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In this simplified version of a system designed to produce hydrogen from pv, I want to find out the lowest possible capacity of the electrolyzer?

The problem is that when I run the model it says that there is no solution avaliable. However, when I fill in the capacity of the electrolyzer by hand I can easily find a solution for the constraints.

%% Problem-Based Optimization

load('CF_pv.mat'); % Hourly data of capacity factor sun

energyprob = optimproblem;

PV = 748; % in MW

Electrolyzer = optimvar('Electrolyzer',1,'LowerBound',0); % Capacity of ELectrolyzer in MW

Electrolyzer_costs =[(200+0.7*200)];

costs = Electrolyzer_costs*Electrolyzer;

%Objective Function

energyprob.Objective = costs;

%% Optimization constraints

PV_Load = PV*CF_pv;

T = 8760; % hours in a year

Bat_In = optimvar('Bat_In',T,'LowerBound',0); % Electricity send to battery

Bat_Out = optimvar('Bat_Out',T,'LowerBound',0); % Electricity send from battery to Electrolyzer

Bat_In_c = optimconstr(T);

Bat_Out_c = optimconstr(T);

for t=1:T

Bat_In_c(t) = Bat_In(t) == (PV_Load(t)-1.1*Electrolyzer); % Abundant Electricity, above 110% of the limit of the electrolyzer

Bat_Out_c(t) = Bat_Out(t) == 0.1*Electrolyzer-PV_Load(t); % Electricity necessary to keep electrolyzer running

end

Elec_In = PV_Load - Bat_In + Bat_Out; % Generated electricity - input in battery + electricty from battery to electrolyzer

energyprob.Constraints.Bat_In_c = Bat_In_c;

energyprob.Constraints.Bat_Out_c = Bat_Out_c;

Desired_Elec_In = 1.7618*10^6; % Desired electricty input for a whole year

cons1 = Elec_In == sum(Desired_Elec_In);

energyprob.Constraints.cons1 = cons1;

[sol,fval] = solve(energyprob);

sol.Electrolyzer % display electrolyzer capacity

Alan Weiss
on 2 Jun 2021

Your problem is infeasible as given. Using the routines in Investigate Linear Infeasibilities, I found the following. Convert the problem to LP matrices:

problem = prob2struct(energyprob);

Add a null Aineq and bineq inequality constraint.

Aineq = zeros(1,size(problem.Aeq,2));

bineq = 0; % The code needs an Aineq argument of the correct size

I then ran the code in Remove iIS In A Loop, and found that the following are conflicting lines in the problem.Aeq matrix together with the problem.beq data (conflict with the bounds):

Row 8760 and 17513

Row 8759 and 17512

Row 8758 and 17511

etc.

It just kept spitting them out, so I stopped the process. Armed with this knowledge I am sure that you can find the error in your setup.

By the way, I recently found some errors in the published code for the generatecover function. The corrections you must make in the generatecover code:

% Look for this line

[ineq_iis,eq_iis,ncalls,fval] = elasticfilter(Aineq(activeA,:),bineq(activeA),Aeq(activeAeq),beq(activeAeq),lb,ub);

% change it to

[ineq_iis,eq_iis,ncalls,fval] = elasticfilter(Aineq(activeA,:),bineq(activeA),Aeq(activeAeq,:),beq(activeAeq),lb,ub);

% Look for this line

[ineq_iis,eq_iis,ncalls,fval] = elasticfilter(Aineq(activeA),bineq(activeA),Aeq(activeAeq,:),beq(activeAeq),lb,ub);

% change it to

[ineq_iis,eq_iis,ncalls,fval] = elasticfilter(Aineq(activeA,:),bineq(activeA),Aeq(activeAeq,:),beq(activeAeq),lb,ub);

But I suggest that you do not run generatecover on this problem; I have been running it for hours and it is still not finished.

Good luck,

Alan Weiss

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