + 0.0001i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0006 - 0.0000i -0.0006 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i -0.0251 + 0.0018i -0.0050 + 0.0004i -0.0016 + 0.0001i -0.0006 + 0.0000i 0.0329 - 0.0011i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0013 - 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0152 - 0.0070i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.3171 - 0.0460i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i -0.0006 + 0.0000i -0.0013 + 0.0000i -0.0152 + 0.0140i -0.3171 + 0.0953i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i Columns 10 through 12 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i -0.0006 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i -0.0013 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i -0.0152 + 0.0140i 0.0000 + 0.0000i 0.0000 + 0.0000i -0.3171 + 0.0953i 0.0000 + 0.0000i 0.0902 - 0.0422i -0.0902 + 0.0844i 0.0000 + 0.0000i -0.0902 + 0.0844i 2.1079 - 0.3764i -1.6835 + 0.5612i 0.0000 + 0.0000i -1.6835 + 0.5612i 1.6835 - 0.2812i Br Matrix at t = 4 -0.0500 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1.2544
% Matrices
for t = 1:h
% Compute the linear model for each time step using your Model matrices
Model.MM = [(Model.Br(:,:,t) + Model.Cr(:,:)), (Model.Bi(:,:,t) - Model.Ci(:,:));
(Model.Bi(:,:,t) + Model.Ci(:,:)), (-Model.Br(:,:,t) + Model.Cr(:,:))];
% Calculate real and imaginary parts of voltages (VRI)
VRI = inv(Model.MM) * [-(Model.Ar(:,t)); -(Model.Ai(:,t))]; % Inversion of matrix to solve for voltages
Vs(:,t) = VRI(1:end/2) + 1j * VRI(end/2+1:end); % voltages still without slack
% Now calculate the absolute values of the voltages (magnitude) for all buses
Vs_abs = abs([Vs(1:slack-1,t); VS*ones(1,1); Vs(slack:end,t)]); % Adding the slack voltage in the results
% Store the results for time t
Voltage(:,t) = Vs_abs; % Store voltage magnitudes for comparison or output
end
% Output the final voltage magnitudes for all buses over all time steps
disp('Voltage Magnitudes over 1 hour:')
Voltage Magnitudes over 1 hour:
disp(Voltage);
1.0000 1.0000 1.0000 1.0000 0.9998 0.9998 0.9998 0.9998 1.5328 1.5328 1.5328 1.5328 1.5012 1.5012 1.5012 1.5012 1.4997 1.4997 1.4997 1.4997 1.4986 1.4986 1.4986 1.4986 1.4984 1.4984 1.4984 1.4984 0.0023 0.0023 0.0023 0.0023 0.0029 0.0029 0.0029 0.0029 0.0024 0.0024 0.0024 0.0024 0.0029 0.0029 0.0029 0.0029 0.0023 0.0023 0.0023 0.0023 0.0022 0.0022 0.0022 0.0022
% Create optimization variables
P_PV = optimvar('P_PV', nbus, h, 'LowerBound', 0, 'UpperBound', Array_pv_max_gen); % Power from PV at Bus 2
P_PV_AC = optimvar('P_PV_AC', nbus, h, 'LowerBound', 0, 'UpperBound', Array_pv_max_gen * inverter_efficiency);
Pb_AC = optimvar('Pb_AC', nbus, h, 'LowerBound', -Array_Pb_AC, 'UpperBound', Array_Pb_AC );
P_import = optimvar('P_import', nbus, h, 'LowerBound', 0, 'UpperBound', Array_P_import_max); % Power imported from the grid (Bus 1)
P_export = optimvar('P_export', nbus, h, 'LowerBound', 0, 'UpperBound', Array_P_Export_Max); % Power exported to the grid (Bus 1)
LC = optimvar('LC', nbus, h, 'LowerBound', 0, 'UpperBound', Array_Pd./baseMVA); % Load curtailment
QLC = optimvar('QLC', nbus, h, 'LowerBound', 0, 'UpperBound', Array_Qd./baseMVA); % Load curtailment
PV_Curtailed = optimvar('PV_Curtailed', nbus, h, 'LowerBound', 0, 'UpperBound', Array_pv_max_gen); % PV curtailment
Power_Flow_ft = optimvar('Power_Flow_ft', nbranch, h); % Real power flow between buses
P_ch = optimvar('P_ch', nbus, h, 'LowerBound', 0, 'UpperBound', Array_P_ch_max); % Charging power at Bus 3
P_dis = optimvar('P_dis', nbus, h, 'LowerBound', 0, 'UpperBound', Array_P_dis_max); % Discharging power at Bus 3
SOC = optimvar('SOC', nbus, h, 'LowerBound', 0.2 * Array_SOCmax, 'UpperBound', Array_SOCmax); % State of Charge
Qb = optimvar('Qb', nbus, h, 'LowerBound', Array_Qb_min, 'UpperBound', Array_Qb_max); % Reactive power injection at each bus
Qij = optimvar('Qij', nbranch, h); % Reactive power flow between buses
% Voltage variables for AC linear power flow
Vre = optimvar('Vre',nbus, h, 'LowerBound', 0.9, 'UpperBound', 1.1); % Real part of voltage
Vim = optimvar('Vim',nbus, h, 'LowerBound', -0.5, 'UpperBound', 0.5);
Ps=optimvar('Ps', nbus, h, 'LowerBound', -inf, 'UpperBound', inf);
Ps1=optimvar('Ps1', nbus, h, 'LowerBound', -inf, 'UpperBound', inf);
% Real and imaginary current variables for each branch and time step
Ire = optimvar('Ire', nbranch, h, 'LowerBound', -Array_Line_Rating, 'UpperBound', Array_Line_Rating); % Real current part
Iim = optimvar('Iim', nbranch, h, 'LowerBound', -Array_Line_Rating, 'UpperBound', Array_Line_Rating); % Imaginary current part
Pb_AC_plus = optimvar('Pb_plus', nbus, h, 'LowerBound', 0); % Positive part of Pb_AC
Pb_AC_minus = optimvar('Pb_minus', nbus, h, 'LowerBound', 0); % Negative part of Pb_AC
Qb_plus = optimvar('Qb_plus', nbus, h,'LowerBound', 0); % Positive part of Qb
Qb_minus = optimvar('Qb_minus', nbus, h, 'LowerBound', 0); % Negative part of Qb
% Create the optimization problem
linprob = optimproblem('ObjectiveSense', 'minimize');
% Objective function: Minimize cost
linprob.Objective = sum(sum(cost_import_grid * P_import - cost_export_grid * P_export+ LC .* LC_COST.*baseMVA+ QLC .* QLC_COST.*baseMVA + PV_Curtailed .* PV_Curtailed_Cost.*baseMVA));
% Real Power Balance Constraints for each bus and time step
for t = 1:h
for i = 1:nbus
outFlow = sum(Power_Flow_ft(lines(:, 1) == i, t));
inFlow = sum(Power_Flow_ft(lines(:, 2) == i, t));
linprob.Constraints.(sprintf('NodeFlow_Real_%d_%d', i, t)) = ...
P_PV_AC(i, t) + LC(i, t) + P_import(i, t) - P_export(i, t) - outFlow + inFlow + P_dis(i, t).*inverter_efficiency - P_ch(i, t)./inverter_efficiency == Array_Pd(i, t)./baseMVA;
end
end
% Reactive power balance constraint for Bus 3 (Battery bus)
for t = 1:h
for j = 1:nbus
inFlowQ1 = sum(Qij(lines(:, 2) == j, t)); % Incoming reactive power to Bus 3
outFlowQ1 = sum(Qij(lines(:, 1) == j, t)); % Outgoing reactive power from Bus 3
linprob.Constraints.(sprintf('NodeFlow_Reactive_3_%d', j,t)) = ...
Qb(j, t)+QLC(j, t) - Array_Qd(j, t)./baseMVA +inFlowQ1 - outFlowQ1== 0;
end
end
% Initial SOC constraint
linprob.Constraints.InitialSOC = SOC(:, 1) == SOC0;
% SOC update equation and limits for each hour
for t = 2:h
for i = 1:nbus
linprob.Constraints.(sprintf('SOC_update_%d_%d', i, t)) = ...
SOC(i, t) == SOC(i, t-1) + charge_eff * P_ch(i, t-1) - (1 / discharge_eff) * P_dis(i, t-1);
end
end
for U = 1:h
linprob.Constraints.(sprintf('Inverter_ActivePower_PV_%d', U)) =P_PV_AC(:, U) == P_PV(:, U) * inverter_efficiency;
% Active power relation for discharging and charging
linprob.Constraints.(sprintf('Inverter_ActivePower_battery_%d', U)) = Pb_AC(:, U) ==(-P_ch(:, U) / charge_eff)+ P_dis(:, U) * discharge_eff;
linprob.Constraints.absConstraint = Pb_AC_plus(:, U) + Pb_AC_minus(:, U) + Qb_plus(:, U) + Qb_minus(:, U) <=S_max(:, U) ;
linprob.Constraints.Pb_AC_decomposition = Pb_AC_plus(:, U) - Pb_AC_minus(:, U) == Pb_AC(:, U); % Define Pb
linprob.Constraints.Qb_decomposition = Qb_plus(:, U) - Qb_minus(:, U) == Qb(:, U); % Define Qb
end
% From A,B,C matrixes
for t = 1:h
for bus = 2:nbus % Apply constraints only for non-slack buses
nonslack_bus_idx = bus - 1; % Adjust index for non-slack buses
% Extract voltage components for the current time step `t`
Vre_bus_t = reshape(Vre(2:nbus, t), [1, nbus - 1]);
Vim_bus_t = reshape(Vim(2:nbus, t), [1, nbus - 1]);
% Active power balance (const1) for current time `t`
linprob.Constraints.(sprintf('const1_%d_%d', bus, t)) = ...
Model.Ar(nonslack_bus_idx, t) == ...
sum((-Model.Br(nonslack_bus_idx, :, t) - Model.Cr(nonslack_bus_idx, :)) .* Vre_bus_t, 2) + ...
sum((-Model.Bi(nonslack_bus_idx, :, t) + Model.Ci(nonslack_bus_idx, :)) .* Vim_bus_t, 2) + ...
(-P_ch(bus, t) + P_dis(bus, t))+Ps(bus,t);
% Reactive power balance (const2) for current time `t`
linprob.Constraints.(sprintf('const2_%d_%d', bus, t)) = ...
Model.Ai(nonslack_bus_idx, t) == ...
sum((-Model.Bi(nonslack_bus_idx, :, t) - Model.Ci(nonslack_bus_idx, :)) .* Vre_bus_t, 2) + ...
sum((+Model.Br(nonslack_bus_idx, :, t) - Model.Cr(nonslack_bus_idx, :)) .* Vim_bus_t, 2) - ...
Qb(i, t)+Ps1(bus,t);
end
end
% Line rating constraints
linprob.Constraints.cons1 = Power_Flow_ft <= Array_Line_Rating;
linprob.Constraints.cons2 = Power_Flow_ft >= -Array_Line_Rating;
linprob.Constraints.cons3 = Qij <= Array_Line_Rating;
linprob.Constraints.cons4 = Qij >= -Array_Line_Rating;
% PV curtailment constraint
linprob.Constraints.cons5 = PV_Curtailed == Array_pv_max_gen - P_PV;
% current constraints
% Loop through each time step and branch
for t = 1:h
for branchIdx = 1:nbranch
% Extract bus indices for each branch
bus_from = fb(branchIdx);
bus_to = tb(branchIdx);
% Ire constraint: Vre_h - Vre_k = R_b * Ire_b - X_b * Iim_b
linprob.Constraints.(sprintf('Ire_eq_%d_%d', branchIdx, t)) = ...
Vre(bus_from, t) - Vre(bus_to, t) == r(branchIdx) * Ire(branchIdx, t) ...
- x(branchIdx) * Iim(branchIdx, t);
% Iim constraint: Vim_h - Vim_k = X_b * Ire_b + R_b * Iim_b
linprob.Constraints.(sprintf('Iim_eq_%d_%d', branchIdx, t)) = ...
Vim(bus_from, t) - Vim(bus_to, t) == x(branchIdx) * Ire(branchIdx, t) ...
+ r(branchIdx) * Iim(branchIdx, t);
end
end
% Display and solve the optimization problem
show(linprob);
OptimizationProblem : Solve for: Iim, Ire, LC, PV_Curtailed, P_PV, P_PV_AC, P_ch, P_dis, P_export, P_import, Pb_AC, Pb_minus, Pb_plus, Power_Flow_ft, Ps, Ps1, QLC, Qb, Qb_minus, Qb_plus, Qij, SOC, Vim, Vre minimize : 60*P_import(1, 1) + 60*P_import(2, 1) + 60*P_import(3, 1) + 60*P_import(4, 1) + 60*P_import(5, 1) + 60*P_import(6, 1) + 60*P_import(7, 1) + 60*P_import(8, 1) + 60*P_import(9, 1) + 60*P_import(10, 1) + 60*P_import(11, 1) + 60*P_import(12, 1) + 60*P_import(13, 1) + 60*P_import(1, 2) + 60*P_import(2, 2) + 60*P_import(3, 2) + 60*P_import(4, 2) + 60*P_import(5, 2) + 60*P_import(6, 2) + 60*P_import(7, 2) + 60*P_import(8, 2) + 60*P_import(9, 2) + 60*P_import(10, 2) + 60*P_import(11, 2) + 60*P_import(12, 2) + 60*P_import(13, 2) + 60*P_import(1, 3) + 60*P_import(2, 3) + 60*P_import(3, 3) + 60*P_import(4, 3) + 60*P_import(5, 3) + 60*P_import(6, 3) + 60*P_import(7, 3) + 60*P_import(8, 3) + 60*P_import(9, 3) + 60*P_import(10, 3) + 60*P_import(11, 3) + 60*P_import(12, 3) + 60*P_import(13, 3) + 60*P_import(1, 4) + 60*P_import(2, 4) + 60*P_import(3, 4) + 60*P_import(4, 4) + 60*P_import(5, 4) + 60*P_import(6, 4) + 60*P_import(7, 4) + 60*P_import(8, 4) + 60*P_import(9, 4) + 60*P_import(10, 4) + 60*P_import(11, 4) + 60*P_import(12, 4) + 60*P_import(13, 4) - 10*P_export(1, 1) - 10*P_export(2, 1) - 10*P_export(3, 1) - 10*P_export(4, 1) - 10*P_export(5, 1) - 10*P_export(6, 1) - 10*P_export(7, 1) - 10*P_export(8, 1) - 10*P_export(9, 1) - 10*P_export(10, 1) - 10*P_export(11, 1) - 10*P_export(12, 1) - 10*P_export(13, 1) - 10*P_export(1, 2) - 10*P_export(2, 2) - 10*P_export(3, 2) - 10*P_export(4, 2) - 10*P_export(5, 2) - 10*P_export(6, 2) - 10*P_export(7, 2) - 10*P_export(8, 2) - 10*P_export(9, 2) - 10*P_export(10, 2) - 10*P_export(11, 2) - 10*P_export(12, 2) - 10*P_export(13, 2) - 10*P_export(1, 3) - 10*P_export(2, 3) - 10*P_export(3, 3) - 10*P_export(4, 3) - 10*P_export(5, 3) - 10*P_export(6, 3) - 10*P_export(7, 3) - 10*P_export(8, 3) - 10*P_export(9, 3) - 10*P_export(10, 3) - 10*P_export(11, 3) - 10*P_export(12, 3) - 10*P_export(13, 3) - 10*P_export(1, 4) - 10*P_export(2, 4) - 10*P_export(3, 4) - 10*P_export(4, 4) - 10*P_export(5, 4) - 10*P_export(6, 4) - 10*P_export(7, 4) - 10*P_export(8, 4) - 10*P_export(9, 4) - 10*P_export(10, 4) - 10*P_export(11, 4) - 10*P_export(12, 4) - 10*P_export(13, 4) + 750*LC(1, 1) + 750*LC(2, 1) + 750*LC(3, 1) + 750*LC(4, 1) + 750*LC(5, 1) + 750*LC(6, 1) + 750*LC(7, 1) + 750*LC(8, 1) + 750*LC(9, 1) + 750*LC(10, 1) + 750*LC(11, 1) + 750*LC(12, 1) + 750*LC(13, 1) + 750*LC(1, 2) + 750*LC(2, 2) + 750*LC(3, 2) + 750*LC(4, 2) + 750*LC(5, 2) + 750*LC(6, 2) + 750*LC(7, 2) + 750*LC(8, 2) + 750*LC(9, 2) + 750*LC(10, 2) + 750*LC(11, 2) + 750*LC(12, 2) + 750*LC(13, 2) + 750*LC(1, 3) + 750*LC(2, 3) + 750*LC(3, 3) + 750*LC(4, 3) + 750*LC(5, 3) + 750*LC(6, 3) + 750*LC(7, 3) + 750*LC(8, 3) + 750*LC(9, 3) + 750*LC(10, 3) + 750*LC(11, 3) + 750*LC(12, 3) + 750*LC(13, 3) + 750*LC(1, 4) + 750*LC(2, 4) + 750*LC(3, 4) + 750*LC(4, 4) + 750*LC(5, 4) + 750*LC(6, 4) + 750*LC(7, 4) + 750*LC(8, 4) + 750*LC(9, 4) + 750*LC(10, 4) + 750*LC(11, 4) + 750*LC(12, 4) + 750*LC(13, 4) + 900*QLC(1, 1) + 900*QLC(2, 1) + 900*QLC(3, 1) + 900*QLC(4, 1) + 900*QLC(5, 1) + 900*QLC(6, 1) + 900*QLC(7, 1) + 900*QLC(8, 1) + 900*QLC(9, 1) + 900*QLC(10, 1) + 900*QLC(11, 1) + 900*QLC(12, 1) + 900*QLC(13, 1) + 900*QLC(1, 2) + 900*QLC(2, 2) + 900*QLC(3, 2) + 900*QLC(4, 2) + 900*QLC(5, 2) + 900*QLC(6, 2) + 900*QLC(7, 2) + 900*QLC(8, 2) + 900*QLC(9, 2) + 900*QLC(10, 2) + 900*QLC(11, 2) + 900*QLC(12, 2) + 900*QLC(13, 2) + 900*QLC(1, 3) + 900*QLC(2, 3) + 900*QLC(3, 3) + 900*QLC(4, 3) + 900*QLC(5, 3) + 900*QLC(6, 3) + 900*QLC(7, 3) + 900*QLC(8, 3) + 900*QLC(9, 3) + 900*QLC(10, 3) + 900*QLC(11, 3) + 900*QLC(12, 3) + 900*QLC(13, 3) + 900*QLC(1, 4) + 900*QLC(2, 4) + 900*QLC(3, 4) + 900*QLC(4, 4) + 900*QLC(5, 4) + 900*QLC(6, 4) + 900*QLC(7, 4) + 900*QLC(8, 4) + 900*QLC(9, 4) + 900*QLC(10, 4) + 900*QLC(11, 4) + 900*QLC(12, 4) + 900*QLC(13, 4) + 75*PV_Curtailed(1, 1) + 75*PV_Curtailed(2, 1) + 75*PV_Curtailed(3, 1) + 75*PV_Curtailed(4, 1) + 75*PV_Curtailed(5, 1) + 75*PV_Curtailed(6, 1) + 75*PV_Curtailed(7, 1) + 75*PV_Curtailed(8, 1) + 75*PV_Curtailed(9, 1) + 75*PV_Curtailed(10, 1) + 75*PV_Curtailed(11, 1) + 75*PV_Curtailed(12, 1) + 75*PV_Curtailed(13, 1) + 75*PV_Curtailed(1, 2) + 75*PV_Curtailed(2, 2) + 75*PV_Curtailed(3, 2) + 75*PV_Curtailed(4, 2) + 75*PV_Curtailed(5, 2) + 75*PV_Curtailed(6, 2) + 75*PV_Curtailed(7, 2) + 75*PV_Curtailed(8, 2) + 75*PV_Curtailed(9, 2) + 75*PV_Curtailed(10, 2) + 75*PV_Curtailed(11, 2) + 75*PV_Curtailed(12, 2) + 75*PV_Curtailed(13, 2) + 75*PV_Curtailed(1, 3) + 75*PV_Curtailed(2, 3) + 75*PV_Curtailed(3, 3) + 75*PV_Curtailed(4, 3) + 