Optimal dispatch of power generators - matlab

Question

I want to write a matlab code that can optimally dispatch power generators to satisfy electric demand by considering profit too. I used below code that is in matlab website. https://ww2.mathworks.cn/help/optim/examples/optimal-dispatch-of-power-generators.html?requestedDomain=en
But in this code they are not considering the demand.
My target is , there are 20 power plants and I want to schedule this plants to satisfy demand. And the running power level can be any value in between the max and minimum power value of each power plant. High cost power plants should dispatch too.
name = 'generationcost.xlsx';
poolPrice = xlsread(name,'AD3:AD50'); % Revenue in dollars per MWh in interval
demand = xlsread(name,'AC3:AC52');
month = numel(demand);
e = xlsread(name,'W2:W4')'; %Cost for a unit of fuel
fuelPrice = repmat(e,1,1,2);
nPeriods = length(poolPrice);
nGens = 3;
genhigh = xlsread(name,'F2:F4');
genlow = xlsread(name,'Q2:Q4');
gen = [genlow(:),genhigh(:),]; %MW
fuel = [50,330;45,325;55,750]; % Fuel consumption for generator
startCost = [10000;10000;10000]; %Cost in dollars to start a generator after it has been off
y = optimvar('y',nPeriods,nGens,{'Low','High'},'Type','integer','LowerBound',0,'UpperBound',1);
z = optimvar('z',nPeriods,nGens,'Type','integer','LowerBound',0,'UpperBound',1);
powercons = y(:,:,'Low') + y(:,:,'High') <= 1;
yFuel = zeros(nPeriods,nGens,2);
yFuel(:,1,1) = fuel(1,1);
yFuel(:,1,2) = fuel(1,2);
yFuel(:,2,1) = fuel(2,1);
yFuel(:,2,2) = fuel(2,2);
yFuel(:,3,1) = fuel(3,1);
yFuel(:,3,2) = fuel(3,2);
fuelUsed = sum(reshape((sum(y.*yFuel)),[3 2])');
%fuelcons = fuelUsed <= totalFuel;
w = optimexpr(nPeriods,nGens);
idx = 1:(nPeriods-1);
w(idx,:) = y(idx+1,:,'Low') - y(idx,:,'Low') + y(idx+1,:,'High') -
y(idx,:,'High');
w(nPeriods,:) = y(1,:,'Low') - y(nPeriods,:,'Low') + y(1,:,'High') -
y(nPeriods,:,'High');
switchcons = w - z <= 0;
generatorlevel = zeros(size(yFuel));
generatorlevel(:,1,1) = gen(1,1);
generatorlevel(:,1,2) = gen(1,2);
generatorlevel(:,2,1) = gen(2,1);
generatorlevel(:,2,2) = gen(2,2);
generatorlevel(:,3,1) = gen(3,1);
generatorlevel(:,3,2) = gen(3,2);
revenue = optimexpr(size(y));
for ii = 1:nPeriods
revenue(ii,:,:) = poolPrice(ii)*y(ii,:,:).*generatorlevel(ii,:,:);
end
val = optimexpr(size(y));
demands = optimexpr(nPeriods,1);
id = 1:nPeriods;
val(id,:,:)= y(id,:,:).*generatorlevel(id,:,:);
demands(id,:)= sum(sum(val,3),2);
demandcons = demands-demand ;
fuelCost = sum(sum(fuelPrice.*sum(y.*yFuel)));
startingCost = z*startCost;
profit = sum(sum(sum(revenue))) - fuelCost - sum(startingCost);
dispatch = optimproblem('ObjectiveSense','maximize');
dispatch.Objective = profit;
dispatch.Constraints.powercons = powercons;
dispatch.Constraints.demandcons = demands - demand <= 0 ;
options = optimoptions('intlinprog','Display','final');
[dispatchsol,fval,exitflag,output] = solve(dispatch,'options',options);
subplot(5,1,1)
bar(dispatchsol.y(:,1,1)*gen(1,1)+dispatchsol.y(:,1,2)*gen(1,2),.5,'g')
xlim([.5,48.5])
ylabel('MW')
title('Generator 1 Optimal Schedule','FontWeight','bold')
subplot(5,1,2)
bar(dispatchsol.y(:,2,1)*gen(2,1)+dispatchsol.y(:,2,2)*gen(2,2),.5,'c')
title('Generator 2 Optimal Schedule','FontWeight','bold')
xlim([.5,48.5])
ylabel('MW')
subplot(5,1,3)
bar(dispatchsol.y(:,3,1)*gen(3,1)+dispatchsol.y(:,3,2)*gen(3,2),.5,'c')
title('Generator 3 Optimal Schedule','FontWeight','bold')
xlim([.5,48.5])
ylabel('MW')
subplot(5,1,4)
bar(demand,.5)
xlim([.5,48.5])
title('Daily Demand','FontWeight','bold')
xlabel('Period')
ylabel('MW')
starttimes = find(round(dispatchsol.z) == 1);
[theperiod,thegenerator] = ind2sub(size(dispatchsol.z),starttimes)
This code is not satisfying Demand. The output demand value is more lesser than the actual demand value. And also here only use 'High' or 'Low' power levels only. In between power values not using.