75*PV_Curtailed(5, 3) + 75*PV_Curtailed(6, 3) + 75*PV_Curtailed(7, 3) + 75*PV_Curtailed(8, 3) + 75*PV_Curtailed(9, 3) + 75*PV_Curtailed(10, 3) + 75*PV_Curtailed(11, 3) + 75*PV_Curtailed(12, 3) + 75*PV_Curtailed(13, 3) + 75*PV_Curtailed(1, 4) + 75*PV_Curtailed(2, 4) + 75*PV_Curtailed(3, 4) + 75*PV_Curtailed(4, 4) + 75*PV_Curtailed(5, 4) + 75*PV_Curtailed(6, 4) + 75*PV_Curtailed(7, 4) + 75*PV_Curtailed(8, 4) + 75*PV_Curtailed(9, 4) + 75*PV_Curtailed(10, 4) + 75*PV_Curtailed(11, 4) + 75*PV_Curtailed(12, 4) + 75*PV_Curtailed(13, 4) subject to NodeFlow_Real_1_1: LC(1, 1) + P_PV_AC(1, 1) - P_export(1, 1) + P_import(1, 1) - Power_Flow_ft(1, 1) - Power_Flow_ft(2, 1) + 0.95*P_dis(1, 1) - 1.0526*P_ch(1, 1) == 0 subject to NodeFlow_Real_2_1: LC(2, 1) + P_PV_AC(2, 1) - P_export(2, 1) + P_import(2, 1) + Power_Flow_ft(1, 1) + 0.95*P_dis(2, 1) - 1.0526*P_ch(2, 1) == 0.05 subject to NodeFlow_Real_3_1: P_PV_AC(3, 1) + LC(3, 1) + P_import(3, 1) - P_export(3, 1) + Power_Flow_ft(2, 1) - Power_Flow_ft(3, 1) + 0.95*P_dis(3, 1) - 1.0526*P_ch(3, 1) == 0 subject to NodeFlow_Real_4_1: LC(4, 1) + P_PV_AC(4, 1) - P_export(4, 1) + P_import(4, 1) - Power_Flow_ft(4, 1) + 0.95*P_dis(4, 1) - 1.0526*P_ch(4, 1) == 0 subject to NodeFlow_Real_5_1: LC(5, 1) + P_PV_AC(5, 1) - P_export(5, 1) + P_import(5, 1) - Power_Flow_ft(5, 1) + 0.95*P_dis(5, 1) - 1.0526*P_ch(5, 1) == 0 subject to NodeFlow_Real_6_1: LC(6, 1) + P_PV_AC(6, 1) - P_export(6, 1) + P_import(6, 1) - Power_Flow_ft(6, 1) + 0.95*P_dis(6, 1) - 1.0526*P_ch(6, 1) == 0 subject to NodeFlow_Real_7_1: P_PV_AC(7, 1) + LC(7, 1) + P_import(7, 1) - P_export(7, 1) + Power_Flow_ft(3, 1) + Power_Flow_ft(4, 1) + Power_Flow_ft(5, 1) + Power_Flow_ft(6, 1) - Power_Flow_ft(7, 1) + 0.95*P_dis(7, 1) - 1.0526*P_ch(7, 1) == 0 subject to NodeFlow_Real_8_1: LC(8, 1) + P_PV_AC(8, 1) - P_export(8, 1) + P_import(8, 1) - Power_Flow_ft(8, 1) + 0.95*P_dis(8, 1) - 1.0526*P_ch(8, 1) == 0 subject to NodeFlow_Real_9_1: LC(9, 1) + P_PV_AC(9, 1) - P_export(9, 1) + P_import(9, 1) - Power_Flow_ft(9, 1) + 0.95*P_dis(9, 1) - 1.0526*P_ch(9, 1) == 0 subject to NodeFlow_Real_10_1: LC(10, 1) + P_PV_AC(10, 1) - P_export(10, 1) + P_import(10, 1) - Power_Flow_ft(10, 1) + 0.95*P_dis(10, 1) - 1.0526*P_ch(10, 1) == 0 subject to NodeFlow_Real_11_1: LC(11, 1) + P_PV_AC(11, 1) - P_export(11, 1) + P_import(11, 1) - Power_Flow_ft(11, 1) + 0.95*P_dis(11, 1) - 1.0526*P_ch(11, 1) == 0 subject to NodeFlow_Real_12_1: P_PV_AC(12, 1) + LC(12, 1) + P_import(12, 1) - P_export(12, 1) + Power_Flow_ft(7, 1) + Power_Flow_ft(8, 1) + Power_Flow_ft(9, 1) + Power_Flow_ft(10, 1) + Power_Flow_ft(11, 1) - Power_Flow_ft(12, 1) + 0.95*P_dis(12, 1) - 1.0526*P_ch(12, 1) == 0 subject to NodeFlow_Real_13_1: LC(13, 1) + P_PV_AC(13, 1) - P_export(13, 1) + P_import(13, 1) + Power_Flow_ft(12, 1) + 0.95*P_dis(13, 1) - 1.0526*P_ch(13, 1) == 1.2544 subject to NodeFlow_Real_1_2: LC(1, 2) + P_PV_AC(1, 2) - P_export(1, 2) + P_import(1, 2) - Power_Flow_ft(1, 2) - Power_Flow_ft(2, 2) + 0.95*P_dis(1, 2) - 1.0526*P_ch(1, 2) == 0 subject to NodeFlow_Real_2_2: LC(2, 2) + P_PV_AC(2, 2) - P_export(2, 2) + P_import(2, 2) + Power_Flow_ft(1, 2) + 0.95*P_dis(2, 2) - 1.0526*P_ch(2, 2) == 0.05 subject to NodeFlow_Real_3_2: P_PV_AC(3, 2) + LC(3, 2) + P_import(3, 2) - P_export(3, 2) + Power_Flow_ft(2, 2) - Power_Flow_ft(3, 2) + 0.95*P_dis(3, 2) - 1.0526*P_ch(3, 2) == 0 subject to NodeFlow_Real_4_2: LC(4, 2) + P_PV_AC(4, 2) - P_export(4, 2) + P_import(4, 2) - Power_Flow_ft(4, 2) + 0.95*P_dis(4, 2) - 1.0526*P_ch(4, 2) == 0 subject to NodeFlow_Real_5_2: LC(5, 2) + P_PV_AC(5, 2) - P_export(5, 2) + P_import(5, 2) - Power_Flow_ft(5, 2) + 0.95*P_dis(5, 2) - 1.0526*P_ch(5, 2) == 0 subject to NodeFlow_Real_6_2: LC(6, 2) + P_PV_AC(6, 2) - P_export(6, 2) + P_import(6, 2) - Power_Flow_ft(6, 2) + 0.95*P_dis(6, 2) - 1.0526*P_ch(6, 2) == 0 subject to NodeFlow_Real_7_2: P_PV_AC(7, 2) + LC(7, 2) + P_import(7, 2) - P_export(7, 2) + Power_Flow_ft(3, 2) + Power_Flow_ft(4, 2) + Power_Flow_ft(5, 2) + Power_Flow_ft(6, 2) - Power_Flow_ft(7, 2) + 0.95*P_dis(7, 2) - 1.0526*P_ch(7, 2) == 0 subject to NodeFlow_Real_8_2: LC(8, 2) + P_PV_AC(8, 2) - P_export(8, 2) + P_import(8, 2) - Power_Flow_ft(8, 2) + 0.95*P_dis(8, 2) - 1.0526*P_ch(8, 2) == 0 subject to NodeFlow_Real_9_2: LC(9, 2) + P_PV_AC(9, 2) - P_export(9, 2) + P_import(9, 2) - Power_Flow_ft(9, 2) + 0.95*P_dis(9, 2) - 1.0526*P_ch(9, 2) == 0 subject to NodeFlow_Real_10_2: LC(10, 2) + P_PV_AC(10, 2) - P_export(10, 2) + P_import(10, 2) - Power_Flow_ft(10, 2) + 0.95*P_dis(10, 2) - 1.0526*P_ch(10, 2) == 0 subject to NodeFlow_Real_11_2: LC(11, 2) + P_PV_AC(11, 2) - P_export(11, 2) + P_import(11, 2) - Power_Flow_ft(11, 2) + 0.95*P_dis(11, 2) - 1.0526*P_ch(11, 2) == 0 subject to NodeFlow_Real_12_2: P_PV_AC(12, 2) + LC(12, 2) + P_import(12, 2) - P_export(12, 2) + Power_Flow_ft(7, 2) + Power_Flow_ft(8, 2) + Power_Flow_ft(9, 2) + Power_Flow_ft(10, 2) + Power_Flow_ft(11, 2) - Power_Flow_ft(12, 2) + 0.95*P_dis(12, 2) - 1.0526*P_ch(12, 2) == 0 subject to NodeFlow_Real_13_2: LC(13, 2) + P_PV_AC(13, 2) - P_export(13, 2) + P_import(13, 2) + Power_Flow_ft(12, 2) + 0.95*P_dis(13, 2) - 1.0526*P_ch(13, 2) == 1.2544 subject to NodeFlow_Real_1_3: LC(1, 3) + P_PV_AC(1, 3) - P_export(1, 3) + P_import(1, 3) - Power_Flow_ft(1, 3) - Power_Flow_ft(2, 3) + 0.95*P_dis(1, 3) - 1.0526*P_ch(1, 3) == 0 subject to NodeFlow_Real_2_3: LC(2, 3) + P_PV_AC(2, 3) - P_export(2, 3) + P_import(2, 3) + Power_Flow_ft(1, 3) + 0.95*P_dis(2, 3) - 1.0526*P_ch(2, 3) == 0.05 subject to NodeFlow_Real_3_3: P_PV_AC(3, 3) + LC(3, 3) + P_import(3, 3) - P_export(3, 3) + Power_Flow_ft(2, 3) - Power_Flow_ft(3, 3) + 0.95*P_dis(3, 3) - 1.0526*P_ch(3, 3) == 0 subject to NodeFlow_Real_4_3: LC(4, 3) + P_PV_AC(4, 3) - P_export(4, 3) + P_import(4, 3) - Power_Flow_ft(4, 3) + 0.95*P_dis(4, 3) - 1.0526*P_ch(4, 3) == 0 subject to NodeFlow_Real_5_3: LC(5, 3) + P_PV_AC(5, 3) - P_export(5, 3) + P_import(5, 3) - Power_Flow_ft(5, 3) + 0.95*P_dis(5, 3) - 1.0526*P_ch(5, 3) == 0 subject to NodeFlow_Real_6_3: LC(6, 3) + P_PV_AC(6, 3) - P_export(6, 3) + P_import(6, 3) - Power_Flow_ft(6, 3) + 0.95*P_dis(6, 3) - 1.0526*P_ch(6, 3) == 0 subject to NodeFlow_Real_7_3: P_PV_AC(7, 3) + LC(7, 3) + P_import(7, 3) - P_export(7, 3) + Power_Flow_ft(3, 3) + Power_Flow_ft(4, 3) + Power_Flow_ft(5, 3) + Power_Flow_ft(6, 3) - Power_Flow_ft(7, 3) + 0.95*P_dis(7, 3) - 1.0526*P_ch(7, 3) == 0 subject to NodeFlow_Real_8_3: LC(8, 3) + P_PV_AC(8, 3) - P_export(8, 3) + P_import(8, 3) - Power_Flow_ft(8, 3) + 0.95*P_dis(8, 3) - 1.0526*P_ch(8, 3) == 0 subject to NodeFlow_Real_9_3: LC(9, 3) + P_PV_AC(9, 3) - P_export(9, 3) + P_import(9, 3) - Power_Flow_ft(9, 3) + 0.95*P_dis(9, 3) - 1.0526*P_ch(9, 3) == 0 subject to NodeFlow_Real_10_3: LC(10, 3) + P_PV_AC(10, 3) - P_export(10, 3) + P_import(10, 3) - Power_Flow_ft(10, 3) + 0.95*P_dis(10, 3) - 1.0526*P_ch(10, 3) == 0 subject to NodeFlow_Real_11_3: LC(11, 3) + P_PV_AC(11, 3) - P_export(11, 3) + P_import(11, 3) - Power_Flow_ft(11, 3) + 0.95*P_dis(11, 3) - 1.0526*P_ch(11, 3) == 0 subject to NodeFlow_Real_12_3: P_PV_AC(12, 3) + LC(12, 3) + P_import(12, 3) - P_export(12, 3) + Power_Flow_ft(7, 3) + Power_Flow_ft(8, 3) + Power_Flow_ft(9, 3) + Power_Flow_ft(10, 3) + Power_Flow_ft(11, 3) - Power_Flow_ft(12, 3) + 0.95*P_dis(12, 3) - 1.0526*P_ch(12, 3) == 0 subject to NodeFlow_Real_13_3: LC(13, 3) + P_PV_AC(13, 3) - P_export(13, 3) + P_import(13, 3) + Power_Flow_ft(12, 3) + 0.95*P_dis(13, 3) - 1.0526*P_ch(13, 3) == 1.2544 subject to NodeFlow_Real_1_4: LC(1, 4) + P_PV_AC(1, 4) - P_export(1, 4) + P_import(1, 4) - Power_Flow_ft(1, 4) - Power_Flow_ft(2, 4) + 0.95*P_dis(1, 4) - 1.0526*P_ch(1, 4) == 0 subject to NodeFlow_Real_2_4: LC(2, 4) + P_PV_AC(2, 4) - P_export(2, 4) + P_import(2, 4) + Power_Flow_ft(1, 4) + 0.95*P_dis(2, 4) - 1.0526*P_ch(2, 4) == 0.05 subject to NodeFlow_Real_3_4: P_PV_AC(3, 4) + LC(3, 4) + P_import(3, 4) - P_export(3, 4) + Power_Flow_ft(2, 4) - Power_Flow_ft(3, 4) + 0.95*P_dis(3, 4) - 1.0526*P_ch(3, 4) == 0 subject to NodeFlow_Real_4_4: LC(4, 4) + P_PV_AC(4, 4) - P_export(4, 4) + P_import(4, 4) - Power_Flow_ft(4, 4) + 0.95*P_dis(4, 4) - 1.0526*P_ch(4, 4) == 0 subject to NodeFlow_Real_5_4: LC(5, 4) + P_PV_AC(5, 4) - P_export(5, 4) + P_import(5, 4) - Power_Flow_ft(5, 4) + 0.95*P_dis(5, 4) - 1.0526*P_ch(5, 4) == 0 subject to NodeFlow_Real_6_4: LC(6, 4) + P_PV_AC(6, 4) - P_export(6, 4) + P_import(6, 4) - Power_Flow_ft(6, 4) + 0.95*P_dis(6, 4) - 1.0526*P_ch(6, 4) == 0 subject to NodeFlow_Real_7_4: P_PV_AC(7, 4) + LC(7, 4) + P_import(7, 4) - P_export(7, 4) + Power_Flow_ft(3, 4) + Power_Flow_ft(4, 4) + Power_Flow_ft(5, 4) + Power_Flow_ft(6, 4) - Power_Flow_ft(7, 4) + 0.95*P_dis(7, 4) - 1.0526*P_ch(7, 4) == 0 subject to NodeFlow_Real_8_4: LC(8, 4) + P_PV_AC(8, 4) - P_export(8, 4) + P_import(8, 4) - Power_Flow_ft(8, 4) + 0.95*P_dis(8, 4) - 1.0526*P_ch(8, 4) == 0 subject to NodeFlow_Real_9_4: LC(9, 4) + P_PV_AC(9, 4) - P_export(9, 4) + P_import(9, 4) - Power_Flow_ft(9, 4) + 0.95*P_dis(9, 4) - 1.0526*P_ch(9, 4) == 0 subject to NodeFlow_Real_10_4: LC(10, 4) + P_PV_AC(10, 4) - P_export(10, 4) + P_import(10, 4) - Power_Flow_ft(10, 4) + 0.95*P_dis(10, 4) - 1.0526*P_ch(10, 4) == 0 subject to NodeFlow_Real_11_4: LC(11, 4) + P_PV_AC(11, 4) - P_export(11, 4) + P_import(11, 4) - Power_Flow_ft(11, 4) + 0.95*P_dis(11, 4) - 1.0526*P_ch(11, 4) == 0 subject to NodeFlow_Real_12_4: P_PV_AC(12, 4) + LC(12, 4) + P_import(12, 4) - P_export(12, 4) + Power_Flow_ft(7, 4) + Power_Flow_ft(8, 4) + Power_Flow_ft(9, 4) + Power_Flow_ft(10, 4) + Power_Flow_ft(11, 4) - Power_Flow_ft(12, 4) + 0.95*P_dis(12, 4) - 1.0526*P_ch(12, 4) == 0 subject to NodeFlow_Real_13_4: LC(13, 4) + P_PV_AC(13, 4) - P_export(13, 4) + P_import(13, 4) + Power_Flow_ft(12, 4) + 0.95*P_dis(13, 4) - 1.0526*P_ch(13, 4) == 1.2544 subject to NodeFlow_Reactive_3_1NodeFlow_Reactive_3_1: QLC(1, 1) + Qb(1, 1) - Qij(1, 1) - Qij(2, 1) == 0 subject to NodeFlow_Reactive_3_2NodeFlow_Reactive_3_1: QLC(2, 1) + Qb(2, 1) + Qij(1, 1) == 0 subject to NodeFlow_Reactive_3_3NodeFlow_Reactive_3_1: QLC(3, 1) + Qb(3, 1) + Qij(2, 1) - Qij(3, 1) == 0 subject to NodeFlow_Reactive_3_4NodeFlow_Reactive_3_1: QLC(4, 1) + Qb(4, 1) - Qij(4, 1) == 0 subject to NodeFlow_Reactive_3_5NodeFlow_Reactive_3_1: QLC(5, 1) + Qb(5, 1) - Qij(5, 1) == 0 subject to NodeFlow_Reactive_3_6NodeFlow_Reactive_3_1: QLC(6, 1) + Qb(6, 1) - Qij(6, 1) == 0 subject to NodeFlow_Reactive_3_7NodeFlow_Reactive_3_1: QLC(7, 1) + Qb(7, 1) + Qij(3, 1) + Qij(4, 1) + Qij(5, 1) + Qij(6, 1) - Qij(7, 1) == 0 subject to NodeFlow_Reactive_3_8NodeFlow_Reactive_3_1: QLC(8, 1) + Qb(8, 1) - Qij(8, 1) == 0 subject to NodeFlow_Reactive_3_9NodeFlow_Reactive_3_1: QLC(9, 1) + Qb(9, 1) - Qij(9, 1) == 0 subject to NodeFlow_Reactive_3_10NodeFlow_Reactive_3_1: QLC(10, 1) + Qb(10, 1) - Qij(10, 1) == 0 subject to NodeFlow_Reactive_3_11NodeFlow_Reactive_3_1: QLC(11, 1) + Qb(11, 1) - Qij(11, 1) == 0 subject to NodeFlow_Reactive_3_12NodeFlow_Reactive_3_1: QLC(12, 1) + Qb(12, 1) + Qij(7, 1) + Qij(8, 1) + Qij(9, 1) + Qij(10, 1) + Qij(11, 1) - Qij(12, 1) == 0 subject to NodeFlow_Reactive_3_13NodeFlow_Reactive_3_1: QLC(13, 1) + Qb(13, 1) + Qij(12, 1) == 0.36587 subject to NodeFlow_Reactive_3_1NodeFlow_Reactive_3_2: QLC(1, 2) + Qb(1, 2) - Qij(1, 2) - Qij(2, 2) == 0 subject to NodeFlow_Reactive_3_2NodeFlow_Reactive_3_2: QLC(2, 2) + Qb(2, 2) + Qij(1, 2) == 0 subject to NodeFlow_Reactive_3_3NodeFlow_Reactive_3_2: QLC(3, 2) + Qb(3, 2) + Qij(2, 2) - Qij(3, 2) == 0 subject to NodeFlow_Reactive_3_4NodeFlow_Reactive_3_2: QLC(4, 2) + Qb(4, 2) - Qij(4, 2) == 0 subject to NodeFlow_Reactive_3_5NodeFlow_Reactive_3_2: QLC(5, 2) + Qb(5, 2) - Qij(5, 2) == 0 subject to NodeFlow_Reactive_3_6NodeFlow_Reactive_3_2: QLC(6, 2) + Qb(6, 2) - Qij(6, 2) == 0 subject to NodeFlow_Reactive_3_7NodeFlow_Reactive_3_2: QLC(7, 2) + Qb(7, 2) + Qij(3, 2) + Qij(4, 2) + Qij(5, 2) + Qij(6, 2) - Qij(7, 2) == 0 subject to NodeFlow_Reactive_3_8NodeFlow_Reactive_3_2: QLC(8, 2) + Qb(8, 2) - Qij(8, 2) == 0 subject to NodeFlow_Reactive_3_9NodeFlow_Reactive_3_2: QLC(9, 2) + Qb(9, 2) - Qij(9, 2) == 0 subject to NodeFlow_Reactive_3_10NodeFlow_Reactive_3_2: QLC(10, 2) + Qb(10, 2) - Qij(10, 2) == 0 subject to NodeFlow_Reactive_3_11NodeFlow_Reactive_3_2: QLC(11, 2) + Qb(11, 2) - Qij(11, 2) == 0 subject to NodeFlow_Reactive_3_12NodeFlow_Reactive_3_2: QLC(12, 2) + Qb(12, 2) + Qij(7, 2) + Qij(8, 2) + Qij(9, 2) + Qij(10, 2) + Qij(11, 2) - Qij(12, 2) == 0 subject to NodeFlow_Reactive_3_13NodeFlow_Reactive_3_2: QLC(13, 2) + Qb(13, 2) + Qij(12, 2) == 0.36587 subject to NodeFlow_Reactive_3_1NodeFlow_Reactive_3_3: QLC(1, 3) + Qb(1, 3) - Qij(1, 3) - Qij(2, 3) == 0 subject to NodeFlow_Reactive_3_2NodeFlow_Reactive_3_3: QLC(2, 3) + Qb(2, 3) + Qij(1, 3) == 0 subject to NodeFlow_Reactive_3_3NodeFlow_Reactive_3_3: QLC(3, 3) + Qb(3, 3) + Qij(2, 3) - Qij(3, 3) == 0 subject to NodeFlow_Reactive_3_4NodeFlow_Reactive_3_3: QLC(4, 3) + Qb(4, 3) - Qij(4, 3) == 0 subject to NodeFlow_Reactive_3_5NodeFlow_Reactive_3_3: QLC(5, 3) + Qb(5, 3) - Qij(5, 3) == 0 subject to NodeFlow_Reactive_3_6NodeFlow_Reactive_3_3: QLC(6, 3) + Qb(6, 3) - Qij(6, 3) == 0 subject to NodeFlow_Reactive_3_7NodeFlow_Reactive_3_3: QLC(7, 3) + Qb(7, 3) + Qij(3, 3) + Qij(4, 3) + Qij(5, 3) + Qij(6, 3) - Qij(7, 3) == 0 subject to NodeFlow_Reactive_3_8NodeFlow_Reactive_3_3: QLC(8, 3) + Qb(8, 3) - Qij(8, 3) == 0 subject to NodeFlow_Reactive_3_9NodeFlow_Reactive_3_3: QLC(9, 3) + Qb(9, 3) - Qij(9, 3) == 0 subject to NodeFlow_Reactive_3_10NodeFlow_Reactive_3_3: QLC(10, 3) + Qb(10, 3) - Qij(10, 3) == 0 subject to NodeFlow_Reactive_3_11NodeFlow_Reactive_3_3: QLC(11, 3) + Qb(11, 3) - Qij(11, 3) == 0 subject to NodeFlow_Reactive_3_12NodeFlow_Reactive_3_3: QLC(12, 3) + Qb(12, 3) + Qij(7, 3) + Qij(8, 3) + Qij(9, 3) + Qij(10, 3) + Qij(11, 3) - Qij(12, 3) == 0 subject to NodeFlow_Reactive_3_13NodeFlow_Reactive_3_3: QLC(13, 3) + Qb(13, 3) + Qij(12, 3) == 0.36587 subject to NodeFlow_Reactive_3_1NodeFlow_Reactive_3_4: QLC(1, 4) + Qb(1, 4) - Qij(1, 4) - Qij(2, 4) == 0 subject to NodeFlow_Reactive_3_2NodeFlow_Reactive_3_4: QLC(2, 4) + Qb(2, 4) + Qij(1, 4) == 0 subject to NodeFlow_Reactive_3_3NodeFlow_Reactive_3_4: QLC(3, 4) + Qb(3, 4) + Qij(2, 4) - Qij(3, 4) == 0 subject to NodeFlow_Reactive_3_4NodeFlow_Reactive_3_4: QLC(4, 4) + Qb(4, 4) - Qij(4, 4) == 0 subject to NodeFlow_Reactive_3_5NodeFlow_Reactive_3_4: QLC(5, 4) + Qb(5, 4) - Qij(5, 4) == 0 subject to NodeFlow_Reactive_3_6NodeFlow_Reactive_3_4: QLC(6, 4) + Qb(6, 4) - Qij(6, 4) == 0 subject to NodeFlow_Reactive_3_7NodeFlow_Reactive_3_4: QLC(7, 4) + Qb(7, 4) + Qij(3, 4) + Qij(4, 4) + Qij(5, 4) + Qij(6, 4) - Qij(7, 4) == 0 subject to NodeFlow_Reactive_3_8NodeFlow_Reactive_3_4: QLC(8, 4) + Qb(8, 4) - Qij(8, 4) == 0 subject to NodeFlow_Reactive_3_9NodeFlow_Reactive_3_4: QLC(9, 4) + Qb(9, 4) - Qij(9, 4) == 0 subject to NodeFlow_Reactive_3_10NodeFlow_Reactive_3_4: QLC(10, 4) + Qb(10, 4) - Qij(10, 4) == 0 subject to NodeFlow_Reactive_3_11NodeFlow_Reactive_3_4: QLC(11, 4) + Qb(11, 4) - Qij(11, 4) == 0 subject to NodeFlow_Reactive_3_12NodeFlow_Reactive_3_4: QLC(12, 4) + Qb(12, 4) + Qij(7, 4) + Qij(8, 4) + Qij(9, 4) + Qij(10, 4) + Qij(11, 4) - Qij(12, 4) == 0 subject to NodeFlow_Reactive_3_13NodeFlow_Reactive_3_4: QLC(13, 4) + Qb(13, 4) + Qij(12, 4) == 0.36587 subject to InitialSOC: SOC(1, 1) == 0 SOC(2, 1) == 0 SOC(3, 1) == 0 SOC(4, 1) == 0 SOC(5, 1) == 0 SOC(6, 1) == 0 SOC(7, 1) == 0 SOC(8, 1) == 0.664 SOC(9, 1) == 0 SOC(10, 1) == 0 SOC(11, 1) == 0 SOC(12, 1) == 0 SOC(13, 1) == 0 subject to SOC_update_1_2: -0.95*P_ch(1, 1) + 1.1111*P_dis(1, 1) - SOC(1, 1) + SOC(1, 2) == 0 subject to SOC_update_2_2: -0.95*P_ch(2, 1) + 1.1111*P_dis(2, 1) - SOC(2, 1) + SOC(2, 2) == 0 subject to SOC_update_3_2: -0.95*P_ch(3, 1) + 1.1111*P_dis(3, 1) - SOC(3, 1) + SOC(3, 2) == 0 subject to SOC_update_4_2: -0.95*P_ch(4, 1) + 1.1111*P_dis(4, 1) - SOC(4, 1) + SOC(4, 2) == 0 subject to SOC_update_5_2: -0.95*P_ch(5, 1) + 1.1111*P_dis(5, 1) - SOC(5, 1) + SOC(5, 2) == 0 subject to SOC_update_6_2: -0.95*P_ch(6, 1) + 1.1111*P_dis(6, 1) - SOC(6, 1) + SOC(6, 2) == 0 subject to SOC_update_7_2: -0.95*P_ch(7, 1) + 1.1111*P_dis(7, 1) - SOC(7, 1) + SOC(7, 2) == 0 subject to SOC_update_8_2: -0.95*P_ch(8, 1) + 1.1111*P_dis(8, 1) - SOC(8, 1) + SOC(8, 2) == 0 subject to SOC_update_9_2: -0.95*P_ch(9, 1) + 1.1111*P_dis(9, 1) - SOC(9, 1) + SOC(9, 2) == 0 subject to SOC_update_10_2: -0.95*P_ch(10, 1) + 1.1111*P_dis(10, 1) - SOC(10, 1) + SOC(10, 2) == 0 subject to SOC_update_11_2: -0.95*P_ch(11, 1) + 1.1111*P_dis(11, 1) - SOC(11, 1) + SOC(11, 2) == 0 subject to SOC_update_12_2: -0.95*P_ch(12, 1) + 1.1111*P_dis(12, 1) - SOC(12, 1) + SOC(12, 2) == 0 subject to SOC_update_13_2: -0.95*P_ch(13, 1) + 1.1111*P_dis(13, 1) - SOC(13, 1) + SOC(13, 2) == 0 subject to SOC_update_1_3: -0.95*P_ch(1, 2) + 1.1111*P_dis(1, 2) - SOC(1, 2) + SOC(1, 3) == 0 subject to SOC_update_2_3: -0.95*P_ch(2, 2) + 1.1111*P_dis(2, 2) - SOC(2, 2) + SOC(2, 3) == 0 subject to SOC_update_3_3: -0.95*P_ch(3, 2) + 1.1111*P_dis(3, 2) - SOC(3, 2) + SOC(3, 3) == 0 subject to SOC_update_4_3: -0.95*P_ch(4, 2) + 1.1111*P_dis(4, 2) - SOC(4, 2) + SOC(4, 3) == 0 subject to SOC_update_5_3: -0.95*P_ch(5, 2) + 1.1111*P_dis(5, 2) - SOC(5, 2) + SOC(5, 3) == 0 subject to SOC_update_6_3: -0.95*P_ch(6, 2) + 1.1111*P_dis(6, 2) - SOC(6, 2) + SOC(6, 3) == 0 subject to SOC_update_7_3: -0.95*P_ch(7, 2) + 1.1111*P_dis(7, 2) - SOC(7, 2) + SOC(7, 3) == 0 subject to SOC_update_8_3: -0.95*P_ch(8, 2) + 1.1111*P_dis(8, 2) - SOC(8, 2) + SOC(8, 3) == 0 subject to SOC_update_9_3: -0.95*P_ch(9, 2) + 1.1111*P_dis(9, 2) - SOC(9, 2) + SOC(9, 3) == 0 subject to SOC_update_10_3: -0.95*P_ch(10, 2) + 1.1111*P_dis(10, 2) - SOC(10, 2) + SOC(10, 3) == 0 subject to SOC_update_11_3: -0.95*P_ch(11, 2) + 1.1111*P_dis(11, 2) - SOC(11, 2) + SOC(11, 3) == 0 subject to SOC_update_12_3: -0.95*P_ch(12, 2) + 1.1111*P_dis(12, 2) - SOC(12, 2) + SOC(12, 3) == 0 subject to SOC_update_13_3: -0.95*P_ch(13, 2) + 1.1111*P_dis(13, 2) - SOC(13, 2) + SOC(13, 3) == 0 subject to SOC_update_1_4: -0.95*P_ch(1, 3) + 1.1111*P_dis(1, 3) - SOC(1, 3) + SOC(1, 4) == 0 subject to SOC_update_2_4: -0.95*P_ch(2, 3) + 1.1111*P_dis(2, 3) - SOC(2, 3) + SOC(2, 4) == 0 subject to SOC_update_3_4: -0.95*P_ch(3, 3) + 1.1111*P_dis(3, 3) - SOC(3, 3) + SOC(3, 4) == 0 subject to SOC_update_4_4: -0.95*P_ch(4, 3) + 1.1111*P_dis(4, 3) - SOC(4, 3) + SOC(4, 4) == 0 subject to SOC_update_5_4: -0.95*P_ch(5, 3) + 1.1111*P_dis(5, 3) - SOC(5, 3) + SOC(5, 4) == 0 subject to SOC_update_6_4: -0.95*P_ch(6, 3) + 1.1111*P_dis(6, 3) - SOC(6, 3) + SOC(6, 4) == 0 subject to SOC_update_7_4: -0.95*P_ch(7, 3) + 1.1111*P_dis(7, 3) - SOC(7, 3) + SOC(7, 4) == 0 subject to SOC_update_8_4: -0.95*P_ch(8, 3) + 1.1111*P_dis(8, 3) - SOC(8, 3) + SOC(8, 4) == 0 subject to SOC_update_9_4: -0.95*P_ch(9, 3) + 1.1111*P_dis(9, 3) - SOC(9, 3) + SOC(9, 4) == 0 subject to SOC_update_10_4: -0.95*P_ch(10, 3) + 1.1111*P_dis(10, 3) - SOC(10, 3) + SOC(10, 4) == 0 subject to SOC_update_11_4: -0.95*P_ch(11, 3) + 1.1111*P_dis(11, 3) - SOC(11, 3) + SOC(11, 4) == 0 subject to SOC_update_12_4: -0.95*P_ch(12, 3) + 1.1111*P_dis(12, 3) - SOC(12, 3) + SOC(12, 4) == 0 subject to SOC_update_13_4: -0.95*P_ch(13, 3) + 1.1111*P_dis(13, 3) - SOC(13, 3) + SOC(13, 4) == 0 subject to Inverter_ActivePower_PV_1: P_PV_AC(1, 1) - 0.95*P_PV(1, 1) == 0 P_PV_AC(2, 1) - 0.95*P_PV(2, 1) == 0 P_PV_AC(3, 1) - 0.95*P_PV(3, 1) == 0 P_PV_AC(4, 1) - 0.95*P_PV(4, 1) == 0 P_PV_AC(5, 1) - 0.95*P_PV(5, 1) == 0 P_PV_AC(6, 1) - 0.95*P_PV(6, 1) == 0 P_PV_AC(7, 1) - 0.95*P_PV(7, 1) == 0 P_PV_AC(8, 1) - 0.95*P_PV(8, 1) == 0 P_PV_AC(9, 1) - 0.95*P_PV(9, 1) == 0 P_PV_AC(10, 1) - 0.95*P_PV(10, 1) == 0 P_PV_AC(11, 1) - 0.95*P_PV(11, 1) == 0 P_PV_AC(12, 1) - 0.95*P_PV(12, 1) == 0 P_PV_AC(13, 1) - 0.95*P_PV(13, 1) == 0 subject to Inverter_ActivePower_battery_1: 1.0526*P_ch(1, 1) - 0.9*P_dis(1, 1) + Pb_AC(1, 1) == 0 1.0526*P_ch(2, 1) - 0.9*P_dis(2, 1) + Pb_AC(2, 1) == 0 1.0526*P_ch(3, 1) - 0.9*P_dis(3, 1) + Pb_AC(3, 1) == 0 1.0526*P_ch(4, 1) - 0.9*P_dis(4, 1) + Pb_AC(4, 1) == 0 1.0526*P_ch(5, 1) - 0.9*P_dis(5, 1) + Pb_AC(5, 1) == 0 1.0526*P_ch(6, 1) - 0.9*P_dis(6, 1) + Pb_AC(6, 1) == 0 1.0526*P_ch(7, 1) - 0.9*P_dis(7, 1) + Pb_AC(7, 1) == 0 1.0526*P_ch(8, 1) - 0.9*P_dis(8, 1) + Pb_AC(8, 1) == 0 1.0526*P_ch(9, 1) - 0.9*P_dis(9, 1) + Pb_AC(9, 1) == 0 1.0526*P_ch(10, 1) - 0.9*P_dis(10, 1) + Pb_AC(10, 1) == 0 1.0526*P_ch(11, 1) - 0.9*P_dis(11, 1) + Pb_AC(11, 1) == 0 1.0526*P_ch(12, 1) - 0.9*P_dis(12, 1) + Pb_AC(12, 1) == 0 1.0526*P_ch(13, 1) - 0.9*P_dis(13, 1) + Pb_AC(13, 1) == 0 subject to absConstraint: Pb_plus(1, 4) + Pb_minus(1, 4) + Qb_plus(1, 4) + Qb_minus(1, 4) <= 0 Pb_plus(2, 4) + Pb_minus(2, 4) + Qb_plus(2, 4) + Qb_minus(2, 4) <= 0 Pb_plus(3, 4) + Pb_minus(3, 4) + Qb_plus(3, 4) + Qb_minus(3, 4) <= 0 Pb_plus(4, 4) + Pb_minus(4, 4) + Qb_plus(4, 4) + Qb_minus(4, 4) <= 0 Pb_plus(5, 4) + Pb_minus(5, 4) + Qb_plus(5, 4) + Qb_minus(5, 4) <= 0 Pb_plus(6, 4) + Pb_minus(6, 4) + Qb_plus(6, 4) + Qb_minus(6, 4) <= 0 Pb_plus(7, 4) + Pb_minus(7, 4) + Qb_plus(7, 4) + Qb_minus(7, 4) <= 0 Pb_plus(8, 4) + Pb_minus(8, 4) + Qb_plus(8, 4) + Qb_minus(8, 4) <= 1.328 Pb_plus(9, 4) + Pb_minus(9, 4) + Qb_plus(9, 4) + Qb_minus(9, 4) <= 0 Pb_plus(10, 4) + Pb_minus(10, 4) + Qb_plus(10, 4) + Qb_minus(10, 4) <= 0 Pb_plus(11, 4) + Pb_minus(11, 4) + Qb_plus(11, 4) + Qb_minus(11, 4) <= 0 Pb_plus(12, 4) + Pb_minus(12, 4) + Qb_plus(12, 4) + Qb_minus(12, 4) <= 0 Pb_plus(13, 4) + Pb_minus(13, 4) + Qb_plus(13, 4) + Qb_minus(13, 4) <= 0 subject to Pb_AC_decomposition: Pb_plus(1, 4) - Pb_minus(1, 4) - Pb_AC(1, 4) == 0 Pb_plus(2, 4) - Pb_minus(2, 4) - Pb_AC(2, 4) == 0 Pb_plus(3, 4) - Pb_minus(3, 4) - Pb_AC(3, 4) == 0 Pb_plus(4, 4) - Pb_minus(4, 4) - Pb_AC(4, 4) == 0 Pb_plus(5, 4) - Pb_minus(5, 4) - Pb_AC(5, 4) == 0 Pb_plus(6, 4) - Pb_minus(6, 4) - Pb_AC(6, 4) == 0 Pb_plus(7, 4) - Pb_minus(7, 4) - Pb_AC(7, 4) == 0 Pb_plus(8, 4) - Pb_minus(8, 4) - Pb_AC(8, 4) == 0 Pb_plus(9, 4) - Pb_minus(9, 4) - Pb_AC(9, 4) == 0 Pb_plus(10, 4) - Pb_minus(10, 4) - Pb_AC(10, 4) == 0 Pb_plus(11, 4) - Pb_minus(11, 4) - Pb_AC(11, 4) == 0 Pb_plus(12, 4) - Pb_minus(12, 4) - Pb_AC(12, 4) == 0 Pb_plus(13, 4) - Pb_minus(13, 4) - Pb_AC(13, 4) == 0 subject to Qb_decomposition: Qb_plus(1, 4) - Qb_minus(1, 4) - Qb(1, 4) == 0 Qb_plus(2, 4) - Qb_minus(2, 4) - Qb(2, 4) == 0 Qb_plus(3, 4) - Qb_minus(3, 4) - Qb(3, 4) == 0 Qb_plus(4, 4) - Qb_minus(4, 4) - Qb(4, 4) == 0 Qb_plus(5, 4) - Qb_minus(5, 4) - Qb(5, 4) == 0 Qb_plus(6, 4) - Qb_minus(6, 4) - Qb(6, 4) == 0 Qb_plus(7, 4) - Qb_minus(7, 4) - Qb(7, 4) == 0 Qb_plus(8, 4) - Qb_minus(8, 4) - Qb(8, 4) == 0 Qb_plus(9, 4) - Qb_minus(9, 4) - Qb(9, 4) == 0 Qb_plus(10, 4) - Qb_minus(10, 4) - Qb(10, 4) == 0 Qb_plus(11, 4) - Qb_minus(11, 4) - Qb(11, 4) == 0 Qb_plus(12, 4) - Qb_minus(12, 4) - Qb(12, 4) == 0 Qb_plus(13, 4) - Qb_minus(13, 4) - Qb(13, 4) == 0 subject to Inverter_ActivePower_PV_2: P_PV_AC(1, 2) - 0.95*P_PV(1, 2) == 0 P_PV_AC(2, 2) - 0.95*P_PV(2, 2) == 0 P_PV_AC(3, 2) - 0.95*P_PV(3, 2) == 0 P_PV_AC(4, 2) - 0.95*P_PV(4, 2) == 0 P_PV_AC(5, 2) - 0.95*P_PV(5, 2) == 0 P_PV_AC(6, 2) - 0.95*P_PV(6, 2) == 0 P_PV_AC(7, 2) - 0.95*P_PV(7, 2) == 0 P_PV_AC(8, 2) - 0.95*P_PV(8, 2) == 0 P_PV_AC(9, 2) - 0.95*P_PV(9, 2) == 0 P_PV_AC(10, 2) - 0.95*P_PV(10, 2) == 0 P_PV_AC(11, 2) - 0.95*P_PV(11, 2) == 0 P_PV_AC(12, 2) - 0.95*P_PV(12, 2) == 0 P_PV_AC(13, 2) - 0.95*P_PV(13, 2) == 0 subject to Inverter_ActivePower_battery_2: 1.0526*P_ch(1, 2) - 0.9*P_dis(1, 2) + Pb_AC(1, 2) == 0 1.0526*P_ch(2, 2) - 0.9*P_dis(2, 2) + Pb_AC(2, 2) == 0 1.0526*P_ch(3, 2) - 0.9*P_dis(3, 2) + Pb_AC(3, 2) == 0 1.0526*P_ch(4, 2) - 0.9*P_dis(4, 2) + Pb_AC(4, 2) == 0 1.0526*P_ch(5, 2) - 0.9*P_dis(5, 2) + Pb_AC(5, 2) == 0 1.0526*P_ch(6, 2) - 0.9*P_dis(6, 2) + Pb_AC(6, 2) == 0 1.0526*P_ch(7, 2) - 0.9*P_dis(7, 2) + Pb_AC(7, 2) == 0 1.0526*P_ch(8, 2) - 0.9*P_dis(8, 2) + Pb_AC(8, 2) == 0 1.0526*P_ch(9, 2) - 0.9*P_dis(9, 2) + Pb_AC(9, 2) == 0 1.0526*P_ch(10, 2) - 0.9*P_dis(10, 2) + Pb_AC(10, 2) == 0 1.0526*P_ch(11, 2) - 0.9*P_dis(11, 2) + Pb_AC(11, 2) == 0 1.0526*P_ch(12, 2) - 0.9*P_dis(12, 2) + Pb_AC(12, 2) == 0 1.0526*P_ch(13, 2) - 0.9*P_dis(13, 2) + Pb_AC(13, 2) == 0 subject to Inverter_ActivePower_PV_3: P_PV_AC(1, 3) - 0.95*P_PV(1, 3) == 0 P_PV_AC(2, 3) - 0.95*P_PV(2, 3) == 0 P_PV_AC(3, 3) - 0.95*P_PV(3, 3) == 0 P_PV_AC(4, 3) - 0.95*P_PV(4, 3) == 0 P_PV_AC(5, 3) - 0.95*P_PV(5, 3) == 0 P_PV_AC(6, 3) - 0.95*P_PV(6, 3) == 0 P_PV_AC(7, 3) - 0.95*P_PV(7, 3) == 0 P_PV_AC(8, 3) - 0.95*P_PV(8, 3) == 0 P_PV_AC(9, 3) - 0.95*P_PV(9, 3) == 0 P_PV_AC(10, 3) - 0.95*P_PV(10, 3) == 0 P_PV_AC(11, 3) - 0.95*P_PV(11, 3) == 0 P_PV_AC(12, 3) - 0.95*P_PV(12, 3) == 0 P_PV_AC(13, 3) - 0.95*P_PV(13, 3) == 0 subject to Inverter_ActivePower_battery_3: 1.0526*P_ch(1, 3) - 0.9*P_dis(1, 3) + Pb_AC(1, 3) == 0 1.0526*P_ch(2, 3) - 0.9*P_dis(2, 3) + Pb_AC(2, 3) == 0 1.0526*P_ch(3, 3) - 0.9*P_dis(3, 3) + Pb_AC(3, 3) == 0 1.0526*P_ch(4, 3) - 0.9*P_dis(4, 3) + Pb_AC(4, 3) == 0 1.0526*P_ch(5, 3) - 0.9*P_dis(5, 3) + Pb_AC(5, 3) == 0 1.0526*P_ch(6, 3) - 0.9*P_dis(6, 3) + Pb_AC(6, 3) == 0 1.0526*P_ch(7, 3) - 0.9*P_dis(7, 3) + Pb_AC(7, 3) == 0 1.0526*P_ch(8, 3) - 0.9*P_dis(8, 3) + Pb_AC(8, 3) == 0 1.0526*P_ch(9, 3) - 0.9*P_dis(9, 3) + Pb_AC(9, 3) == 0 1.0526*P_ch(10, 3) - 0.9*P_dis(10, 3) + Pb_AC(10, 3) == 0 1.0526*P_ch(11, 3) - 0.9*P_dis(11, 3) + Pb_AC(11, 3) == 0 1.0526*P_ch(12, 3) - 0.9*P_dis(12, 3) + Pb_AC(12, 3) == 0 1.0526*P_ch(13, 3) - 0.9*P_dis(13, 3) + Pb_AC(13, 3) == 0 subject to Inverter_ActivePower_PV_4: P_PV_AC(1, 4) - 0.95*P_PV(1, 4) == 0 P_PV_AC(2, 4) - 0.95*P_PV(2, 4) == 0 P_PV_AC(3, 4) - 0.95*P_PV(3, 4) == 0 P_PV_AC(4, 4) - 0.95*P_PV(4, 4) == 0 P_PV_AC(5, 4) - 0.95*P_PV(5, 4) == 0 P_PV_AC(6, 4) - 0.95*P_PV(6, 4) == 0 P_PV_AC(7, 4) - 0.95*P_PV(7, 4) == 0 P_PV_AC(8, 4) - 0.95*P_PV(8, 4) == 0 P_PV_AC(9, 4) - 0.95*P_PV(9, 4) == 0 P_PV_AC(10, 4) - 0.95*P_PV(10, 4) == 0 P_PV_AC(11, 4) - 0.95*P_PV(11, 4) == 0 P_PV_AC(12, 4) - 0.95*P_PV(12, 4) == 0 P_PV_AC(13, 4) - 0.95*P_PV(13, 4) == 0 subject to Inverter_ActivePower_battery_4: 1.0526*P_ch(1, 4) - 0.9*P_dis(1, 4) + Pb_AC(1, 4) == 0 1.0526*P_ch(2, 4) - 0.9*P_dis(2, 4) + Pb_AC(2, 4) == 0 1.0526*P_ch(3, 4) - 0.9*P_dis(3, 4) + Pb_AC(3, 4) == 0 1.0526*P_ch(4, 4) - 0.9*P_dis(4, 4) + Pb_AC(4, 4) == 0 1.0526*P_ch(5, 4) - 0.9*P_dis(5, 4) + Pb_AC(5, 4) == 0 1.0526*P_ch(6, 4) - 0.9*P_dis(6, 4) + Pb_AC(6, 4) == 0 1.0526*P_ch(7, 4) - 0.9*P_dis(7, 4) + Pb_AC(7, 4) == 0 1.0526*P_ch(8, 4) - 0.9*P_dis(8, 4) + Pb_AC(8, 4) == 0 1.0526*P_ch(9, 4) - 0.9*P_dis(9, 4) + Pb_AC(9, 4) == 0 1.0526*P_ch(10, 4) - 0.9*P_dis(10, 4) + Pb_AC(10, 4) == 0 1.0526*P_ch(11, 4) - 0.9*P_dis(11, 4) + Pb_AC(11, 4) == 0 1.0526*P_ch(12, 4) - 0.9*P_dis(12, 4) + Pb_AC(12, 4) == 0 1.0526*P_ch(13, 4) - 0.9*P_dis(13, 4) + Pb_AC(13, 4) == 0 subject to const1_2_1: 0.1 == -P_ch(2, 1) + P_dis(2, 1) - 2.7778*Vim(2, 1) + 0.05*Vre(2, 1) + Ps(2, 1) subject to const2_2_1: 2.7778 == 2.7778*Vre(2, 1) - 0.05*Vim(2, 1) - Qb(13, 1) + Ps1(2, 1) subject to const1_3_1: 0 == -P_ch(3, 1) + P_dis(3, 1) - 6.91511*Vim(3, 1) + 1.78222*Vim(7, 1) - 25.0597*Vre(3, 1) + 25.0597*Vre(7, 1) + Ps(3, 1) subject to const2_3_1: 6.0241 == 6.91511*Vre(3, 1) - 1.78222*Vre(7, 1) - 25.0597*Vim(3, 1) + 25.0597*Vim(7, 1) - Qb(13, 1) + Ps1(3, 1) subject to const1_4_1: 0 == -P_ch(4, 1) + P_dis(4, 1) - 0.17824*Vim(4, 1) + 0.35644*Vim(7, 1) - 5.0119*Vre(4, 1) + 5.0119*Vre(7, 1) + Ps(4, 1) subject to const2_4_1: 0 == 0.17824*Vre(4, 1) - 0.35644*Vre(7, 1) - 5.0119*Vim(4, 1) + 5.0119*Vim(7, 1) - Qb(13, 1) + Ps1(4, 1) subject to const1_5_1: 0 == -P_ch(5, 1) + P_dis(5, 1) - 0.037622*Vim(5, 1) + 0.075272*Vim(7, 1) - 1.5833*Vre(5, 1) + 1.5833*Vre(7, 1) + Ps(5, 1) subject to const2_5_1: 0 == 0.037622*Vre(5, 1) - 0.075272*Vre(7, 1) - 1.5833*Vim(5, 1) + 1.5833*Vim(7, 1) - Qb(13, 1) + Ps1(5, 1) subject to const1_6_1: 0 == -P_ch(6, 1) + P_dis(6, 1) - 0.0067717*Vim(6, 1) + 0.013522*Vim(7, 1) - 0.62964*Vre(6, 1) + 0.62964*Vre(7, 1) + Ps(6, 1) subject to const2_6_1: 0 == 0.0067717*Vre(6, 1) - 0.013522*Vre(7, 1) - 0.62964*Vim(6, 1) + 0.62964*Vim(7, 1) - Qb(13, 1) + Ps1(6, 1) subject to const1_7_1: 0 == -P_ch(7, 1) + P_dis(7, 1) + 1.78222*Vim(3, 1) + 0.356444*Vim(4, 1) + 0.075272*Vim(5, 1) + 0.0135217*Vim(6, 1) - 1.12043*Vim(7, 1) + 0.0135217*Vim(12, 1) + 25.0597*Vre(3, 1) + 5.01194*Vre(4, 1) + 1.58331*Vre(5, 1) + 0.629645*Vre(6, 1) - 32.9143*Vre(7, 1) + 0.629645*Vre(12, 1) + Ps(7, 1) subject to const2_7_1: 0 == -1.78222*Vre(3, 1) - 0.356444*Vre(4, 1) - 0.075272*Vre(5, 1) - 0.0135217*Vre(6, 1) + 1.12043*Vre(7, 1) - 0.0135217*Vre(12, 1) + 25.0597*Vim(3, 1) + 5.01194*Vim(4, 1) + 1.58331*Vim(5, 1) + 0.629645*Vim(6, 1) - 32.9143*Vim(7, 1) + 0.629645*Vim(12, 1) - Qb(13, 1) + Ps1(7, 1) subject to const1_8_1: 0 == -P_ch(8, 1) + P_dis(8, 1) - 0.013543*Vim(8, 1) + 0.027043*Vim(12, 1) - 1.2593*Vre(8, 1) + 1.2593*Vre(12, 1) + Ps(8, 1) subject to const2_8_1: 0 == 0.013543*Vre(8, 1) - 0.027043*Vre(12, 1) - 1.2593*Vim(8, 1) + 1.2593*Vim(12, 1) - Qb(13, 1) + Ps1(8, 1) subject to const1_9_1: 0 == -P_ch(9, 1) + P_dis(9, 1) - 6.98913*Vim(9, 1) + 13.9776*Vim(12, 1) - 15.2283*Vre(9, 1) + 15.2283*Vre(12, 1) + Ps(9, 1) subject to const2_9_1: 0 == 6.98913*Vre(9, 1) - 13.9776*Vre(12, 1) - 15.2283*Vim(9, 1) + 15.2283*Vim(12, 1) - Qb(13, 1) + Ps1(9, 1) subject to const1_10_1: 0 == -P_ch(10, 1) + P_dis(10, 1) - 46.01775*Vim(10, 1) + 95.30825*Vim(12, 1) - 317.0651*Vre(10, 1) + 317.0651*Vre(12, 1) + Ps(10, 1) subject to const2_10_1: 0 == 46.01775*Vre(10, 1) - 95.30825*Vre(12, 1) - 317.0651*Vim(10, 1) + 317.0651*Vim(12, 1) - Qb(13, 1) + Ps1(10, 1) subject to const1_11_1: 0 == -P_ch(11, 1) + P_dis(11, 1) - 42.2145*Vim(11, 1) + 84.43*Vim(12, 1) - 90.2129*Vre(11, 1) + 90.2129*Vre(12, 1) + Ps(11, 1) subject to const2_11_1: 0 == 42.2145*Vre(11, 1) - 84.43*Vre(12, 1) - 90.2129*Vim(11, 1) + 90.2129*Vim(12, 1) - Qb(13, 1) + Ps1(11, 1) subject to const1_12_1: 0 == -P_ch(12, 1) + P_dis(12, 1) + 0.013521651*Vim(7, 1) + 0.027043302*Vim(8, 1) + 13.977631*Vim(9, 1) + 95.308253*Vim(10, 1) + 84.430036*Vim(11, 1) - 376.44716*Vim(12, 1) + 561.15942*Vim(13, 1) + 0.62964455*Vre(7, 1) + 1.2592891*Vre(8, 1) + 15.228261*Vre(9, 1) + 317.06508*Vre(10, 1) + 90.212915*Vre(11, 1) - 2107.8734*Vre(12, 1) + 1683.4783*Vre(13, 1) + Ps(12, 1) subject to const2_12_1: 0 == -0.013521651*Vre(7, 1) - 0.027043302*Vre(8, 1) - 13.977631*Vre(9, 1) - 95.308253*Vre(10, 1) - 84.430036*Vre(11, 1) + 376.44716*Vre(12, 1) - 561.15942*Vre(13, 1) + 0.62964455*Vim(7, 1) + 1.2592891*Vim(8, 1) + 15.228261*Vim(9, 1) + 317.06508*Vim(10, 1) + 90.212915*Vim(11, 1) - 2107.8734*Vim(12, 1) + 1683.4783*Vim(13, 1) - Qb(13, 1) + Ps1(12, 1) subject to const1_13_1: 2.5088 == -P_ch(13, 1) + P_dis(13, 1) + 561.15942*Vim(12, 1) - 281.57129*Vim(13, 1) + 1683.4783*Vre(12, 1) - 1682.2239*Vre(13, 1) + Ps(13, 1) subject to const2_13_1: -0.73173 == -561.15942*Vre(12, 1) + 280.83955*Vre(13, 1) + 1683.4783*Vim(12, 1) - 1684.7327*Vim(13, 1) - Qb(13, 1) + Ps1(13, 1) subject to const1_2_2: 0.1 == -P_ch(2, 2) + P_dis(2, 2) - 2.7778*Vim(2, 2) + 0.05*Vre(2, 2) + Ps(2, 2) subject to const2_2_2: 2.7778 == 2.7778*Vre(2, 2) - 0.05*Vim(2, 2) - Qb(13, 2) + Ps1(2, 2) subject to const1_3_2: 0 == -P_ch(3, 2) + P_dis(3, 2) - 6.91511*Vim(3, 2) + 1.78222*Vim(7, 2) - 25.0597*Vre(3, 2) + 25.0597*Vre(7, 2) + Ps(3, 2) subject to const2_3_2: 6.0241 == 6.91511*Vre(3, 2) - 1.78222*Vre(7, 2) - 25.0597*Vim(3, 2) + 25.0597*Vim(7, 2) - Qb(13, 2) + Ps1(3, 2) subject to const1_4_2: 0 == -P_ch(4, 2) + P_dis(4, 2) - 0.17824*Vim(4, 2) + 0.35644*Vim(7, 2) - 5.0119*Vre(4, 2) + 5.0119*Vre(7, 2) + Ps(4, 2) subject to const2_4_2: 0 == 0.17824*Vre(4, 2) - 0.35644*Vre(7, 2) - 5.0119*Vim(4, 2) + 5.0119*Vim(7, 2) - Qb(13, 2) + Ps1(4, 2) subject to const1_5_2: 0 == -P_ch(5, 2) + P_dis(5, 2) - 0.037622*Vim(5, 2) + 0.075272*Vim(7, 2) - 1.5833*Vre(5, 2) + 1.5833*Vre(7, 2) + Ps(5, 2) subject to const2_5_2: 0 == 0.037622*Vre(5, 2) - 0.075272*Vre(7, 2) - 1.5833*Vim(5, 2) + 1.5833*Vim(7, 2) - Qb(13, 2) + Ps1(5, 2) subject to const1_6_2: 0 == -P_ch(6, 2) + P_dis(6, 2) - 0.0067717*Vim(6, 2) + 0.013522*Vim(7, 2) - 0.62964*Vre(6, 2) + 0.62964*Vre(7, 2) + Ps(6, 2) subject to const2_6_2: 0 == 0.0067717*Vre(6, 2) - 0.013522*Vre(7, 2) - 0.62964*Vim(6, 2) + 0.62964*Vim(7, 2) - Qb(13, 2) + Ps1(6, 2) subject to const1_7_2: 0 == -P_ch(7, 2) + P_dis(7, 2) + 1.78222*Vim(3, 2) + 0.356444*Vim(4, 2) + 0.075272*Vim(5, 2) + 0.0135217*Vim(6, 2) - 1.12043*Vim(7, 2) + 0.0135217*Vim(12, 2) + 25.0597*Vre(3, 2) + 5.01194*Vre(4, 2) + 1.58331*Vre(5, 2) + 0.629645*Vre(6, 2) - 32.9143*Vre(7, 2) + 0.629645*Vre(12, 2) + Ps(7, 2) subject to const2_7_2: 0 == -1.78222*Vre(3, 2) - 0.356444*Vre(4, 2) - 0.075272*Vre(5, 2) - 0.0135217*Vre(6, 2) + 1.12043*Vre(7, 2) - 0.0135217*Vre(12, 2) + 25.0597*Vim(3, 2) + 5.01194*Vim(4, 2) + 1.58331*Vim(5, 2) + 0.629645*Vim(6, 2) - 32.9143*Vim(7, 2) + 0.629645*Vim(12, 2) - Qb(13, 2) + Ps1(7, 2) subject to const1_8_2: 0 == -P_ch(8, 2) + P_dis(8, 2) - 0.013543*Vim(8, 2) + 0.027043*Vim(12, 2) - 1.2593*Vre(8, 2) + 1.2593*Vre(12, 2) + Ps(8, 2) subject to const2_8_2: 0 == 0.013543*Vre(8, 2) - 0.027043*Vre(12, 2) - 1.2593*Vim(8, 2) + 1.2593*Vim(12, 2) - Qb(13, 2) + Ps1(8, 2) subject to const1_9_2: 0 == -P_ch(9, 2) + P_dis(9, 2) - 6.98913*Vim(9, 2) + 13.9776*Vim(12, 2) - 15.2283*Vre(9, 2) + 15.2283*Vre(12, 2) + Ps(9, 2) subject to const2_9_2: 0 == 6.98913*Vre(9, 2) - 13.9776*Vre(12, 2) - 15.2283*Vim(9, 2) + 15.2283*Vim(12, 2) - Qb(13, 2) + Ps1(9, 2) subject to const1_10_2: 0 == -P_ch(10, 2) + P_dis(10, 2) - 46.01775*Vim(10, 2) + 95.30825*Vim(12, 2) - 317.0651*Vre(10, 2) + 317.0651*Vre(12, 2) + Ps(10, 2) subject to const2_10_2: 0 == 46.01775*Vre(10, 2) - 95.30825*Vre(12, 2) - 317.0651*Vim(10, 2) + 317.0651*Vim(12, 2) - Qb(13, 2) + Ps1(10, 2) subject to const1_11_2: 0 == -P_ch(11, 2) + P_dis(11, 2) - 42.2145*Vim(11, 2) + 84.43*Vim(12, 2) - 90.2129*Vre(11, 2) + 90.2129*Vre(12, 2) + Ps(11, 2) subject to const2_11_2: 0 == 42.2145*Vre(11, 2) - 84.43*Vre(12, 2) - 90.2129*Vim(11, 2) + 90.2129*Vim(12, 2) - Qb(13, 2) + Ps1(11, 2) subject to const1_12_2: 0 == -P_ch(12, 2) + P_dis(12, 2) + 0.013521651*Vim(7, 2) + 0.027043302*Vim(8, 2) + 13.977631*Vim(9, 2) + 95.308253*Vim(10, 2) + 84.430036*Vim(11, 2) - 376.44716*Vim(12, 2) + 561.15942*Vim(13, 2) + 0.62964455*Vre(7, 2) + 1.2592891*Vre(8, 2) + 15.228261*Vre(9, 2) + 317.06508*Vre(10, 2) + 90.212915*Vre(11, 2) - 2107.8734*Vre(12, 2) + 1683.4783*Vre(13, 2) + Ps(12, 2) subject to const2_12_2: 0 == -0.013521651*Vre(7, 2) - 0.027043302*Vre(8, 2) - 13.977631*Vre(9, 2) - 95.308253*Vre(10, 2) - 84.430036*Vre(11, 2) + 376.44716*Vre(12, 2) - 561.15942*Vre(13, 2) + 0.62964455*Vim(7, 2) + 1.2592891*Vim(8, 2) + 15.228261*Vim(9, 2) + 317.06508*Vim(10, 2) + 90.212915*Vim(11, 2) - 2107.8734*Vim(12, 2) + 1683.4783*Vim(13, 2) - Qb(13, 2) + Ps1(12, 2) subject to const1_13_2: 2.5088 == -P_ch(13, 2) + P_dis(13, 2) + 561.15942*Vim(12, 2) - 281.57129*Vim(13, 2) + 1683.4783*Vre(12, 2) - 1682.2239*Vre(13, 2) + Ps(13, 2) subject to const2_13_2: -0.73173 == -561.15942*Vre(12, 2) + 280.83955*Vre(13, 2) + 1683.4783*Vim(12, 2) - 1684.7327*Vim(13, 2) - Qb(13, 2) + Ps1(13, 2) subject to const1_2_3: 0.1 == -P_ch(2, 3) + P_dis(2, 3) - 2.7778*Vim(2, 3) + 0.05*Vre(2, 3) + Ps(2, 3) subject to const2_2_3: 2.7778 == 2.7778*Vre(2, 3) - 0.05*Vim(2, 3) - Qb(13, 3) + Ps1(2, 3) subject to const1_3_3: 0 == -P_ch(3, 3) + P_dis(3, 3) - 6.91511*Vim(3, 3) + 1.78222*Vim(7, 3) - 25.0597*Vre(3, 3) + 25.0597*Vre(7, 3) + Ps(3, 3) subject to const2_3_3: 6.0241 == 6.91511*Vre(3, 3) - 1.78222*Vre(7, 3) - 25.0597*Vim(3, 3) + 25.0597*Vim(7, 3) - Qb(13, 3) + Ps1(3, 3) subject to const1_4_3: 0 == -P_ch(4, 3) + P_dis(4, 3) - 0.17824*Vim(4, 3) + 0.35644*Vim(7, 3) - 5.0119*Vre(4, 3) + 5.0119*Vre(7, 3) + Ps(4, 3) subject to const2_4_3: 0 == 0.17824*Vre(4, 3) - 0.35644*Vre(7, 3) - 5.0119*Vim(4, 3) + 5.0119*Vim(7, 3) - Qb(13, 3) + Ps1(4, 3) subject to const1_5_3: 0 == -P_ch(5, 3) + P_dis(5, 3) - 0.037622*Vim(5, 3) + 0.075272*Vim(7, 3) - 1.5833*Vre(5, 3) + 1.5833*Vre(7, 3) + Ps(5, 3) subject to const2_5_3: 0 == 0.037622*Vre(5, 3) - 0.075272*Vre(7, 3) - 1.5833*Vim(5, 3) + 1.5833*Vim(7, 3) - Qb(13, 3) + Ps1(5, 3) subject to const1_6_3: 0 == -P_ch(6, 3) + P_dis(6, 3) - 0.0067717*Vim(6, 3) + 0.013522*Vim(7, 3) - 0.62964*Vre(6, 3) + 0.62964*Vre(7, 3) + Ps(6, 3) subject to const2_6_3: 0 == 0.0067717*Vre(6, 3) - 0.013522*Vre(7, 3) - 0.62964*Vim(6, 3) + 0.62964*Vim(7, 3) - Qb(13, 3) + Ps1(6, 3) subject to const1_7_3: 0 == -P_ch(7, 3) + P_dis(7, 3) + 1.78222*Vim(3, 3) + 0.356444*Vim(4, 3) + 0.075272*Vim(5, 3) + 0.0135217*Vim(6, 3) - 1.12043*Vim(7, 3) + 0.0135217*Vim(12, 3) + 25.0597*Vre(3, 3) + 5.01194*Vre(4, 3) + 1.58331*Vre(5, 3) + 0.629645*Vre(6, 3) - 32.9143*Vre(7, 3) + 0.629645*Vre(12, 3) + Ps(7, 3) subject to const2_7_3: 0 == -1.78222*Vre(3, 3) - 0.356444*Vre(4, 3) - 0.075272*Vre(5, 3) - 0.0135217*Vre(6, 3) + 1.12043*Vre(7, 3) - 0.0135217*Vre(12, 3) + 25.0597*Vim(3, 3) + 5.01194*Vim(4, 3) + 1.58331*Vim(5, 3) + 0.629645*Vim(6, 3) - 32.9143*Vim(7, 3) + 0.629645*Vim(12, 3) - Qb(13, 3) + Ps1(7, 3) subject to const1_8_3: 0 == -P_ch(8, 3) + P_dis(8, 3) - 0.013543*Vim(8, 3) + 0.027043*Vim(12, 3) - 1.2593*Vre(8, 3) + 1.2593*Vre(12, 3) + Ps(8, 3) subject to const2_8_3: 0 == 0.013543*Vre(8, 3) - 0.027043*Vre(12, 3) - 1.2593*Vim(8, 3) + 1.2593*Vim(12, 3) - Qb(13, 3) + Ps1(8, 3) subject to const1_9_3: 0 == -P_ch(9, 3) + P_dis(9, 3) - 6.98913*Vim(9, 3) + 13.9776*Vim(12, 3) - 15.2283*Vre(9, 3) + 15.2283*Vre(12, 3) + Ps(9, 3) subject to const2_9_3: 0 == 6.98913*Vre(9, 3) - 13.9776*Vre(12, 3) - 15.2283*Vim(9, 3) + 15.2283*Vim(12, 3) - Qb(13, 3) + Ps1(9, 3) subject to const1_10_3: 0 == -P_ch(10, 3) + P_dis(10, 3) - 46.01775*Vim(10, 3) + 95.30825*Vim(12, 3) - 317.0651*Vre(10, 3) + 317.0651*Vre(12, 3) + Ps(10, 3) subject to const2_10_3: 0 == 46.01775*Vre(10, 3) - 95.30825*Vre(12, 3) - 317.0651*Vim(10, 3) + 317.0651*Vim(12, 3) - Qb(13, 3) + Ps1(10, 3) subject to const1_11_3: 0 == -P_ch(11, 3) + P_dis(11, 3) - 42.2145*Vim(11, 3) + 84.43*Vim(12, 3) - 90.2129*Vre(11, 3) + 90.2129*Vre(12, 3) + Ps(11, 3) subject to const2_11_3: 0 == 42.2145*Vre(11, 3) - 84.43*Vre(12, 3) - 90.2129*Vim(11, 3) + 90.2129*Vim(12, 3) - Qb(13, 3) + Ps1(11, 3) subject to const1_12_3: 0 == -P_ch(12, 3) + P_dis(12, 3) + 0.013521651*Vim(7, 3) + 0.027043302*Vim(8, 3) + 13.977631*Vim(9, 3) + 95.308253*Vim(10, 3) + 84.430036*Vim(11, 3) - 376.44716*Vim(12, 3) + 561.15942*Vim(13, 3) + 0.62964455*Vre(7, 3) + 1.2592891*Vre(8, 3) + 15.228261*Vre(9, 3) + 317.06508*Vre(10, 3) + 90.212915*Vre(11, 3) - 2107.8734*Vre(12, 3) + 1683.4783*Vre(13, 3) + Ps(12, 3) subject to const2_12_3: 0 == -0.013521651*Vre(7, 3) - 0.027043302*Vre(8, 3) - 13.977631*Vre(9, 3) - 95.308253*Vre(10, 3) - 84.430036*Vre(11, 3) + 376.44716*Vre(12, 3) - 561.15942*Vre(13, 3) + 0.62964455*Vim(7, 3) + 1.2592891*Vim(8, 3) + 15.228261*Vim(9, 3) + 317.06508*Vim(10, 3) + 90.212915*Vim(11, 3) - 2107.8734*Vim(12, 3) + 1683.4783*Vim(13, 3) - Qb(13, 3) + Ps1(12, 3) subject to const1_13_3: 2.5088 == -P_ch(13, 3) + P_dis(13, 3) + 561.15942*Vim(12, 3) - 281.57129*Vim(13, 3) + 1683.4783*Vre(12, 3) - 1682.2239*Vre(13, 3) + Ps(13, 3) subject to const2_13_3: -0.73173 == -561.15942*Vre(12, 3) + 280.83955*Vre(13, 3) + 1683.4783*Vim(12, 3) - 1684.7327*Vim(13, 3) - Qb(13, 3) + Ps1(13, 3) subject to const1_2_4: 0.1 == -P_ch(2, 4) + P_dis(2, 4) - 2.7778*Vim(2, 4) + 0.05*Vre(2, 4) + Ps(2, 4) subject to const2_2_4: 2.7778 == 2.7778*Vre(2, 4) - 0.05*Vim(2, 4) - Qb(13, 4) + Ps1(2, 4) subject to const1_3_4: 0 == -P_ch(3, 4) + P_dis(3, 4) - 6.91511*Vim(3, 4) + 1.78222*Vim(7, 4) - 25.0597*Vre(3, 4) + 25.0597*Vre(7, 4) + Ps(3, 4) subject to const2_3_4: 6.0241 == 6.91511*Vre(3, 4) - 1.78222*Vre(7, 4) - 25.0597*Vim(3, 4) + 25.0597*Vim(7, 4) - Qb(13, 4) + Ps1(3, 4) subject to const1_4_4: 0 == -P_ch(4, 4) + P_dis(4, 4) - 0.17824*Vim(4, 4) + 0.35644*Vim(7, 4) - 5.0119*Vre(4, 4) + 5.0119*Vre(7, 4) + Ps(4, 4) subject to const2_4_4: 0 == 0.17824*Vre(4, 4) - 0.35644*Vre(7, 4) - 5.0119*Vim(4, 4) + 5.0119*Vim(7, 4) - Qb(13, 4) + Ps1(4, 4) subject to const1_5_4: 0 == -P_ch(5, 4) + P_dis(5, 4) - 0.037622*Vim(5, 4) + 0.075272*Vim(7, 4) - 1.5833*Vre(5, 4) + 1.5833*Vre(7, 4) + Ps(5, 4) subject to const2_5_4: 0 == 0.037622*Vre(5, 4) - 0.075272*Vre(7, 4) - 1.5833*Vim(5, 4) + 1.5833*Vim(7, 4) - Qb(13, 4) + Ps1(5, 4) subject to const1_6_4: 0 == -P_ch(6, 4) + P_dis(6, 4) - 0.0067717*Vim(6, 4) + 0.013522*Vim(7, 4) - 0.62964*Vre(6, 4) + 0.62964*Vre(7, 4) + Ps(6, 4) subject to const2_6_4: 0 == 0.0067717*Vre(6, 4) - 0.013522*Vre(7, 4) - 0.62964*Vim(6, 4) + 0.62964*Vim(7, 4) - Qb(13, 4) + Ps1(6, 4) subject to const1_7_4: 0 == -P_ch(7, 4) + P_dis(7, 4) + 1.78222*Vim(3, 4) + 0.356444*Vim(4, 4) + 0.075272*Vim(5, 4) + 0.0135217*Vim(6, 4) - 1.12043*Vim(7, 4) + 0.0135217*Vim(12, 4) + 25.0597*Vre(3, 4) + 5.01194*Vre(4, 4) + 1.58331*Vre(5, 4) + 0.629645*Vre(6, 4) - 32.9143*Vre(7, 4) + 0.629645*Vre(12, 4) + Ps(7, 4) subject to const2_7_4: 0 == -1.78222*Vre(3, 4) - 0.356444*Vre(4, 4) - 0.075272*Vre(5, 4) - 0.0135217*Vre(6, 4) + 1.12043*Vre(7, 4) - 0.0135217*Vre(12, 4) + 25.0597*Vim(3, 4) + 5.01194*Vim(4, 4) + 1.58331*Vim(5, 4) + 0.629645*Vim(6, 4) - 32.9143*Vim(7, 4) + 0.629645*Vim(12, 4) - Qb(13, 4) + Ps1(7, 4) subject to const1_8_4: 0 == -P_ch(8, 4) + P_dis(8, 4) - 0.013543*Vim(8, 4) + 0.027043*Vim(12, 4) - 1.2593*Vre(8, 4) + 1.2593*Vre(12, 4) + Ps(8, 4) subject to const2_8_4: 0 == 0.013543*Vre(8, 4) - 0.027043*Vre(12, 4) - 1.2593*Vim(8, 4) + 1.2593*Vim(12, 4) - Qb(13, 4) + Ps1(8, 4) subject to const1_9_4: 0 == -P_ch(9, 4) + P_dis(9, 4) - 6.98913*Vim(9, 4) + 13.9776*Vim(12, 4) - 15.2283*Vre(9, 4) + 15.2283*Vre(12, 4) + Ps(9, 4) subject to const2_9_4: 0 == 6.98913*Vre(9, 4) - 13.9776*Vre(12, 4) - 15.2283*Vim(9, 4) + 15.2283*Vim(12, 4) - Qb(13, 4) + Ps1(9, 4) subject to const1_10_4: 0 == -P_ch(10, 4) + P_dis(10, 4) - 46.01775*Vim(10, 4) + 95.30825*Vim(12, 4) - 317.0651*Vre(10, 4) + 317.0651*Vre(12, 4) + Ps(10, 4) subject to const2_10_4: 0 == 46.01775*Vre(10, 4) - 95.30825*Vre(12, 4) - 317.0651*Vim(10, 4) + 317.0651*Vim(12, 4) - Qb(13, 4) + Ps1(10, 4) subject to const1_11_4: 0 == -P_ch(11, 4) + P_dis(11, 4) - 42.2145*Vim(11, 4) + 84.43*Vim(12, 4) - 90.2129*Vre(11, 4) + 90.2129*Vre(12, 4) + Ps(11, 4) subject to const2_11_4: 0 == 42.2145*Vre(11, 4) - 84.43*Vre(12, 4) - 90.2129*Vim(11, 4) + 90.2129*Vim(12, 4) - Qb(13, 4) + Ps1(11, 4) subject to const1_12_4: 0 == -P_ch(12, 4) + P_dis(12, 4) + 0.013521651*Vim(7, 4) + 0.027043302*Vim(8, 4) + 13.977631*Vim(9, 4) + 95.308253*Vim(10, 4) + 84.430036*Vim(11, 4) - 376.44716*Vim(12, 4) + 561.15942*Vim(13, 4) + 0.62964455*Vre(7, 4) + 1.2592891*Vre(8, 4) + 15.228261*Vre(9, 4) + 317.06508*Vre(10, 4) + 90.212915*Vre(11, 4) - 2107.8734*Vre(12, 4) + 1683.4783*Vre(13, 4) + Ps(12, 4) subject to const2_12_4: 0 == -0.013521651*Vre(7, 4) - 0.027043302*Vre(8, 4) - 13.977631*Vre(9, 4) - 95.308253*Vre(10, 4) - 84.430036*Vre(11, 4) + 376.44716*Vre(12, 4) - 561.15942*Vre(13, 4) + 0.62964455*Vim(7, 4) + 1.2592891*Vim(8, 4) + 15.228261*Vim(9, 4) + 317.06508*Vim(10, 4) + 90.212915*Vim(11, 4) - 2107.8734*Vim(12, 4) + 1683.4783*Vim(13, 4) - Qb(13, 4) + Ps1(12, 4) subject to const1_13_4: 2.5088 == -P_ch(13, 4) + P_dis(13, 4) + 561.15942*Vim(12, 4) - 281.57129*Vim(13, 4) + 1683.4783*Vre(12, 4) - 1682.2239*Vre(13, 4) + Ps(13, 4) subject to const2_13_4: -0.73173 == -561.15942*Vre(12, 4) + 280.83955*Vre(13, 4) + 1683.4783*Vim(12, 4) - 1684.7327*Vim(13, 4) - Qb(13, 4) + Ps1(13, 4) subject to cons1: Power_Flow_ft(1, 1) <= 0.28867 Power_Flow_ft(2, 1) <= 1.732 Power_Flow_ft(3, 1) <= 0.79667 Power_Flow_ft(4, 1) <= 0.078 Power_Flow_ft(5, 1) <= 0.059733 Power_Flow_ft(6, 1) <= 0.037447 Power_Flow_ft(7, 1) <= 1.0453 Power_Flow_ft(8, 1) <= 0.95609 Power_Flow_ft(9, 1) <= 0.26133 Power_Flow_ft(10, 1) <= 0.2191 Power_Flow_ft(11, 1) <= 0.36491 Power_Flow_ft(12, 1) <= 1.8245 Power_Flow_ft(1, 2) <= 0.28867 Power_Flow_ft(2, 2) <= 1.732 Power_Flow_ft(3, 2) <= 0.79667 Power_Flow_ft(4, 2) <= 0.078 Power_Flow_ft(5, 2) <= 0.059733 Power_Flow_ft(6, 2) <= 0.037447 Power_Flow_ft(7, 2) <= 1.0453 Power_Flow_ft(8, 2) <= 0.95609 Power_Flow_ft(9, 2) <= 0.26133 Power_Flow_ft(10, 2) <= 0.2191 Power_Flow_ft(11, 2) <= 0.36491 Power_Flow_ft(12, 2) <= 1.8245 Power_Flow_ft(1, 3) <= 0.28867 Power_Flow_ft(2, 3) <= 1.732 Power_Flow_ft(3, 3) <= 0.79667 Power_Flow_ft(4, 3) <= 0.078 Power_Flow_ft(5, 3) <= 0.059733 Power_Flow_ft(6, 3) <= 0.037447 Power_Flow_ft(7, 3) <= 1.0453 Power_Flow_ft(8, 3) <= 0.95609 Power_Flow_ft(9, 3) <= 0.26133 Power_Flow_ft(10, 3) <= 0.2191 Power_Flow_ft(11, 3) <= 0.36491 Power_Flow_ft(12, 3) <= 1.8245 Power_Flow_ft(1, 4) <= 0.28867 Power_Flow_ft(2, 4) <= 1.732 Power_Flow_ft(3, 4) <= 0.79667 Power_Flow_ft(4, 4) <= 0.078 Power_Flow_ft(5, 4) <= 0.059733 Power_Flow_ft(6, 4) <= 0.037447 Power_Flow_ft(7, 4) <= 1.0453 Power_Flow_ft(8, 4) <= 0.95609 Power_Flow_ft(9, 4) <= 0.26133 Power_Flow_ft(10, 4) <= 0.2191 Power_Flow_ft(11, 4) <= 0.36491 Power_Flow_ft(12, 4) <= 1.8245 subject to cons2: Power_Flow_ft(1, 1) >= -0.28867 Power_Flow_ft(2, 1) >= -1.732 Power_Flow_ft(3, 1) >= -0.79667 Power_Flow_ft(4, 1) >= -0.078 Power_Flow_ft(5, 1) >= -0.059733 Power_Flow_ft(6, 1) >= -0.037447 Power_Flow_ft(7, 1) >= -1.0453 Power_Flow_ft(8, 1) >= -0.95609 Power_Flow_ft(9, 1) >= -0.26133 Power_Flow_ft(10, 1) >= -0.2191 Power_Flow_ft(11, 1) >= -0.36491 Power_Flow_ft(12, 1) >= -1.8245 Power_Flow_ft(1, 2) >= -0.28867 Power_Flow_ft(2, 2) >= -1.732 Power_Flow_ft(3, 2) >= -0.79667 Power_Flow_ft(4, 2) >= -0.078 Power_Flow_ft(5, 2) >= -0.059733 Power_Flow_ft(6, 2) >= -0.037447 Power_Flow_ft(7, 2) >= -1.0453 Power_Flow_ft(8, 2) >= -0.95609 Power_Flow_ft(9, 2) >= -0.26133 Power_Flow_ft(10, 2) >= -0.2191 Power_Flow_ft(11, 2) >= -0.36491 Power_Flow_ft(12, 2) >= -1.8245 Power_Flow_ft(1, 3) >= -0.28867 Power_Flow_ft(2, 3) >= -1.732 Power_Flow_ft(3, 3) >= -0.79667 Power_Flow_ft(4, 3) >= -0.078 Power_Flow_ft(5, 3) >= -0.059733 Power_Flow_ft(6, 3) >= -0.037447 Power_Flow_ft(7, 3) >= -1.0453 Power_Flow_ft(8, 3) >= -0.95609 Power_Flow_ft(9, 3) >= -0.26133 Power_Flow_ft(10, 3) >= -0.2191 Power_Flow_ft(11, 3) >= -0.36491 Power_Flow_ft(12, 3) >= -1.8245 Power_Flow_ft(1, 4) >= -0.28867 Power_Flow_ft(2, 4) >= -1.732 Power_Flow_ft(3, 4) >= -0.79667 Power_Flow_ft(4, 4) >= -0.078 Power_Flow_ft(5, 4) >= -0.059733 Power_Flow_ft(6, 4) >= -0.037447 Power_Flow_ft(7, 4) >= -1.0453 Power_Flow_ft(8, 4) >= -0.95609 Power_Flow_ft(9, 4) >= -0.26133 Power_Flow_ft(10, 4) >= -0.2191 Power_Flow_ft(11, 4) >= -0.36491 Power_Flow_ft(12, 4) >= -1.8245 subject to cons3: Qij(1, 1) <= 0.28867 Qij(2, 1) <= 1.732 Qij(3, 1) <= 0.79667 Qij(4, 1) <= 0.078 Qij(5, 1) <= 0.059733 Qij(6, 1) <= 0.037447 Qij(7, 1) <= 1.0453 Qij(8, 1) <= 0.95609 Qij(9, 1) <= 0.26133 Qij(10, 1) <= 0.2191 Qij(11, 1) <= 0.36491 Qij(12, 1) <= 1.8245 Qij(1, 2) <= 0.28867 Qij(2, 2) <= 1.732 Qij(3, 2) <= 0.79667 Qij(4, 2) <= 0.078 Qij(5, 2) <= 0.059733 Qij(6, 2) <= 0.037447 Qij(7, 2) <= 1.0453 Qij(8, 2) <= 0.95609 Qij(9, 2) <= 0.26133 Qij(10, 2) <= 0.2191 Qij(11, 2) <= 0.36491 Qij(12, 2) <= 1.8245 Qij(1, 3) <= 0.28867 Qij(2, 3) <= 1.732 Qij(3, 3) <= 0.79667 Qij(4, 3) <= 0.078 Qij(5, 3) <= 0.059733 Qij(6, 3) <= 0.037447 Qij(7, 3) <= 1.0453 Qij(8, 3) <= 0.95609 Qij(9, 3) <= 0.26133 Qij(10, 3) <= 0.2191 Qij(11, 3) <= 0.36491 Qij(12, 3) <= 1.8245 Qij(1, 4) <= 0.28867 Qij(2, 4) <= 1.732 Qij(3, 4) <= 0.79667 Qij(4, 4) <= 0.078 Qij(5, 4) <= 0.059733 Qij(6, 4) <= 0.037447 Qij(7, 4) <= 1.0453 Qij(8, 4) <= 0.95609 Qij(9, 4) <= 0.26133 Qij(10, 4) <= 0.2191 Qij(11, 4) <= 0.36491 Qij(12, 4) <= 1.8245 subject to cons4: Qij(1, 1) >= -0.28867 Qij(2, 1) >= -1.732 Qij(3, 1) >= -0.79667 Qij(4, 1) >= -0.078 Qij(5, 1) >= -0.059733 Qij(6, 1) >= -0.037447 Qij(7, 1) >= -1.0453 Qij(8, 1) >= -0.95609 Qij(9, 1) >= -0.26133 Qij(10, 1) >= -0.2191 Qij(11, 1) >= -0.36491 Qij(12, 1) >= -1.8245 Qij(1, 2) >= -0.28867 Qij(2, 2) >= -1.732 Qij(3, 2) >= -0.79667 Qij(4, 2) >= -0.078 Qij(5, 2) >= -0.059733 Qij(6, 2) >= -0.037447 Qij(7, 2) >= -1.0453 Qij(8, 2) >= -0.95609 Qij(9, 2) >= -0.26133 Qij(10, 2) >= -0.2191 Qij(11, 2) >= -0.36491 Qij(12, 2) >= -1.8245 Qij(1, 3) >= -0.28867 Qij(2, 3) >= -1.732 Qij(3, 3) >= -0.79667 Qij(4, 3) >= -0.078 Qij(5, 3) >= -0.059733 Qij(6, 3) >= -0.037447 Qij(7, 3) >= -1.0453 Qij(8, 3) >= -0.95609 Qij(9, 3) >= -0.26133 Qij(10, 3) >= -0.2191 Qij(11, 3) >= -0.36491 Qij(12, 3) >= -1.8245 Qij(1, 4) >= -0.28867 Qij(2, 4) >= -1.732 Qij(3, 4) >= -0.79667 Qij(4, 4) >= -0.078 Qij(5, 4) >= -0.059733 Qij(6, 4) >= -0.037447 Qij(7, 4) >= -1.0453 Qij(8, 4) >= -0.95609 Qij(9, 4) >= -0.26133 Qij(10, 4) >= -0.2191 Qij(11, 4) >= -0.36491 Qij(12, 4) >= -1.8245 subject to cons5: PV_Curtailed(1, 1) + P_PV(1, 1) == 0 PV_Curtailed(2, 1) + P_PV(2, 1) == 0 PV_Curtailed(3, 1) + P_PV(3, 1) == 0 PV_Curtailed(4, 1) + P_PV(4, 1) == 0.084267 PV_Curtailed(5, 1) + P_PV(5, 1) == 0.41547 PV_Curtailed(6, 1) + P_PV(6, 1) == 0.45512 PV_Curtailed(7, 1) + P_PV(7, 1) == 0 PV_Curtailed(8, 1) + P_PV(8, 1) == 0 PV_Curtailed(9, 1) + P_PV(9, 1) == 0.2864 PV_Curtailed(10, 1) + P_PV(10, 1) == 0.174 PV_Curtailed(11, 1) + P_PV(11, 1) == 0.095467 PV_Curtailed(12, 1) + P_PV(12, 1) == 0 PV_Curtailed(13, 1) + P_PV(13, 1) == 0 PV_Curtailed(1, 2) + P_PV(1, 2) == 0 PV_Curtailed(2, 2) + P_PV(2, 2) == 0 PV_Curtailed(3, 2) + P_PV(3, 2) == 0 PV_Curtailed(4, 2) + P_PV(4, 2) == 0.084267 PV_Curtailed(5, 2) + P_PV(5, 2) == 0.41547 PV_Curtailed(6, 2) + P_PV(6, 2) == 0.45512 PV_Curtailed(7, 2) + P_PV(7, 2) == 0 PV_Curtailed(8, 2) + P_PV(8, 2) == 0 PV_Curtailed(9, 2) + P_PV(9, 2) == 0.2864 PV_Curtailed(10, 2) + P_PV(10, 2) == 0.174 PV_Curtailed(11, 2) + P_PV(11, 2) == 0.095467 PV_Curtailed(12, 2) + P_PV(12, 2) == 0 PV_Curtailed(13, 2) + P_PV(13, 2) == 0 PV_Curtailed(1, 3) + P_PV(1, 3) == 0 PV_Curtailed(2, 3) + P_PV(2, 3) == 0 PV_Curtailed(3, 3) + P_PV(3, 3) == 0 PV_Curtailed(4, 3) + P_PV(4, 3) == 0.084267 PV_Curtailed(5, 3) + P_PV(5, 3) == 0.41547 PV_Curtailed(6, 3) + P_PV(6, 3) == 0.45512 PV_Curtailed(7, 3) + P_PV(7, 3) == 0 PV_Curtailed(8, 3) + P_PV(8, 3) == 0 PV_Curtailed(9, 3) + P_PV(9, 3) == 0.2864 PV_Curtailed(10, 3) + P_PV(10, 3) == 0.174 PV_Curtailed(11, 3) + P_PV(11, 3) == 0.095467 PV_Curtailed(12, 3) + P_PV(12, 3) == 0 PV_Curtailed(13, 3) + P_PV(13, 3) == 0 PV_Curtailed(1, 4) + P_PV(1, 4) == 0 PV_Curtailed(2, 4) + P_PV(2, 4) == 0 PV_Curtailed(3, 4) + P_PV(3, 4) == 0 PV_Curtailed(4, 4) + P_PV(4, 4) == 0.084267 PV_Curtailed(5, 4) + P_PV(5, 4) == 0.41547 PV_Curtailed(6, 4) + P_PV(6, 4) == 0.45512 PV_Curtailed(7, 4) + P_PV(7, 4) == 0 PV_Curtailed(8, 4) + P_PV(8, 4) == 0 PV_Curtailed(9, 4) + P_PV(9, 4) == 0.2864 PV_Curtailed(10, 4) + P_PV(10, 4) == 0.174 PV_Curtailed(11, 4) + P_PV(11, 4) == 0.095467 PV_Curtailed(12, 4) + P_PV(12, 4) == 0 PV_Curtailed(13, 4) + P_PV(13, 4) == 0 subject to Ire_eq_1_1: 0.36*Iim(1, 1) + Vre(1, 1) - Vre(2, 1) == 0 subject to Iim_eq_1_1: -0.36*Ire(1, 1) + Vim(1, 1) - Vim(2, 1) == 0 subject to Ire_eq_2_1: 0.166*Iim(2, 1) + Vre(1, 1) - Vre(3, 1) == 0 subject to Iim_eq_2_1: -0.166*Ire(2, 1) + Vim(1, 1) - Vim(3, 1) == 0 subject to Ire_eq_3_1: 0.0028237*Iim(3, 1) - 0.039704*Ire(3, 1) + Vre(3, 1) - Vre(7, 1) == 0 subject to Iim_eq_3_1: -0.039704*Iim(3, 1) - 0.0028237*Ire(3, 1) + Vim(3, 1) - Vim(7, 1) == 0 subject to Ire_eq_4_1: 0.014118*Iim(4, 1) - 0.19852*Ire(4, 1) + Vre(4, 1) - Vre(7, 1) == 0 subject to Iim_eq_4_1: -0.19852*Iim(4, 1) - 0.014118*Ire(4, 1) + Vim(4, 1) - Vim(7, 1) == 0 subject to Ire_eq_5_1: 0.029959*Iim(5, 1) - 0.63017*Ire(5, 1) + Vre(5, 1) - Vre(7, 1) == 0 subject to Iim_eq_5_1: -0.63017*Iim(5, 1) - 0.029959*Ire(5, 1) + Vim(5, 1) - Vim(7, 1) == 0 subject to Ire_eq_6_1: 0.034091*Iim(6, 1) - 1.5875*Ire(6, 1) + Vre(6, 1) - Vre(7, 1) == 0 subject to Iim_eq_6_1: -1.5875*Iim(6, 1) - 0.034091*Ire(6, 1) + Vim(6, 1) - Vim(7, 1) == 0 subject to Ire_eq_7_1: 0.034091*Iim(7, 1) - 1.5875*Ire(7, 1) + Vre(7, 1) - Vre(12, 1) == 0 subject to Iim_eq_7_1: -1.5875*Iim(7, 1) - 0.034091*Ire(7, 1) + Vim(7, 1) - Vim(12, 1) == 0 subject to Ire_eq_8_1: 0.017045*Iim(8, 1) - 0.79373*Ire(8, 1) + Vre(8, 1) - Vre(12, 1) == 0 subject to Iim_eq_8_1: -0.79373*Iim(8, 1) - 0.017045*Ire(8, 1) + Vim(8, 1) - Vim(12, 1) == 0 subject to Ire_eq_9_1: 0.032713*Iim(9, 1) - 0.03564*Ire(9, 1) + Vre(9, 1) - Vre(12, 1) == 0 subject to Iim_eq_9_1: -0.03564*Iim(9, 1) - 0.032713*Ire(9, 1) + Vim(9, 1) - Vim(12, 1) == 0 subject to Ire_eq_10_1: 0.00086949*Iim(10, 1) - 0.0028926*Ire(10, 1) + Vre(10, 1) - Vre(12, 1) == 0 subject to Iim_eq_10_1: -0.0028926*Iim(10, 1) - 0.00086949*Ire(10, 1) + Vim(10, 1) - Vim(12, 1) == 0 subject to Ire_eq_11_1: 0.0055303*Iim(11, 1) - 0.0059091*Ire(11, 1) + Vre(11, 1) - Vre(12, 1) == 0 subject to Iim_eq_11_1: -0.0059091*Iim(11, 1) - 0.0055303*Ire(11, 1) + Vim(11, 1) - Vim(12, 1) == 0 subject to Ire_eq_12_1: 0.0001782*Iim(12, 1) - 0.00053461*Ire(12, 1) + Vre(12, 1) - Vre(13, 1) == 0 subject to Iim_eq_12_1: -0.00053461*Iim(12, 1) - 0.0001782*Ire(12, 1) + Vim(12, 1) - Vim(13, 1) == 0 subject to Ire_eq_1_2: 0.36*Iim(1, 2) + Vre(1, 2) - Vre(2, 2) == 0 subject to Iim_eq_1_2: -0.36*Ire(1, 2) + Vim(1, 2) - Vim(2, 2) == 0 subject to Ire_eq_2_2: 0.166*Iim(2, 2) + Vre(1, 2) - Vre(3, 2) == 0 subject to Iim_eq_2_2: -0.166*Ire(2, 2) + Vim(1, 2) - Vim(3, 2) == 0 subject to Ire_eq_3_2: 0.0028237*Iim(3, 2) - 0.039704*Ire(3, 2) + Vre(3, 2) - Vre(7, 2) == 0 subject to Iim_eq_3_2: -0.039704*Iim(3, 2) - 0.0028237*Ire(3, 2) + Vim(3, 2) - Vim(7, 2) == 0 subject to Ire_eq_4_2: 0.014118*Iim(4, 2) - 0.19852*Ire(4, 2) + Vre(4, 2) - Vre(7, 2) == 0 subject to Iim_eq_4_2: -0.19852*Iim(4, 2) - 0.014118*Ire(4, 2) + Vim(4, 2) - Vim(7, 2) == 0 subject to Ire_eq_5_2: 0.029959*Iim(5, 2) - 0.63017*Ire(5, 2) + Vre(5, 2) - Vre(7, 2) == 0 subject to Iim_eq_5_2: -0.63017*Iim(5, 2) - 0.029959*Ire(5, 2) + Vim(5, 2) - Vim(7, 2) == 0 subject to Ire_eq_6_2: 0.034091*Iim(6, 2) - 1.5875*Ire(6, 2) + Vre(6, 2) - Vre(7, 2) == 0 subject to Iim_eq_6_2: -1.5875*Iim(6, 2) - 0.034091*Ire(6, 2) + Vim(6, 2) - Vim(7, 2) == 0 subject to Ire_eq_7_2: 0.034091*Iim(7, 2) - 1.5875*Ire(7, 2) + Vre(7, 2) - Vre(12, 2) == 0 subject to Iim_eq_7_2: -1.5875*Iim(7, 2) - 0.034091*Ire(7, 2) + Vim(7, 2) - Vim(12, 2) == 0 subject to Ire_eq_8_2: 0.017045*Iim(8, 2) - 0.79373*Ire(8, 2) + Vre(8, 2) - Vre(12, 2) == 0 subject to Iim_eq_8_2: -0.79373*Iim(8, 2) - 0.017045*Ire(8, 2) + Vim(8, 2) - Vim(12, 2) == 0 subject to Ire_eq_9_2: 0.032713*Iim(9, 2) - 0.03564*Ire(9, 2) + Vre(9, 2) - Vre(12, 2) == 0 subject to Iim_eq_9_2: -0.03564*Iim(9, 2) - 0.032713*Ire(9, 2) + Vim(9, 2) - Vim(12, 2) == 0 subject to Ire_eq_10_2: 0.00086949*Iim(10, 2) - 0.0028926*Ire(10, 2) + Vre(10, 2) - Vre(12, 2) == 0 subject to Iim_eq_10_2: -0.0028926*Iim(10, 2) - 0.00086949*Ire(10, 2) + Vim(10, 2) - Vim(12, 2) == 0 subject to Ire_eq_11_2: 0.0055303*Iim(11, 2) - 0.0059091*Ire(11, 2) + Vre(11, 2) - Vre(12, 2) == 0 subject to Iim_eq_11_2: -0.0059091*Iim(11, 2) - 0.0055303*Ire(11, 2) + Vim(11, 2) - Vim(12, 2) == 0 subject to Ire_eq_12_2: 0.0001782*Iim(12, 2) - 0.00053461*Ire(12, 2) + Vre(12, 2) - Vre(13, 2) == 0 subject to Iim_eq_12_2: -0.00053461*Iim(12, 2) - 0.0001782*Ire(12, 2) + Vim(12, 2) - Vim(13, 2) == 0 subject to Ire_eq_1_3: 0.36*Iim(1, 3) + Vre(1, 3) - Vre(2, 3) == 0 subject to Iim_eq_1_3: -0.36*Ire(1, 3) + Vim(1, 3) - Vim(2, 3) == 0 subject to Ire_eq_2_3: 0.166*Iim(2, 3) + Vre(1, 3) - Vre(3, 3) == 0 subject to Iim_eq_2_3: -0.166*Ire(2, 3) + Vim(1, 3) - Vim(3, 3) == 0 subject to Ire_eq_3_3: 0.0028237*Iim(3, 3) - 0.039704*Ire(3, 3) + Vre(3, 3) - Vre(7, 3) == 0 subject to Iim_eq_3_3: -0.039704*Iim(3, 3) - 0.0028237*Ire(3, 3) + Vim(3, 3) - Vim(7, 3) == 0 subject to Ire_eq_4_3: 0.014118*Iim(4, 3) - 0.19852*Ire(4, 3) + Vre(4, 3) - Vre(7, 3) == 0 subject to Iim_eq_4_3: -0.19852*Iim(4, 3) - 0.014118*Ire(4, 3) + Vim(4, 3) - Vim(7, 3) == 0 subject to Ire_eq_5_3: 0.029959*Iim(5, 3) - 0.63017*Ire(5, 3) + Vre(5, 3) - Vre(7, 3) == 0 subject to Iim_eq_5_3: -0.63017*Iim(5, 3) - 0.029959*Ire(5, 3) + Vim(5, 3) - Vim(7, 3) == 0 subject to Ire_eq_6_3: 0.034091*Iim(6, 3) - 1.5875*Ire(6, 3) + Vre(6, 3) - Vre(7, 3) == 0 subject to Iim_eq_6_3: -1.5875*Iim(6, 3) - 0.034091*Ire(6, 3) + Vim(6, 3) - Vim(7, 3) == 0 subject to Ire_eq_7_3: 0.034091*Iim(7, 3) - 1.5875*Ire(7, 3) + Vre(7, 3) - Vre(12, 3) == 0 subject to Iim_eq_7_3: -1.5875*Iim(7, 3) - 0.034091*Ire(7, 3) + Vim(7, 3) - Vim(12, 3) == 0 subject to Ire_eq_8_3: 0.017045*Iim(8, 3) - 0.79373*Ire(8, 3) + Vre(8, 3) - Vre(12, 3) == 0 subject to Iim_eq_8_3: -0.79373*Iim(8, 3) - 0.017045*Ire(8, 3) + Vim(8, 3) - Vim(12, 3) == 0 subject to Ire_eq_9_3: 0.032713*Iim(9, 3) - 0.03564*Ire(9, 3) + Vre(9, 3) - Vre(12, 3) == 0 subject to Iim_eq_9_3: -0.03564*Iim(9, 3) - 0.032713*Ire(9, 3) + Vim(9, 3) - Vim(12, 3) == 0 subject to Ire_eq_10_3: 0.00086949*Iim(10, 3) - 0.0028926*Ire(10, 3) + Vre(10, 3) - Vre(12, 3) == 0 subject to Iim_eq_10_3: -0.0028926*Iim(10, 3) - 0.00086949*Ire(10, 3) + Vim(10, 3) - Vim(12, 3) == 0 subject to Ire_eq_11_3: 0.0055303*Iim(11, 3) - 0.0059091*Ire(11, 3) + Vre(11, 3) - Vre(12, 3) == 0 subject to Iim_eq_11_3: -0.0059091*Iim(11, 3) - 0.0055303*Ire(11, 3) + Vim(11, 3) - Vim(12, 3) == 0 subject to Ire_eq_12_3: 0.0001782*Iim(12, 3) - 0.00053461*Ire(12, 3) + Vre(12, 3) - Vre(13, 3) == 0 subject to Iim_eq_12_3: -0.00053461*Iim(12, 3) - 0.0001782*Ire(12, 3) + Vim(12, 3) - Vim(13, 3) == 0 subject to Ire_eq_1_4: 0.36*Iim(1, 4) + Vre(1, 4) - Vre(2, 4) == 0 subject to Iim_eq_1_4: -0.36*Ire(1, 4) + Vim(1, 4) - Vim(2, 4) == 0 subject to Ire_eq_2_4: 0.166*Iim(2, 4) + Vre(1, 4) - Vre(3, 4) == 0 subject to Iim_eq_2_4: -0.166*Ire(2, 4) + Vim(1, 4) - Vim(3, 4) == 0 subject to Ire_eq_3_4: 0.0028237*Iim(3, 4) - 0.039704*Ire(3, 4) + Vre(3, 4) - Vre(7, 4) == 0 subject to Iim_eq_3_4: -0.039704*Iim(3, 4) - 0.0028237*Ire(3, 4) + Vim(3, 4) - Vim(7, 4) == 0 subject to Ire_eq_4_4: 0.014118*Iim(4, 4) - 0.19852*Ire(4, 4) + Vre(4, 4) - Vre(7, 4) == 0 subject to Iim_eq_4_4: -0.19852*Iim(4, 4) - 0.014118*Ire(4, 4) + Vim(4, 4) - Vim(7, 4) == 0 subject to Ire_eq_5_4: 0.029959*Iim(5, 4) - 0.63017*Ire(5, 4) + Vre(5, 4) - Vre(7, 4) == 0 subject to Iim_eq_5_4: -0.63017*Iim(5, 4) - 0.029959*Ire(5, 4) + Vim(5, 4) - Vim(7, 4) == 0 subject to Ire_eq_6_4: 0.034091*Iim(6, 4) - 1.5875*Ire(6, 4) + Vre(6, 4) - Vre(7, 4) == 0 subject to Iim_eq_6_4: -1.5875*Iim(6, 4) - 0.034091*Ire(6, 4) + Vim(6, 4) - Vim(7, 4) == 0 subject to Ire_eq_7_4: 0.034091*Iim(7, 4) - 1.5875*Ire(7, 4) + Vre(7, 4) - Vre(12, 4) == 0 subject to Iim_eq_7_4: -1.5875*Iim(7, 4) - 0.034091*Ire(7, 4) + Vim(7, 4) - Vim(12, 4) == 0 subject to Ire_eq_8_4: 0.017045*Iim(8, 4) - 0.79373*Ire(8, 4) + Vre(8, 4) - Vre(12, 4) == 0 subject to Iim_eq_8_4: -0.79373*Iim(8, 4) - 0.017045*Ire(8, 4) + Vim(8, 4) - Vim(12, 4) == 0 subject to Ire_eq_9_4: 0.032713*Iim(9, 4) - 0.03564*Ire(9, 4) + Vre(9, 4) - Vre(12, 4) == 0 subject to Iim_eq_9_4: -0.03564*Iim(9, 4) - 0.032713*Ire(9, 4) + Vim(9, 4) - Vim(12, 4) == 0 subject to Ire_eq_10_4: 0.00086949*Iim(10, 4) - 0.0028926*Ire(10, 4) + Vre(10, 4) - Vre(12, 4) == 0 subject to Iim_eq_10_4: -0.0028926*Iim(10, 4) - 0.00086949*Ire(10, 4) + Vim(10, 4) - Vim(12, 4) == 0 subject to Ire_eq_11_4: 0.0055303*Iim(11, 4) - 0.0059091*Ire(11, 4) + Vre(11, 4) - Vre(12, 4) == 0 subject to Iim_eq_11_4: -0.0059091*Iim(11, 4) - 0.0055303*Ire(11, 4) + Vim(11, 4) - Vim(12, 4) == 0 subject to Ire_eq_12_4: 0.0001782*Iim(12, 4) - 0.00053461*Ire(12, 4) + Vre(12, 4) - Vre(13, 4) == 0 subject to Iim_eq_12_4: -0.00053461*Iim(12, 4) - 0.0001782*Ire(12, 4) + Vim(12, 4) - Vim(13, 4) == 0 variable bounds: -0.28867 <= Iim(1, 1) <= 0.28867 -1.732 <= Iim(2, 1) <= 1.732 -0.79667 <= Iim(3, 1) <= 0.79667 -0.078 <= Iim(4, 1) <= 0.078 -0.059733 <= Iim(5, 1) <= 0.059733 -0.037447 <= Iim(6, 1) <= 0.037447 -1.0453 <= Iim(7, 1) <= 1.0453 -0.95609 <= Iim(8, 1) <= 0.95609 -0.26133 <= Iim(9, 1) <= 0.26133 -0.2191 <= Iim(10, 1) <= 0.2191 -0.36491 <= Iim(11, 1) <= 0.36491 -1.8245 <= Iim(12, 1) <= 1.8245 -0.28867 <= Iim(1, 2) <= 0.28867 -1.732 <= Iim(2, 2) <= 1.732 -0.79667 <= Iim(3, 2) <= 0.79667 -0.078 <= Iim(4, 2) <= 0.078 -0.059733 <= Iim(5, 2) <= 0.059733 -0.037447 <= Iim(6, 2) <= 0.037447 -1.0453 <= Iim(7, 2) <= 1.0453 -0.95609 <= Iim(8, 2) <= 0.95609 -0.26133 <= Iim(9, 2) <= 0.26133 -0.2191 <= Iim(10, 2) <= 0.2191 -0.36491 <= Iim(11, 2) <= 0.36491 -1.8245 <= Iim(12, 2) <= 1.8245 -0.28867 <= Iim(1, 3) <= 0.28867 -1.732 <= Iim(2, 3) <= 1.732 -0.79667 <= Iim(3, 3) <= 0.79667 -0.078 <= Iim(4, 3) <= 0.078 -0.059733 <= Iim(5, 3) <= 0.059733 -0.037447 <= Iim(6, 3) <= 0.037447 -1.0453 <= Iim(7, 3) <= 1.0453 -0.95609 <= Iim(8, 3) <= 0.95609 -0.26133 <= Iim(9, 3) <= 0.26133 -0.2191 <= Iim(10, 3) <= 0.2191 -0.36491 <= Iim(11, 3) <= 0.36491 -1.8245 <= Iim(12, 3) <= 1.8245 -0.28867 <= Iim(1, 4) <= 0.28867 -1.732 <= Iim(2, 4) <= 1.732 -0.79667 <= Iim(3, 4) <= 0.79667 -0.078 <= Iim(4, 4) <= 0.078 -0.059733 <= Iim(5, 4) <= 0.059733 -0.037447 <= Iim(6, 4) <= 0.037447 -1.0453 <= Iim(7, 4) <= 1.0453 -0.95609 <= Iim(8, 4) <= 0.95609 -0.26133 <= Iim(9, 4) <= 0.26133 -0.2191 <= Iim(10, 4) <= 0.2191 -0.36491 <= Iim(11, 4) <= 0.36491 -1.8245 <= Iim(12, 4) <= 1.8245 -0.28867 <= Ire(1, 1) <= 0.28867 -1.732 <= Ire(2, 1) <= 1.732 -0.79667 <= Ire(3, 1) <= 0.79667 -0.078 <= Ire(4, 1) <= 0.078 -0.059733 <= Ire(5, 1) <= 0.059733 -0.037447 <= Ire(6, 1) <= 0.037447 -1.0453 <= Ire(7, 1) <= 1.0453 -0.95609 <= Ire(8, 1) <= 0.95609 -0.26133 <= Ire(9, 1) <= 0.26133 -0.2191 <= Ire(10, 1) <= 0.2191 -0.36491 <= Ire(11, 1) <= 0.36491 -1.8245 <= Ire(12, 1) <= 1.8245 -0.28867 <= Ire(1, 2) <= 0.28867 -1.732 <= Ire(2, 2) <= 1.732 -0.79667 <= Ire(3, 2) <= 0.79667 -0.078 <= Ire(4, 2) <= 0.078 -0.059733 <= Ire(5, 2) <= 0.059733 -0.037447 <= Ire(6, 2) <= 0.037447 -1.0453 <= Ire(7, 2) <= 1.0453 -0.95609 <= Ire(8, 2) <= 0.95609 -0.26133 <= Ire(9, 2) <= 0.26133 -0.2191 <= Ire(10, 2) <= 0.2191 -0.36491 <= Ire(11, 2) <= 0.36491 -1.8245 <= Ire(12, 2) <= 1.8245 -0.28867 <= Ire(1, 3) <= 0.28867 -1.732 <= Ire(2, 3) <= 1.732 -0.79667 <= Ire(3, 3) <= 0.79667 -0.078 <= Ire(4, 3) <= 0.078 -0.059733 <= Ire(5, 3) <= 0.059733 -0.037447 <= Ire(6, 3) <= 0.037447 -1.0453 <= Ire(7, 3) <= 1.0453 -0.95609 <= Ire(8, 3) <= 0.95609 -0.26133 <= Ire(9, 3) <= 0.26133 -0.2191 <= Ire(10, 3) <= 0.2191 -0.36491 <= Ire(11, 3) <= 0.36491 -1.8245 <= Ire(12, 3) <= 1.8245 -0.28867 <= Ire(1, 4) <= 0.28867 -1.732 <= Ire(2, 4) <= 1.732 -0.79667 <= Ire(3, 4) <= 0.79667 -0.078 <= Ire(4, 4) <= 0.078 -0.059733 <= Ire(5, 4) <= 0.059733 -0.037447 <= Ire(6, 4) <= 0.037447 -1.0453 <= Ire(7, 4) <= 1.0453 -0.95609 <= Ire(8, 4) <= 0.95609 -0.26133 <= Ire(9, 4) <= 0.26133 -0.2191 <= Ire(10, 4) <= 0.2191 -0.36491 <= Ire(11, 4) <= 0.36491 -1.8245 <= Ire(12, 4) <= 1.8245 0 <= LC(1, 1) <= 0 0 <= LC(2, 1) <= 0.05 0 <= LC(3, 1) <= 0 0 <= LC(4, 1) <= 0 0 <= LC(5, 1) <= 0 0 <= LC(6, 1) <= 0 0 <= LC(7, 1) <= 0 0 <= LC(8, 1) <= 0 0 <= LC(9, 1) <= 0 0 <= LC(10, 1) <= 0 0 <= LC(11, 1) <= 0 0 <= LC(12, 1) <= 0 0 <= LC(13, 1) <= 1.2544 0 <= LC(1, 2) <= 0 0 <= LC(2, 2) <= 0.05 0 <= LC(3, 2) <= 0 0 <= LC(4, 2) <= 0 0 <= LC(5, 2) <= 0 0 <= LC(6, 2) <= 0 0 <= LC(7, 2) <= 0 0 <= LC(8, 2) <= 0 0 <= LC(9, 2) <= 0 0 <= LC(10, 2) <= 0 0 <= LC(11, 2) <= 0 0 <= LC(12, 2) <= 0 0 <= LC(13, 2) <= 1.2544 0 <= LC(1, 3) <= 0 0 <= LC(2, 3) <= 0.05 0 <= LC(3, 3) <= 0 0 <= LC(4, 3) <= 0 0 <= LC(5, 3) <= 0 0 <= LC(6, 3) <= 0 0 <= LC(7, 3) <= 0 0 <= LC(8, 3) <= 0 0 <= LC(9, 3) <= 0 0 <= LC(10, 3) <= 0 0 <= LC(11, 3) <= 0 0 <= LC(12, 3) <= 0 0 <= LC(13, 3) <= 1.2544 0 <= LC(1, 4) <= 0 0 <= LC(2, 4) <= 0.05 0 <= LC(3, 4) <= 0 0 <= LC(4, 4) <= 0 0 <= LC(5, 4) <= 0 0 <= LC(6, 4) <= 0 0 <= LC(7, 4) <= 0 0 <= LC(8, 4) <= 0 0 <= LC(9, 4) <= 0 0 <= LC(10, 4) <= 0 0 <= LC(11, 4) <= 0 0 <= LC(12, 4) <= 0 0 <= LC(13, 4) <= 1.2544 0 <= PV_Curtailed(1, 1) <= 0 0 <= PV_Curtailed(2, 1) <= 0 0 <= PV_Curtailed(3, 1) <= 0 0 <= PV_Curtailed(4, 1) <= 0.084267 0 <= PV_Curtailed(5, 1) <= 0.41547 0 <= PV_Curtailed(6, 1) <= 0.45512 0 <= PV_Curtailed(7, 1) <= 0 0 <= PV_Curtailed(8, 1) <= 0 0 <= PV_Curtailed(9, 1) <= 0.2864 0 <= PV_Curtailed(10, 1) <= 0.174 0 <= PV_Curtailed(11, 1) <= 0.095467 0 <= PV_Curtailed(12, 1) <= 0 0 <= PV_Curtailed(13, 1) <= 0 0 <= PV_Curtailed(1, 2) <= 0 0 <= PV_Curtailed(2, 2) <= 0 0 <= PV_Curtailed(3, 2) <= 0 0 <= PV_Curtailed(4, 2) <= 0.084267 0 <= PV_Curtailed(5, 2) <= 0.41547 0 <= PV_Curtailed(6, 2) <= 0.45512 0 <= PV_Curtailed(7, 2) <= 0 0 <= PV_Curtailed(8, 2) <= 0 0 <= PV_Curtailed(9, 2) <= 0.2864 0 <= PV_Curtailed(10, 2) <= 0.174 0 <= PV_Curtailed(11, 2) <= 0.095467 0 <= PV_Curtailed(12, 2) <= 0 0 <= PV_Curtailed(13, 2) <= 0 0 <= PV_Curtailed(1, 3) <= 0 0 <= PV_Curtailed(2, 3) <= 0 0 <= PV_Curtailed(3, 3) <= 0 0 <= PV_Curtailed(4, 3) <= 0.084267 0 <= PV_Curtailed(5, 3) <= 0.41547 0 <= PV_Curtailed(6, 3) <= 0.45512 0 <= PV_Curtailed(7, 3) <= 0 0 <= PV_Curtailed(8, 3) <= 0 0 <= PV_Curtailed(9, 3) <= 0.2864 0 <= PV_Curtailed(10, 3) <= 0.174 0 <= PV_Curtailed(11, 3) <= 0.095467 0 <= PV_Curtailed(12, 3) <= 0 0 <= PV_Curtailed(13, 3) <= 0 0 <= PV_Curtailed(1, 4) <= 0 0 <= PV_Curtailed(2, 4) <= 0 0 <= PV_Curtailed(3, 4) <= 0 0 <= PV_Curtailed(4, 4) <= 0.084267 0 <= PV_Curtailed(5, 4) <= 0.41547 0 <= PV_Curtailed(6, 4) <= 0.45512 0 <= PV_Curtailed(7, 4) <= 0 0 <= PV_Curtailed(8, 4) <= 0 0 <= PV_Curtailed(9, 4) <= 0.2864 0 <= PV_Curtailed(10, 4) <= 0.174 0 <= PV_Curtailed(11, 4) <= 0.095467 0 <= PV_Curtailed(12, 4) <= 0 0 <= PV_Curtailed(13, 4) <= 0 0 <= P_PV(1, 1) <= 0 0 <= P_PV(2, 1) <= 0 0 <= P_PV(3, 1) <= 0 0 <= P_PV(4, 1) <= 0.084267 0 <= P_PV(5, 1) <= 0.41547 0 <= P_PV(6, 1) <= 0.45512 0 <= P_PV(7, 1) <= 0 0 <= P_PV(8, 1) <= 0 0 <= P_PV(9, 1) <= 0.2864 0 <= P_PV(10, 1) <= 0.174 0 <= P_PV(11, 1) <= 0.095467 0 <= P_PV(12, 1) <= 0 0 <= P_PV(13, 1) <= 0 0 <= P_PV(1, 2) <= 0 0 <= P_PV(2, 2) <= 0 0 <= P_PV(3, 2) <= 0 0 <= P_PV(4, 2) <= 0.084267 0 <= P_PV(5, 2) <= 0.41547 0 <= P_PV(6, 2) <= 0.45512 0 <= P_PV(7, 2) <= 0 0 <= P_PV(8, 2) <= 0 0 <= P_PV(9, 2) <= 0.2864 0 <= P_PV(10, 2) <= 0.174 0 <= P_PV(11, 2) <= 0.095467 0 <= P_PV(12, 2) <= 0 0 <= P_PV(13, 2) <= 0 0 <= P_PV(1, 3) <= 0 0 <= P_PV(2, 3) <= 0 0 <= P_PV(3, 3) <= 0 0 <= P_PV(4, 3) <= 0.084267 0 <= P_PV(5, 3) <= 0.41547 0 <= P_PV(6, 3) <= 0.45512 0 <= P_PV(7, 3) <= 0 0 <= P_PV(8, 3) <= 0 0 <= P_PV(9, 3) <= 0.2864 0 <= P_PV(10, 3) <= 0.174 0 <= P_PV(11, 3) <= 0.095467 0 <= P_PV(12, 3) <= 0 0 <= P_PV(13, 3) <= 0 0 <= P_PV(1, 4) <= 0 0 <= P_PV(2, 4) <= 0 0 <= P_PV(3, 4) <= 0 0 <= P_PV(4, 4) <= 0.084267 0 <= P_PV(5, 4) <= 0.41547 0 <= P_PV(6, 4) <= 0.45512 0 <= P_PV(7, 4) <= 0 0 <= P_PV(8, 4) <= 0 0 <= P_PV(9, 4) <= 0.2864 0 <= P_PV(10, 4) <= 0.174 0 <= P_PV(11, 4) <= 0.095467 0 <= P_PV(12, 4) <= 0 0 <= P_PV(13, 4) <= 0 0 <= P_PV_AC(1, 1) <= 0 0 <= P_PV_AC(2, 1) <= 0 0 <= P_PV_AC(3, 1) <= 0 0 <= P_PV_AC(4, 1) <= 0.080053 0 <= P_PV_AC(5, 1) <= 0.39469 0 <= P_PV_AC(6, 1) <= 0.43236 0 <= P_PV_AC(7, 1) <= 0 0 <= P_PV_AC(8, 1) <= 0 0 <= P_PV_AC(9, 1) <= 0.27208 0 <= P_PV_AC(10, 1) <= 0.1653 0 <= P_PV_AC(11, 1) <= 0.090693 0 <= P_PV_AC(12, 1) <= 0 0 <= P_PV_AC(13, 1) <= 0 0 <= P_PV_AC(1, 2) <= 0 0 <= P_PV_AC(2, 2) <= 0 0 <= P_PV_AC(3, 2) <= 0 0 <= P_PV_AC(4, 2) <= 0.080053 0 <= P_PV_AC(5, 2) <= 0.39469 0 <= P_PV_AC(6, 2) <= 0.43236 0 <= P_PV_AC(7, 2) <= 0 0 <= P_PV_AC(8, 2) <= 0 0 <= P_PV_AC(9, 2) <= 0.27208 0 <= P_PV_AC(10, 2) <= 0.1653 0 <= P_PV_AC(11, 2) <= 0.090693 0 <= P_PV_AC(12, 2) <= 0 0 <= P_PV_AC(13, 2) <= 0 0 <= P_PV_AC(1, 3) <= 0 0 <= P_PV_AC(2, 3) <= 0 0 <= P_PV_AC(3, 3) <= 0 0 <= P_PV_AC(4, 3) <= 0.080053 0 <= P_PV_AC(5, 3) <= 0.39469 0 <= P_PV_AC(6, 3) <= 0.43236 0 <= P_PV_AC(7, 3) <= 0 0 <= P_PV_AC(8, 3) <= 0 0 <= P_PV_AC(9, 3) <= 0.27208 0 <= P_PV_AC(10, 3) <= 0.1653 0 <= P_PV_AC(11, 3) <= 0.090693 0 <= P_PV_AC(12, 3) <= 0 0 <= P_PV_AC(13, 3) <= 0 0 <= P_PV_AC(1, 4) <= 0 0 <= P_PV_AC(2, 4) <= 0 0 <= P_PV_AC(3, 4) <= 0 0 <= P_PV_AC(4, 4) <= 0.080053 0 <= P_PV_AC(5, 4) <= 0.39469 0 <= P_PV_AC(6, 4) <= 0.43236 0 <= P_PV_AC(7, 4) <= 0 0 <= P_PV_AC(8, 4) <= 0 0 <= P_PV_AC(9, 4) <= 0.27208 0 <= P_PV_AC(10, 4) <= 0.1653 0 <= P_PV_AC(11, 4) <= 0.090693 0 <= P_PV_AC(12, 4) <= 0 0 <= P_PV_AC(13, 4) <= 0 0 <= P_ch(1, 1) <= 0 0 <= P_ch(2, 1) <= 0 0 <= P_ch(3, 1) <= 0 0 <= P_ch(4, 1) <= 0 0 <= P_ch(5, 1) <= 0 0 <= P_ch(6, 1) <= 0 0 <= P_ch(7, 1) <= 0 0 <= P_ch(8, 1) <= 0.664 0 <= P_ch(9, 1) <= 0 0 <= P_ch(10, 1) <= 0 0 <= P_ch(11, 1) <= 0 0 <= P_ch(12, 1) <= 0 0 <= P_ch(13, 1) <= 0 0 <= P_ch(1, 2) <= 0 0 <= P_ch(2, 2) <= 0 0 <= P_ch(3, 2) <= 0 0 <= P_ch(4, 2) <= 0 0 <= P_ch(5, 2) <= 0 0 <= P_ch(6, 2) <= 0 0 <= P_ch(7, 2) <= 0 0 <= P_ch(8, 2) <= 0.664 0 <= P_ch(9, 2) <= 0 0 <= P_ch(10, 2) <= 0 0 <= P_ch(11, 2) <= 0 0 <= P_ch(12, 2) <= 0 0 <= P_ch(13, 2) <= 0 0 <= P_ch(1, 3) <= 0 0 <= P_ch(2, 3) <= 0 0 <= P_ch(3, 3) <= 0 0 <= P_ch(4, 3) <= 0 0 <= P_ch(5, 3) <= 0 0 <= P_ch(6, 3) <= 0 0 <= P_ch(7, 3) <= 0 0 <= P_ch(8, 3) <= 0.664 0 <= P_ch(9, 3) <= 0 0 <= P_ch(10, 3) <= 0 0 <= P_ch(11, 3) <= 0 0 <= P_ch(12, 3) <= 0 0 <= P_ch(13, 3) <= 0 0 <= P_ch(1, 4) <= 0 0 <= P_ch(2, 4) <= 0 0 <= P_ch(3, 4) <= 0 0 <= P_ch(4, 4) <= 0 0 <= P_ch(5, 4) <= 0 0 <= P_ch(6, 4) <= 0 0 <= P_ch(7, 4) <= 0 0 <= P_ch(8, 4) <= 0.664 0 <= P_ch(9, 4) <= 0 0 <= P_ch(10, 4) <= 0 0 <= P_ch(11, 4) <= 0 0 <= P_ch(12, 4) <= 0 0 <= P_ch(13, 4) <= 0 0 <= P_dis(1, 1) <= 0 0 <= P_dis(2, 1) <= 0 0 <= P_dis(3, 1) <= 0 0 <= P_dis(4, 1) <= 0 0 <= P_dis(5, 1) <= 0 0 <= P_dis(6, 1) <= 0 0 <= P_dis(7, 1) <= 0 0 <= P_dis(8, 1) <= 0.664 0 <= P_dis(9, 1) <= 0 0 <= P_dis(10, 1) <= 0 0 <= P_dis(11, 1) <= 0 0 <= P_dis(12, 1) <= 0 0 <= P_dis(13, 1) <= 0 0 <= P_dis(1, 2) <= 0 0 <= P_dis(2, 2) <= 0 0 <= P_dis(3, 2) <= 0 0 <= P_dis(4, 2) <= 0 0 <= P_dis(5, 2) <= 0 0 <= P_dis(6, 2) <= 0 0 <= P_dis(7, 2) <= 0 0 <= P_dis(8, 2) <= 0.664 0 <= P_dis(9, 2) <= 0 0 <= P_dis(10, 2) <= 0 0 <= P_dis(11, 2) <= 0 0 <= P_dis(12, 2) <= 0 0 <= P_dis(13, 2) <= 0 0 <= P_dis(1, 3) <= 0 0 <= P_dis(2, 3) <= 0 0 <= P_dis(3, 3) <= 0 0 <= P_dis(4, 3) <= 0 0 <= P_dis(5, 3) <= 0 0 <= P_dis(6, 3) <= 0 0 <= P_dis(7, 3) <= 0 0 <= P_dis(8, 3) <= 0.664 0 <= P_dis(9, 3) <= 0 0 <= P_dis(10, 3) <= 0 0 <= P_dis(11, 3) <= 0 0 <= P_dis(12, 3) <= 0 0 <= P_dis(13, 3) <= 0 0 <= P_dis(1, 4) <= 0 0 <= P_dis(2, 4) <= 0 0 <= P_dis(3, 4) <= 0 0 <= P_dis(4, 4) <= 0 0 <= P_dis(5, 4) <= 0 0 <= P_dis(6, 4) <= 0 0 <= P_dis(7, 4) <= 0 0 <= P_dis(8, 4) <= 0.664 0 <= P_dis(9, 4) <= 0 0 <= P_dis(10, 4) <= 0 0 <= P_dis(11, 4) <= 0 0 <= P_dis(12, 4) <= 0 0 <= P_dis(13, 4) <= 0 0 <= P_export(1, 1) 0 <= P_export(2, 1) <= 0 0 <= P_export(3, 1) <= 0 0 <= P_export(4, 1) <= 0 0 <= P_export(5, 1) <= 0 0 <= P_export(6, 1) <= 0 0 <= P_export(7, 1) <= 0 0 <= P_export(8, 1) <= 0 0 <= P_export(9, 1) <= 0 0 <= P_export(10, 1) <= 0 0 <= P_export(11, 1) <= 0 0 <= P_export(12, 1) <= 0 0 <= P_export(13, 1) <= 0 0 <= P_export(1, 2) 0 <= P_export(2, 2) <= 0 0 <= P_export(3, 2) <= 0 0 <= P_export(4, 2) <= 0 0 <= P_export(5, 2) <= 0 0 <= P_export(6, 2) <= 0 0 <= P_export(7, 2) <= 0 0 <= P_export(8, 2) <= 0 0 <= P_export(9, 2) <= 0 0 <= P_export(10, 2) <= 0 0 <= P_export(11, 2) <= 0 0 <= P_export(12, 2) <= 0 0 <= P_export(13, 2) <= 0 0 <= P_export(1, 3) 0 <= P_export(2, 3) <= 0 0 <= P_export(3, 3) <= 0 0 <= P_export(4, 3) <= 0 0 <= P_export(5, 3) <= 0 0 <= P_export(6, 3) <= 0 0 <= P_export(7, 3) <= 0 0 <= P_export(8, 3) <= 0 0 <= P_export(9, 3) <= 0 0 <= P_export(10, 3) <= 0 0 <= P_export(11, 3) <= 0 0 <= P_export(12, 3) <= 0 0 <= P_export(13, 3) <= 0 0 <= P_export(1, 4) 0 <= P_export(2, 4) <= 0 0 <= P_export(3, 4) <= 0 0 <= P_export(4, 4) <= 0 0 <= P_export(5, 4) <= 0 0 <= P_export(6, 4) <= 0 0 <= P_export(7, 4) <= 0 0 <= P_export(8, 4) <= 0 0 <= P_export(9, 4) <= 0 0 <= P_export(10, 4) <= 0 0 <= P_export(11, 4) <= 0 0 <= P_export(12, 4) <= 0 0 <= P_export(13, 4) <= 0 0 <= P_import(1, 1) 0 <= P_import(2, 1) <= 0 0 <= P_import(3, 1) <= 0 0 <= P_import(4, 1) <= 0 0 <= P_import(5, 1) <= 0 0 <= P_import(6, 1) <= 0 0 <= P_import(7, 1) <= 0 0 <= P_import(8, 1) <= 0 0 <= P_import(9, 1) <= 0 0 <= P_import(10, 1) <= 0 0 <= P_import(11, 1) <= 0 0 <= P_import(12, 1) <= 0 0 <= P_import(13, 1) <= 0 0 <= P_import(1, 2) 0 <= P_import(2, 2) <= 0 0 <= P_import(3, 2) <= 0 0 <= P_import(4, 2) <= 0 0 <= P_import(5, 2) <= 0 0 <= P_import(6, 2) <= 0 0 <= P_import(7, 2) <= 0 0 <= P_import(8, 2) <= 0 0 <= P_import(9, 2) <= 0 0 <= P_import(10, 2) <= 0 0 <= P_import(11, 2) <= 0 0 <= P_import(12, 2) <= 0 0 <= P_import(13, 2) <= 0 0 <= P_import(1, 3) 0 <= P_import(2, 3) <= 0 0 <= P_import(3, 3) <= 0 0 <= P_import(4, 3) <= 0 0 <= P_import(5, 3) <= 0 0 <= P_import(6, 3) <= 0 0 <= P_import(7, 3) <= 0 0 <= P_import(8, 3) <= 0 0 <= P_import(9, 3) <= 0 0 <= P_import(10, 3) <= 0 0 <= P_import(11, 3) <= 0 0 <= P_import(12, 3) <= 0 0 <= P_import(13, 3) <= 0 0 <= P_import(1, 4) 0 <= P_import(2, 4) <= 0 0 <= P_import(3, 4) <= 0 0 <= P_import(4, 4) <= 0 0 <= P_import(5, 4) <= 0 0 <= P_import(6, 4) <= 0 0 <= P_import(7, 4) <= 0 0 <= P_import(8, 4) <= 0 0 <= P_import(9, 4) <= 0 0 <= P_import(10, 4) <= 0 0 <= P_import(11, 4) <= 0 0 <= P_import(12, 4) <= 0 0 <= P_import(13, 4) <= 0 0 <= Pb_AC(1, 1) <= 0 0 <= Pb_AC(2, 1) <= 0 0 <= Pb_AC(3, 1) <= 0 0 <= Pb_AC(4, 1) <= 0 0 <= Pb_AC(5, 1) <= 0 0 <= Pb_AC(6, 1) <= 0 0 <= Pb_AC(7, 1) <= 0 -0.664 <= Pb_AC(8, 1) <= 0.664 0 <= Pb_AC(9, 1) <= 0 0 <= Pb_AC(10, 1) <= 0 0 <= Pb_AC(11, 1) <= 0 0 <= Pb_AC(12, 1) <= 0 0 <= Pb_AC(13, 1) <= 0 0 <= Pb_AC(1, 2) <= 0 0 <= Pb_AC(2, 2) <= 0 0 <= Pb_AC(3, 2) <= 0 0 <= Pb_AC(4, 2) <= 0 0 <= Pb_AC(5, 2) <= 0 0 <= Pb_AC(6, 2) <= 0 0 <= Pb_AC(7, 2) <= 0 -0.664 <= Pb_AC(8, 2) <= 0.664 0 <= Pb_AC(9, 2) <= 0 0 <= Pb_AC(10, 2) <= 0 0 <= Pb_AC(11, 2) <= 0 0 <= Pb_AC(12, 2) <= 0 0 <= Pb_AC(13, 2) <= 0 0 <= Pb_AC(1, 3) <= 0 0 <= Pb_AC(2, 3) <= 0 0 <= Pb_AC(3, 3) <= 0 0 <= Pb_AC(4, 3) <= 0 0 <= Pb_AC(5, 3) <= 0 0 <= Pb_AC(6, 3) <= 0 0 <= Pb_AC(7, 3) <= 0 -0.664 <= Pb_AC(8, 3) <= 0.664 0 <= Pb_AC(9, 3) <= 0 0 <= Pb_AC(10, 3) <= 0 0 <= Pb_AC(11, 3) <= 0 0 <= Pb_AC(12, 3) <= 0 0 <= Pb_AC(13, 3) <= 0 0 <= Pb_AC(1, 4) <= 0 0 <= Pb_AC(2, 4) <= 0 0 <= Pb_AC(3, 4) <= 0 0 <= Pb_AC(4, 4) <= 0 0 <= Pb_AC(5, 4) <= 0 0 <= Pb_AC(6, 4) <= 0 0 <= Pb_AC(7, 4) <= 0 -0.664 <= Pb_AC(8, 4) <= 0.664 0 <= Pb_AC(9, 4) <= 0 0 <= Pb_AC(10, 4) <= 0 0 <= Pb_AC(11, 4) <= 0 0 <= Pb_AC(12, 4) <= 0 0 <= Pb_AC(13, 4) <= 0 0 <= Pb_minus(1, 1) 0 <= Pb_minus(2, 1) 0 <= Pb_minus(3, 1) 0 <= Pb_minus(4, 1) 0 <= Pb_minus(5, 1) 0 <= Pb_minus(6, 1) 0 <= Pb_minus(7, 1) 0 <= Pb_minus(8, 1) 0 <= Pb_minus(9, 1) 0 <= Pb_minus(10, 1) 0 <= Pb_minus(11, 1) 0 <= Pb_minus(12, 1) 0 <= Pb_minus(13, 1) 0 <= Pb_minus(1, 2) 0 <= Pb_minus(2, 2) 0 <= Pb_minus(3, 2) 0 <= Pb_minus(4, 2) 0 <= Pb_minus(5, 2) 0 <= Pb_minus(6, 2) 0 <= Pb_minus(7, 2) 0 <= Pb_minus(8, 2) 0 <= Pb_minus(9, 2) 0 <= Pb_minus(10, 2) 0 <= Pb_minus(11, 2) 0 <= Pb_minus(12, 2) 0 <= Pb_minus(13, 2) 0 <= Pb_minus(1, 3) 0 <= Pb_minus(2, 3) 0 <= Pb_minus(3, 3) 0 <= Pb_minus(4, 3) 0 <= Pb_minus(5, 3) 0 <= Pb_minus(6, 3) 0 <= Pb_minus(7, 3) 0 <= Pb_minus(8, 3) 0 <= Pb_minus(9, 3) 0 <= Pb_minus(10, 3) 0 <= Pb_minus(11, 3) 0 <= Pb_minus(12, 3) 0 <= Pb_minus(13, 3) 0 <= Pb_minus(1, 4) 0 <= Pb_minus(2, 4) 0 <= Pb_minus(3, 4) 0 <= Pb_minus(4, 4) 0 <= Pb_minus(5, 4) 0 <= Pb_minus(6, 4) 0 <= Pb_minus(7, 4) 0 <= Pb_minus(8, 4) 0 <= Pb_minus(9, 4) 0 <= Pb_minus(10, 4) 0 <= Pb_minus(11, 4) 0 <= Pb_minus(12, 4) 0 <= Pb_minus(13, 4) 0 <= Pb_plus(1, 1) 0 <= Pb_plus(2, 1) 0 <= Pb_plus(3, 1) 0 <= Pb_plus(4, 1) 0 <= Pb_plus(5, 1) 0 <= Pb_plus(6, 1) 0 <= Pb_plus(7, 1) 0 <= Pb_plus(8, 1) 0 <= Pb_plus(9, 1) 0 <= Pb_plus(10, 1) 0 <= Pb_plus(11, 1) 0 <= Pb_plus(12, 1) 0 <= Pb_plus(13, 1) 0 <= Pb_plus(1, 2) 0 <= Pb_plus(2, 2) 0 <= Pb_plus(3, 2) 0 <= Pb_plus(4, 2) 0 <= Pb_plus(5, 2) 0 <= Pb_plus(6, 2) 0 <= Pb_plus(7, 2) 0 <= Pb_plus(8, 2) 0 <= Pb_plus(9, 2) 0 <= Pb_plus(10, 2) 0 <= Pb_plus(11, 2) 0 <= Pb_plus(12, 2) 0 <= Pb_plus(13, 2) 0 <= Pb_plus(1, 3) 0 <= Pb_plus(2, 3) 0 <= Pb_plus(3, 3) 0 <= Pb_plus(4, 3) 0 <= Pb_plus(5, 3) 0 <= Pb_plus(6, 3) 0 <= Pb_plus(7, 3) 0 <= Pb_plus(8, 3) 0 <= Pb_plus(9, 3) 0 <= Pb_plus(10, 3) 0 <= Pb_plus(11, 3) 0 <= Pb_plus(12, 3) 0 <= Pb_plus(13, 3) 0 <= Pb_plus(1, 4) 0 <= Pb_plus(2, 4) 0 <= Pb_plus(3, 4) 0 <= Pb_plus(4, 4) 0 <= Pb_plus(5, 4) 0 <= Pb_plus(6, 4) 0 <= Pb_plus(7, 4) 0 <= Pb_plus(8, 4) 0 <= Pb_plus(9, 4) 0 <= Pb_plus(10, 4) 0 <= Pb_plus(11, 4) 0 <= Pb_plus(12, 4) 0 <= Pb_plus(13, 4) 0 <= QLC(1, 1) <= 0 0 <= QLC(2, 1) <= 0 0 <= QLC(3, 1) <= 0 0 <= QLC(4, 1) <= 0 0 <= QLC(5, 1) <= 0 0 <= QLC(6, 1) <= 0 0 <= QLC(7, 1) <= 0 0 <= QLC(8, 1) <= 0 0 <= QLC(9, 1) <= 0 0 <= QLC(10, 1) <= 0 0 <= QLC(11, 1) <= 0 0 <= QLC(12, 1) <= 0 0 <= QLC(13, 1) <= 0.36587 0 <= QLC(1, 2) <= 0 0 <= QLC(2, 2) <= 0 0 <= QLC(3, 2) <= 0 0 <= QLC(4, 2) <= 0 0 <= QLC(5, 2) <= 0 0 <= QLC(6, 2) <= 0 0 <= QLC(7, 2) <= 0 0 <= QLC(8, 2) <= 0 0 <= QLC(9, 2) <= 0 0 <= QLC(10, 2) <= 0 0 <= QLC(11, 2) <= 0 0 <= QLC(12, 2) <= 0 0 <= QLC(13, 2) <= 0.36587 0 <= QLC(1, 3) <= 0 0 <= QLC(2, 3) <= 0 0 <= QLC(3, 3) <= 0 0 <= QLC(4, 3) <= 0 0 <= QLC(5, 3) <= 0 0 <= QLC(6, 3) <= 0 0 <= QLC(7, 3) <= 0 0 <= QLC(8, 3) <= 0 0 <= QLC(9, 3) <= 0 0 <= QLC(10, 3) <= 0 0 <= QLC(11, 3) <= 0 0 <= QLC(12, 3) <= 0 0 <= QLC(13, 3) <= 0.36587 0 <= QLC(1, 4) <= 0 0 <= QLC(2, 4) <= 0 0 <= QLC(3, 4) <= 0 0 <= QLC(4, 4) <= 0 0 <= QLC(5, 4) <= 0 0 <= QLC(6, 4) <= 0 0 <= QLC(7, 4) <= 0 0 <= QLC(8, 4) <= 0 0 <= QLC(9, 4) <= 0 0 <= QLC(10, 4) <= 0 0 <= QLC(11, 4) <= 0 0 <= QLC(12, 4) <= 0 0 <= QLC(13, 4) <= 0.36587 0 <= Qb(1, 1) <= 0 0 <= Qb(2, 1) <= 0 0 <= Qb(3, 1) <= 0 0 <= Qb(4, 1) <= 0 0 <= Qb(5, 1) <= 0 0 <= Qb(6, 1) <= 0 0 <= Qb(7, 1) <= 0 -0.664 <= Qb(8, 1) <= 0.664 0 <= Qb(9, 1) <= 0 0 <= Qb(10, 1) <= 0 0 <= Qb(11, 1) <= 0 0 <= Qb(12, 1) <= 0 0 <= Qb(13, 1) <= 0 0 <= Qb(1, 2) <= 0 0 <= Qb(2, 2) <= 0 0 <= Qb(3, 2) <= 0 0 <= Qb(4, 2) <= 0 0 <= Qb(5, 2) <= 0 0 <= Qb(6, 2) <= 0 0 <= Qb(7, 2) <= 0 -0.664 <= Qb(8, 2) <= 0.664 0 <= Qb(9, 2) <= 0 0 <= Qb(10, 2) <= 0 0 <= Qb(11, 2) <= 0 0 <= Qb(12, 2) <= 0 0 <= Qb(13, 2) <= 0 0 <= Qb(1, 3) <= 0 0 <= Qb(2, 3) <= 0 0 <= Qb(3, 3) <= 0 0 <= Qb(4, 3) <= 0 0 <= Qb(5, 3) <= 0 0 <= Qb(6, 3) <= 0 0 <= Qb(7, 3) <= 0 -0.664 <= Qb(8, 3) <= 0.664 0 <= Qb(9, 3) <= 0 0 <= Qb(10, 3) <= 0 0 <= Qb(11, 3) <= 0 0 <= Qb(12, 3) <= 0 0 <= Qb(13, 3) <= 0 0 <= Qb(1, 4) <= 0 0 <= Qb(2, 4) <= 0 0 <= Qb(3, 4) <= 0 0 <= Qb(4, 4) <= 0 0 <= Qb(5, 4) <= 0 0 <= Qb(6, 4) <= 0 0 <= Qb(7, 4) <= 0 -0.664 <= Qb(8, 4) <= 0.664 0 <= Qb(9, 4) <= 0 0 <= Qb(10, 4) <= 0 0 <= Qb(11, 4) <= 0 0 <= Qb(12, 4) <= 0 0 <= Qb(13, 4) <= 0 0 <= Qb_minus(1, 1) 0 <= Qb_minus(2, 1) 0 <= Qb_minus(3, 1) 0 <= Qb_minus(4, 1) 0 <= Qb_minus(5, 1) 0 <= Qb_minus(6, 1) 0 <= Qb_minus(7, 1) 0 <= Qb_minus(8, 1) 0 <= Qb_minus(9, 1) 0 <= Qb_minus(10, 1) 0 <= Qb_minus(11, 1) 0 <= Qb_minus(12, 1) 0 <= Qb_minus(13, 1) 0 <= Qb_minus(1, 2) 0 <= Qb_minus(2, 2) 0 <= Qb_minus(3, 2) 0 <= Qb_minus(4, 2) 0 <= Qb_minus(5, 2) 0 <= Qb_minus(6, 2) 0 <= Qb_minus(7, 2) 0 <= Qb_minus(8, 2) 0 <= Qb_minus(9, 2) 0 <= Qb_minus(10, 2) 0 <= Qb_minus(11, 2) 0 <= Qb_minus(12, 2) 0 <= Qb_minus(13, 2) 0 <= Qb_minus(1, 3) 0 <= Qb_minus(2, 3) 0 <= Qb_minus(3, 3) 0 <= Qb_minus(4, 3) 0 <= Qb_minus(5, 3) 0 <= Qb_minus(6, 3) 0 <= Qb_minus(7, 3) 0 <= Qb_minus(8, 3) 0 <= Qb_minus(9, 3) 0 <= Qb_minus(10, 3) 0 <= Qb_minus(11, 3) 0 <= Qb_minus(12, 3) 0 <= Qb_minus(13, 3) 0 <= Qb_minus(1, 4) 0 <= Qb_minus(2, 4) 0 <= Qb_minus(3, 4) 0 <= Qb_minus(4, 4) 0 <= Qb_minus(5, 4) 0 <= Qb_minus(6, 4) 0 <= Qb_minus(7, 4) 0 <= Qb_minus(8, 4) 0 <= Qb_minus(9, 4) 0 <= Qb_minus(10, 4) 0 <= Qb_minus(11, 4) 0 <= Qb_minus(12, 4) 0 <= Qb_minus(13, 4) 0 <= Qb_plus(1, 1) 0 <= Qb_plus(2, 1) 0 <= Qb_plus(3, 1) 0 <= Qb_plus(4, 1) 0 <= Qb_plus(5, 1) 0 <= Qb_plus(6, 1) 0 <= Qb_plus(7, 1) 0 <= Qb_plus(8, 1) 0 <= Qb_plus(9, 1) 0 <= Qb_plus(10, 1) 0 <= Qb_plus(11, 1) 0 <= Qb_plus(12, 1) 0 <= Qb_plus(13, 1) 0 <= Qb_plus(1, 2) 0 <= Qb_plus(2, 2) 0 <= Qb_plus(3, 2) 0 <= Qb_plus(4, 2) 0 <= Qb_plus(5, 2) 0 <= Qb_plus(6, 2) 0 <= Qb_plus(7, 2) 0 <= Qb_plus(8, 2) 0 <= Qb_plus(9, 2) 0 <= Qb_plus(10, 2) 0 <= Qb_plus(11, 2) 0 <= Qb_plus(12, 2) 0 <= Qb_plus(13, 2) 0 <= Qb_plus(1, 3) 0 <= Qb_plus(2, 3) 0 <= Qb_plus(3, 3) 0 <= Qb_plus(4, 3) 0 <= Qb_plus(5, 3) 0 <= Qb_plus(6, 3) 0 <= Qb_plus(7, 3) 0 <= Qb_plus(8, 3) 0 <= Qb_plus(9, 3) 0 <= Qb_plus(10, 3) 0 <= Qb_plus(11, 3) 0 <= Qb_plus(12, 3) 0 <= Qb_plus(13, 3) 0 <= Qb_plus(1, 4) 0 <= Qb_plus(2, 4) 0 <= Qb_plus(3, 4) 0 <= Qb_plus(4, 4) 0 <= Qb_plus(5, 4) 0 <= Qb_plus(6, 4) 0 <= Qb_plus(7, 4) 0 <= Qb_plus(8, 4) 0 <= Qb_plus(9, 4) 0 <= Qb_plus(10, 4) 0 <= Qb_plus(11, 4) 0 <= Qb_plus(12, 4) 0 <= Qb_plus(13, 4) 0 <= SOC(1, 1) <= 0 0 <= SOC(2, 1) <= 0 0 <= SOC(3, 1) <= 0 0 <= SOC(4, 1) <= 0 0 <= SOC(5, 1) <= 0 0 <= SOC(6, 1) <= 0 0 <= SOC(7, 1) <= 0 0.664 <= SOC(8, 1) <= 3.32 0 <= SOC(9, 1) <= 0 0 <= SOC(10, 1) <= 0 0 <= SOC(11, 1) <= 0 0 <= SOC(12, 1) <= 0 0 <= SOC(13, 1) <= 0 0 <= SOC(1, 2) <= 0 0 <= SOC(2, 2) <= 0 0 <= SOC(3, 2) <= 0 0 <= SOC(4, 2) <= 0 0 <= SOC(5, 2) <= 0 0 <= SOC(6, 2) <= 0 0 <= SOC(7, 2) <= 0 0.664 <= SOC(8, 2) <= 3.32 0 <= SOC(9, 2) <= 0 0 <= SOC(10, 2) <= 0 0 <= SOC(11, 2) <= 0 0 <= SOC(12, 2) <= 0 0 <= SOC(13, 2) <= 0 0 <= SOC(1, 3) <= 0 0 <= SOC(2, 3) <= 0 0 <= SOC(3, 3) <= 0 0 <= SOC(4, 3) <= 0 0 <= SOC(5, 3) <= 0 0 <= SOC(6, 3) <= 0 0 <= SOC(7, 3) <= 0 0.664 <= SOC(8, 3) <= 3.32 0 <= SOC(9, 3) <= 0 0 <= SOC(10, 3) <= 0 0 <= SOC(11, 3) <= 0 0 <= SOC(12, 3) <= 0 0 <= SOC(13, 3) <= 0 0 <= SOC(1, 4) <= 0 0 <= SOC(2, 4) <= 0 0 <= SOC(3, 4) <= 0 0 <= SOC(4, 4) <= 0 0 <= SOC(5, 4) <= 0 0 <= SOC(6, 4) <= 0 0 <= SOC(7, 4) <= 0 0.664 <= SOC(8, 4) <= 3.32 0 <= SOC(9, 4) <= 0 0 <= SOC(10, 4) <= 0 0 <= SOC(11, 4) <= 0 0 <= SOC(12, 4) <= 0 0 <= SOC(13, 4) <= 0 -0.5 <= Vim(1, 1) <= 0.5 -0.5 <= Vim(2, 1) <= 0.5 -0.5 <= Vim(3, 1) <= 0.5 -0.5 <= Vim(4, 1) <= 0.5 -0.5 <= Vim(5, 1) <= 0.5 -0.5 <= Vim(6, 1) <= 0.5 -0.5 <= Vim(7, 1) <= 0.5 -0.5 <= Vim(8, 1) <= 0.5 -0.5 <= Vim(9, 1) <= 0.5 -0.5 <= Vim(10, 1) <= 0.5 -0.5 <= Vim(11, 1) <= 0.5 -0.5 <= Vim(12, 1) <= 0.5 -0.5 <= Vim(13, 1) <= 0.5 -0.5 <= Vim(1, 2) <= 0.5 -0.5 <= Vim(2, 2) <= 0.5 -0.5 <= Vim(3, 2) <= 0.5 -0.5 <= Vim(4, 2) <= 0.5 -0.5 <= Vim(5, 2) <= 0.5 -0.5 <= Vim(6, 2) <= 0.5 -0.5 <= Vim(7, 2) <= 0.5 -0.5 <= Vim(8, 2) <= 0.5 -0.5 <= Vim(9, 2) <= 0.5 -0.5 <= Vim(10, 2) <= 0.5 -0.5 <= Vim(11, 2) <= 0.5 -0.5 <= Vim(12, 2) <= 0.5 -0.5 <= Vim(13, 2) <= 0.5 -0.5 <= Vim(1, 3) <= 0.5 -0.5 <= Vim(2, 3) <= 0.5 -0.5 <= Vim(3, 3) <= 0.5 -0.5 <= Vim(4, 3) <= 0.5 -0.5 <= Vim(5, 3) <= 0.5 -0.5 <= Vim(6, 3) <= 0.5 -0.5 <= Vim(7, 3) <= 0.5 -0.5 <= Vim(8, 3) <= 0.5 -0.5 <= Vim(9, 3) <= 0.5 -0.5 <= Vim(10, 3) <= 0.5 -0.5 <= Vim(11, 3) <= 0.5 -0.5 <= Vim(12, 3) <= 0.5 -0.5 <= Vim(13, 3) <= 0.5 -0.5 <= Vim(1, 4) <= 0.5 -0.5 <= Vim(2, 4) <= 0.5 -0.5 <= Vim(3, 4) <= 0.5 -0.5 <= Vim(4, 4) <= 0.5 -0.5 <= Vim(5, 4) <= 0.5 -0.5 <= Vim(6, 4) <= 0.5 -0.5 <= Vim(7, 4) <= 0.5 -0.5 <= Vim(8, 4) <= 0.5 -0.5 <= Vim(9, 4) <= 0.5 -0.5 <= Vim(10, 4) <= 0.5 -0.5 <= Vim(11, 4) <= 0.5 -0.5 <= Vim(12, 4) <= 0.5 -0.5 <= Vim(13, 4) <= 0.5 0.9 <= Vre(1, 1) <= 1.1 0.9 <= Vre(2, 1) <= 1.1 0.9 <= Vre(3, 1) <= 1.1 0.9 <= Vre(4, 1) <= 1.1 0.9 <= Vre(5, 1) <= 1.1 0.9 <= Vre(6, 1) <= 1.1 0.9 <= Vre(7, 1) <= 1.1 0.9 <= Vre(8, 1) <= 1.1 0.9 <= Vre(9, 1) <= 1.1 0.9 <= Vre(10, 1) <= 1.1 0.9 <= Vre(11, 1) <= 1.1 0.9 <= Vre(12, 1) <= 1.1 0.9 <= Vre(13, 1) <= 1.1 0.9 <= Vre(1, 2) <= 1.1 0.9 <= Vre(2, 2) <= 1.1 0.9 <= Vre(3, 2) <= 1.1 0.9 <= Vre(4, 2) <= 1.1 0.9 <= Vre(5, 2) <= 1.1 0.9 <= Vre(6, 2) <= 1.1 0.9 <= Vre(7, 2) <= 1.1 0.9 <= Vre(8, 2) <= 1.1 0.9 <= Vre(9, 2) <= 1.1 0.9 <= Vre(10, 2) <= 1.1 0.9 <= Vre(11, 2) <= 1.1 0.9 <= Vre(12, 2) <= 1.1 0.9 <= Vre(13, 2) <= 1.1 0.9 <= Vre(1, 3) <= 1.1 0.9 <= Vre(2, 3) <= 1.1 0.9 <= Vre(3, 3) <= 1.1 0.9 <= Vre(4, 3) <= 1.1 0.9 <= Vre(5, 3) <= 1.1 0.9 <= Vre(6, 3) <= 1.1 0.9 <= Vre(7, 3) <= 1.1 0.9 <= Vre(8, 3) <= 1.1 0.9 <= Vre(9, 3) <= 1.1 0.9 <= Vre(10, 3) <= 1.1 0.9 <= Vre(11, 3) <= 1.1 0.9 <= Vre(12, 3) <= 1.1 0.9 <= Vre(13, 3) <= 1.1 0.9 <= Vre(1, 4) <= 1.1 0.9 <= Vre(2, 4) <= 1.1 0.9 <= Vre(3, 4) <= 1.1 0.9 <= Vre(4, 4) <= 1.1 0.9 <= Vre(5, 4) <= 1.1 0.9 <= Vre(6, 4) <= 1.1 0.9 <= Vre(7, 4) <= 1.1 0.9 <= Vre(8, 4) <= 1.1 0.9 <= Vre(9, 4) <= 1.1 0.9 <= Vre(10, 4) <= 1.1 0.9 <= Vre(11, 4) <= 1.1 0.9 <= Vre(12, 4) <= 1.1 0.9 <= Vre(13, 4) <= 1.1
[sol, fval] = solve(linprob);
Solving problem using linprog. Optimal solution found.
% Display results
fprintf('Optimal Results:\n');
Optimal Results:
disp('Optimal PV Generation:');
Optimal PV Generation:
disp(sol.P_PV);
0 0 0 0 0 0 0 0 0 0 0 0 0.0821 0.0821 0.0821 0.0821 0.0629 0.0629 0.0629 0.0629 0.0394 0.0394 0.0394 0.0394 0 0 0 0 0 0 0 0 0.2751 0.2751 0.2751 0.2751 0.1740 0.1740 0.1740 0.1740 0.0955 0.0955 0.0955 0.0955 0 0 0 0 0 0 0 0
disp('Power Imported from Grid at Bus 1:');
Power Imported from Grid at Bus 1:
disp(sol.P_import);
0.6119 0.6119 0.6119 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
disp('Power Exported to Grid at Bus 1:');
Power Exported to Grid at Bus 1:
disp(sol.P_export);
0 0 0 0.0189 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
disp('Load Curtailment:');
Load Curtailment:
disp(sol.LC);
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
disp('solar Curtailment:');
solar Curtailment:
disp(sol.PV_Curtailed);
0 0 0 0 0 0 0 0 0 0 0 0 0.0022 0.0022 0.0022 0.0022 0.3526 0.3526 0.3526 0.3526 0.4157 0.4157 0.4157 0.4157 0 0 0 0 0 0 0 0 0.0113 0.0113 0.0113 0.0113 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
disp('Reactive Power Flow (Qij):');
Reactive Power Flow (Qij):
disp(sol.Qij);
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.3659 0.3659 0.3659 0.3659 0 0 0 0 0 0 0 0 0 0 0 0 0.3659 0.3659 0.3659 0.3659
disp('Reactive Load Curtailment:');
Reactive Load Curtailment:
disp(sol.QLC);
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
disp('Active Power Flow (Pij):');
Active Power Flow (Pij):
disp(sol.Power_Flow_ft);
0.0500 0.0500 0.0500 0.0500 0.5619 0.5619 0.5619 -0.0689 0.5619 0.5619 0.5619 -0.0689 0.0780 0.0780 0.0780 0.0780 0.0597 0.0597 0.0597 0.0597 0.0374 0.0374 0.0374 0.0374 0.7371 0.7371 0.7371 0.1063 0 0 0 0.6308 0.2613 0.2613 0.2613 0.2613 0.1653 0.1653 0.1653 0.1653 0.0907 0.0907 0.0907 0.0907 1.2544 1.2544 1.2544 1.2544
disp('State of Charge (SOC):');
State of Charge (SOC):
disp(sol.SOC);
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.6640 0.6640 0.6640 0.6640 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
disp('Real Part of Current (Ire):');
Real Part of Current (Ire):
disp(sol.Ire); % Display real part of current for each branch and time step
-0.2887 -0.2887 -0.2887 -0.2887 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -0.0000 -0.0000 -0.0000 -0.0000 0.2518 0.2518 0.2518 0.2518 -0.0151 -0.0151 -0.0097 -0.0151 -0.0659 -0.0659 -0.0659 -0.0659 -0.0915 -0.0915 -0.0583 -0.0915 0.6082 0.6082 0.3878 0.6082
disp('Imaginary Part of Current (Iim):');
Imaginary Part of Current (Iim):
disp(sol.Iim); % Display imaginary part of current for each branch and time step
-0.2887 -0.2887 -0.2887 -0.2887 -0.6260 -0.6260 -0.6260 -0.6260 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -0.0007 -0.0007 -0.0004 -0.0007 -0.0068 -0.0068 -0.0063 -0.0068 -0.0165 -0.0165 -0.0105 -0.0165 -0.2191 -0.2191 -0.2191 -0.2191 -0.0978 -0.0978 -0.0623 -0.0978 1.8245 1.8245 1.1633 1.8245
disp('Battery charging power:');
Battery charging power:
disp(sol.P_ch);
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
disp('Battery discharging power:');
Battery discharging power:
disp(sol.P_dis);
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.6640 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
disp('Battery AC real power:');
Battery AC real power:
disp(sol.Pb_AC);
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.5976 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
disp('Battery AC reactive power:');
Battery AC reactive power:
disp(sol.Qb);
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.3659 0.3659 0.3659 0.3659 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
disp('PV AC power:');
PV AC power:
disp(sol.P_PV_AC);
0 0 0 0 0 0 0 0 0 0 0 0 0.0780 0.0780 0.0780 0.0780 0.0597 0.0597 0.0597 0.0597 0.0374 0.0374 0.0374 0.0374 0 0 0 0 0 0 0 0 0.2613 0.2613 0.2613 0.2613 0.1653 0.1653 0.1653 0.1653 0.0907 0.0907 0.0907 0.0907 0 0 0 0 0 0 0 0
disp('PV Ire:');
PV Ire:
disp(sol.Ire);
-0.2887 -0.2887 -0.2887 -0.2887 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -0.0000 -0.0000 -0.0000 -0.0000 0.2518 0.2518 0.2518 0.2518 -0.0151 -0.0151 -0.0097 -0.0151 -0.0659 -0.0659 -0.0659 -0.0659 -0.0915 -0.0915 -0.0583 -0.0915 0.6082 0.6082 0.3878 0.6082
disp('PV Iim:');
PV Iim:
disp(sol.Iim);
-0.2887 -0.2887 -0.2887 -0.2887 -0.6260 -0.6260 -0.6260 -0.6260 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -0.0007 -0.0007 -0.0004 -0.0007 -0.0068 -0.0068 -0.0063 -0.0068 -0.0165 -0.0165 -0.0105 -0.0165 -0.2191 -0.2191 -0.2191 -0.2191 -0.0978 -0.0978 -0.0623 -0.0978 1.8245 1.8245 1.1633 1.8245
disp('Vre:');
Vre:
disp(sol.Vre);
1.0039 1.0039 1.0039 1.0039 0.9000 0.9000 0.9000 0.9000 0.9000 0.9000 0.9000 0.9000 0.9000 0.9000 0.9000 0.9000 0.9000 0.9000 0.9000 0.9000 0.9000 0.9000 0.9000 0.9000 0.9000 0.9000 0.9000 0.9000 1.1000 1.1000 1.1000 1.1000 0.9000 0.9000 0.9000 0.9000 0.9000 0.9000 0.9000 0.9000 0.9000 0.9000 0.9000 0.9000 0.9000 0.9000 0.9000 0.9000 0.9000 0.9000 0.9000 0.9000
disp('Vim:');
Vim:
disp(sol.Vim);
-0.5000 -0.5000 -0.5000 -0.5000 -0.3961 -0.3961 -0.3961 -0.3961 -0.5000 -0.5000 -0.5000 -0.5000 -0.5000 -0.5000 -0.5000 -0.5000 -0.5000 -0.5000 -0.5000 -0.5000 -0.5000 -0.5000 -0.5000 -0.5000 -0.5000 -0.5000 -0.5000 -0.5000 -0.5000 -0.5000 -0.5000 -0.5000 -0.5000 -0.5000 -0.5000 -0.5000 -0.4996 -0.4996 -0.5000 -0.4996 -0.5000 -0.5000 -0.5000 -0.5000 -0.4989 -0.4989 -0.4993 -0.4989 -0.5000 -0.5000 -0.5000 -0.5000
% Extract the solution for (slack variable)
Ps_solution = sol.Ps1;
Ps_solution1 = sol.Ps;
% Display the slack variable for each bus and time step
for bus = 1:nbus
for t = 1:h
fprintf('Slack variable at Bus %d, Time step %d: %.4f\n', bus, t, Ps_solution(bus, t))
end
end
Slack variable at Bus 1, Time step 1: 0.0000 Slack variable at Bus 1, Time step 2: 0.0000 Slack variable at Bus 1, Time step 3: 0.0000 Slack variable at Bus 1, Time step 4: 0.0000 Slack variable at Bus 2, Time step 1: 0.2580 Slack variable at Bus 2, Time step 2: 0.2580 Slack variable at Bus 2, Time step 3: 0.2580 Slack variable at Bus 2, Time step 4: 0.2580 Slack variable at Bus 3, Time step 1: 1.4045 Slack variable at Bus 3, Time step 2: 1.4045 Slack variable at Bus 3, Time step 3: 1.4045 Slack variable at Bus 3, Time step 4: 1.4045 Slack variable at Bus 4, Time step 1: 0.1604 Slack variable at Bus 4, Time step 2: 0.1604 Slack variable at Bus 4, Time step 3: 0.1604 Slack variable at Bus 4, Time step 4: 0.1604 Slack variable at Bus 5, Time step 1: 0.0339 Slack variable at Bus 5, Time step 2: 0.0339 Slack variable at Bus 5, Time step 3: 0.0339 Slack variable at Bus 5, Time step 4: 0.0339 Slack variable at Bus 6, Time step 1: 0.0061 Slack variable at Bus 6, Time step 2: 0.0061 Slack variable at Bus 6, Time step 3: 0.0061 Slack variable at Bus 6, Time step 4: 0.0061 Slack variable at Bus 7, Time step 1: 1.0078 Slack variable at Bus 7, Time step 2: 1.0078 Slack variable at Bus 7, Time step 3: 1.0081 Slack variable at Bus 7, Time step 4: 1.0078 Slack variable at Bus 8, Time step 1: 0.0081 Slack variable at Bus 8, Time step 2: 0.0081 Slack variable at Bus 8, Time step 3: 0.0086 Slack variable at Bus 8, Time step 4: 0.0081 Slack variable at Bus 9, Time step 1: 6.2731 Slack variable at Bus 9, Time step 2: 6.2731 Slack variable at Bus 9, Time step 3: 6.2791 Slack variable at Bus 9, Time step 4: 6.2731 Slack variable at Bus 10, Time step 1: 44.1423 Slack variable at Bus 10, Time step 2: 44.1423 Slack variable at Bus 10, Time step 3: 44.1423 Slack variable at Bus 10, Time step 4: 44.1423 Slack variable at Bus 11, Time step 1: 37.8962 Slack variable at Bus 11, Time step 2: 37.8962 Slack variable at Bus 11, Time step 3: 37.9316 Slack variable at Bus 11, Time step 4: 37.8962 Slack variable at Bus 12, Time step 1: 342.7872 Slack variable at Bus 12, Time step 2: 342.7872 Slack variable at Bus 12, Time step 3: 342.0839 Slack variable at Bus 12, Time step 4: 342.7872 Slack variable at Bus 13, Time step 1: 249.1044 Slack variable at Bus 13, Time step 2: 249.1044 Slack variable at Bus 13, Time step 3: 249.7656 Slack variable at Bus 13, Time step 4: 249.1044
% Display the slack variable for each bus and time step
for bus = 1:nbus
for t = 1:h
fprintf('Slack variable at Bus %d, Time step %d: %.4f\n', bus, t, Ps_solution1(bus, t))
end
end
Slack variable at Bus 1, Time step 1: 0.0000 Slack variable at Bus 1, Time step 2: 0.0000 Slack variable at Bus 1, Time step 3: 0.0000 Slack variable at Bus 1, Time step 4: 0.0000 Slack variable at Bus 2, Time step 1: -1.0452 Slack variable at Bus 2, Time step 2: -1.0452 Slack variable at Bus 2, Time step 3: -1.0452 Slack variable at Bus 2, Time step 4: -1.0452 Slack variable at Bus 3, Time step 1: -2.5664 Slack variable at Bus 3, Time step 2: -2.5664 Slack variable at Bus 3, Time step 3: -2.5664 Slack variable at Bus 3, Time step 4: -2.5664 Slack variable at Bus 4, Time step 1: 0.0891 Slack variable at Bus 4, Time step 2: 0.0891 Slack variable at Bus 4, Time step 3: 0.0891 Slack variable at Bus 4, Time step 4: 0.0891 Slack variable at Bus 5, Time step 1: 0.0188 Slack variable at Bus 5, Time step 2: 0.0188 Slack variable at Bus 5, Time step 3: 0.0188 Slack variable at Bus 5, Time step 4: 0.0188 Slack variable at Bus 6, Time step 1: 0.0034 Slack variable at Bus 6, Time step 2: 0.0034 Slack variable at Bus 6, Time step 3: 0.0034 Slack variable at Bus 6, Time step 4: 0.0034 Slack variable at Bus 7, Time step 1: 0.5603 Slack variable at Bus 7, Time step 2: 0.5603 Slack variable at Bus 7, Time step 3: 0.5603 Slack variable at Bus 7, Time step 4: 0.5603 Slack variable at Bus 8, Time step 1: 0.2586 Slack variable at Bus 8, Time step 2: 0.2586 Slack variable at Bus 8, Time step 3: 0.2586 Slack variable at Bus 8, Time step 4: -0.4054 Slack variable at Bus 9, Time step 1: 3.4791 Slack variable at Bus 9, Time step 2: 3.4791 Slack variable at Bus 9, Time step 3: 3.4846 Slack variable at Bus 9, Time step 4: 3.4791 Slack variable at Bus 10, Time step 1: 24.5600 Slack variable at Bus 10, Time step 2: 24.5600 Slack variable at Bus 10, Time step 3: 24.5794 Slack variable at Bus 10, Time step 4: 24.5600 Slack variable at Bus 11, Time step 1: 21.0162 Slack variable at Bus 11, Time step 2: 21.0162 Slack variable at Bus 11, Time step 3: 21.0494 Slack variable at Bus 11, Time step 4: 21.0162 Slack variable at Bus 12, Time step 1: 189.3531 Slack variable at Bus 12, Time step 2: 189.3531 Slack variable at Bus 12, Time step 3: 189.2427 Slack variable at Bus 12, Time step 4: 189.3531 Slack variable at Bus 13, Time step 1: 140.5657 Slack variable at Bus 13, Time step 2: 140.5657 Slack variable at Bus 13, Time step 3: 140.7861 Slack variable at Bus 13, Time step 4: 140.5657
fprintf('Total Cost: %.2f\n', fval);
Total Cost: 344.48
%And below is linearized volt/var function calculating A,B,C matrixes
function Matrix = Linear_Load_Flow_Matrixx(branch, bus, baseMVA, VS, slack)
% Inputs:
% branch: matrix of branch data [from_bus, to_bus, r, x, b]
% bus: matrix of bus data [bus_id, P_load, Q_load]
% baseMVA: base power for system normalization
for t = 1:size(bus, 3)
NL = size(branch, 1); % number of lines
NN = size(bus, 1); % number of buses
Ybus = zeros(NN); % Initialize Ybus matrix
SP = zeros(NN, 1); % Constant power loads
SZ = zeros(NN, 1); % Constant impedance loads (optional, unused here)
SI = zeros(NN, 1); % Constant current loads (optional, unused here)
% Constructing the Ybus matrix
for k = 1:NL
N1 = branch(k, 1); % From bus
N2 = branch(k, 2); % To bus
r = branch(k, 3); % Resistance
x = branch(k, 4); % Reactance
b = branch(k, 5); % Line charging susceptance
ykm = 1 / (r + 1j * x); % Admittance (ykm)
bkm = 1j * b / 2; % Susceptance (bkm/2)
% Adding the elements to Ybus
Ybus(N1, N1) = Ybus(N1, N1) + ykm + bkm;
Ybus(N1, N2) = Ybus(N1, N2) - ykm;
Ybus(N2, N1) = Ybus(N2, N1) - ykm;
Ybus(N2, N2) = Ybus(N2, N2) + ykm + bkm;
end
% Display the Ybus matrix for the current time step
disp(['Ybus Matrix at t = ', num2str(t)]);
disp(Ybus);
% Calculating the constant power loads
for k = 1:NN
% Calculate power demand in per unit (pu) for time 't'
S = (bus(k, 2, t) + 1j * bus(k, 3, t)) / baseMVA;
SP(k) = -S; % Store the constant power load for time 't'
end
% Display SP for the current time step
disp(['SP (Constant Power Loads) at t = ', num2str(t)]);
disp(SP);
% Indices of all buses except the slack bus
kN = [1:slack-1, slack+1:NN];
% Display non-slack bus indices
disp('Non-Slack Bus Indices:');
disp(kN);
% Partition the Ybus matrix
YNS = Ybus(kN, slack); % Ybus terms related to the slack bus
YNN = Ybus(kN, kN); % Ybus terms related to non-slack buses
disp('YNS:');
disp(YNS);
disp('YNN');
disp(YNN);
% Calculation of Matrices
Matrix.Ar(:, t) = (real(YNS * VS - 2 * conj(SP(kN)))); % real(A)
Matrix.Ai(:, t) = (imag(YNS * VS - 2 * conj(SP(kN)))); % imag(A)
Matrix.Br(:, :, t) = (real(diag(conj(SP(kN))))); % matrix B
Matrix.Bi(:, :, t) = (imag(diag(conj(SP(kN))))); % matrix B
Matrix.Cr(:, :) = (real(YNN - diag(conj(SZ(kN))))); % matrix C
Matrix.Ci(:, :) = (imag(YNN - diag(conj(SZ(kN))))); % matrix C
% Debug: Display the Br matrix for the current time step
disp(['Br Matrix at t = ', num2str(t)]);
disp(Matrix.Br(:, :, t));
end
end
data file is also attached with it.If i increase load to see charging and discharging effect then Ps and Ps.1 used as slack variables in these two consraints (shown below also for clarification) make the model infeasible, can aynone resolve issue. I think voltage or current makesome issue
% Active power balance (const1) for current time `t`
linprob.Constraints.(sprintf('const1_%d_%d', bus, t)) = ...
Model.Ar(nonslack_bus_idx, t) == ...
sum((-Model.Br(nonslack_bus_idx, :, t) - Model.Cr(nonslack_bus_idx, :)) .* Vre_bus_t, 2) + ...
sum((-Model.Bi(nonslack_bus_idx, :, t) + Model.Ci(nonslack_bus_idx, :)) .* Vim_bus_t, 2) + ...
(-P_ch(bus, t) + P_dis(bus, t))+Ps(bus,t);
% Reactive power balance (const2) for current time `t`
linprob.Constraints.(sprintf('const2_%d_%d', bus, t)) = ...
Model.Ai(nonslack_bus_idx, t) == ...
sum((-Model.Bi(nonslack_bus_idx, :, t) - Model.Ci(nonslack_bus_idx, :)) .* Vre_bus_t, 2) + ...
sum((+Model.Br(nonslack_bus_idx, :, t) - Model.Cr(nonslack_bus_idx, :)) .* Vim_bus_t, 2) - ...
Qb(i, t)+Ps1(bus,t);
  4 Comments
Show 2 older comments
Ayesha
Ayesha about 10 hours ago
Yes, you have run the code with its output, issue is in Ps and Ps1 which are acting as slack variables, why code don't run without these slack variables. May be value of susceptance is high, but i used assumes values of B which are small but again there is need for slack variables. why? Talking about these constraints
% Active power balance (const1) for current time `t`
linprob.Constraints.(sprintf('const1_%d_%d', bus, t)) = ...
Model.Ar(nonslack_bus_idx, t) == ...
sum((-Model.Br(nonslack_bus_idx, :, t) - Model.Cr(nonslack_bus_idx, :)) .* Vre_bus_t, 2) + ...
sum((-Model.Bi(nonslack_bus_idx, :, t) + Model.Ci(nonslack_bus_idx, :)) .* Vim_bus_t, 2) + ...
(-P_ch(bus, t) + P_dis(bus, t))+Ps(bus,t);
% Reactive power balance (const2) for current time `t`
linprob.Constraints.(sprintf('const2_%d_%d', bus, t)) = ...
Model.Ai(nonslack_bus_idx, t) == ...
sum((-Model.Bi(nonslack_bus_idx, :, t) - Model.Ci(nonslack_bus_idx, :)) .* Vre_bus_t, 2) + ...
sum((+Model.Br(nonslack_bus_idx, :, t) - Model.Cr(nonslack_bus_idx, :)) .* Vim_bus_t, 2) - ...
Qb(i, t)+Ps1(bus,t);
Torsten
Torsten about 8 hours ago
To answer your question, I had to have a deep insight into your model which I don't have.

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