Energy storage optimisation problem - separate charge and discharge constraint

Hi

I'm currently working on an optimization problem to minimize the cost of energy dispatch where we have solar generation and energy storage system. My fmincon function is working, however after i added the constraints for the battery charging and discharging I'm getting an error :

Unable to perform assignment because value of type 'optim.problemdef.OptimizationExpression' is not convertible to 'double'.

Caused by:

Error using double

Conversion to double from optim.problemdef.OptimizationExpression is not possible.

Failure in initial nonlinear constraint function evaluation. FMINCON cannot continue.

I'm not sure what is causing the issue, any help would be great in fixing this.

options = optimoptions('fmincon',...

'Algorithm','sqp','Display', 'iter', 'ConstraintTolerance', 1e-10);

[p, C] = fmincon (@myfun, p0, [], [], [], [], lb, ub, @mycon, options);

% Cost Function that needs to be minimized..

function C = myfun (p)

C =0;

for t = 1:24

for i = 1:4

cost = ce(i) + b(i)*p(t,i) + a(i)*p(t,i)^2;

C = C + cost;

end

end

end

function [c, ceq] = mycon(p) % function [ceq] = mycon(p) in Octave

global Pd P_solar

N= 24;

dt = 1;

BattEnergy = 650;

Einit = 0.5 * BattEnergy;

Emax = 0.8*BattEnergy;

Emin = 0.2*BattEnergy;

Pch = optimvar('Pch',N,'LowerBound',0,'UpperBound',Emax);

Pdisch = optimvar('Pdisch',N,'LowerBound',0,'UpperBound',Emin);

c =0;

c1 =zeros(24,1);

c2 =zeros(24,1);

c3 =zeros(24,1);

c4 =zeros(24,1);

c5 =zeros(24,1);

c6 =zeros(24,1);

for t = 1:24

c1(t) = ( 0 - Pdisch(t));

c2(t) = ( Pdisch(t) - Pdischmax(t));

c3(t) = ( 0 - Pch(t));

c4(t) = ( Pch(t) - Pchmax(t));

c5(t) = Emin - (sum(Pch(t) - Pdisch(t)) * dt) ;

c6(t) = (sum(Pch(t) - Pdisch(t)) * dt) - Emax;

end

c = [c1;c2;c3;c4;c5;c6];

c=c(:);

ceq=0;

for t = 1:24

ceq1(t) = Pch(t) * Pdisch(t);

ceq2(t) = sum(Pch(t) - Pdisch(t)) * dt;

ceq3(t) = sum(p(t,:)) + Pdisch(t) - Pch(t) - Pd(t);

ceq = [ceq1;ceq2;ceq3];

ceq=ceq(:);

end

end

[Iñigo Azpiri]

Dear Hussain,

Could you share the code with the solution you reached? I am also trying to solve a similar problem.

Thanks,

Iñigo

Answer 1

[Alan Weiss]

You are mixing up the problem-based and solver-based formulations. You need to choose one or the other. If you are using the solver-based formulation so that you can call fmincon, then do not create any optimization variables using optimvar. Alternatively, if you are using the problem-based formulation, do not call fmincon. In all cases, don't create optimization variables in the nonlinear constraint function. Create them, if they are needed, in the main workspace.

If you want to create your constraints using the problem-based formulation and then export to the solver-based, use prob2struct. But I think that you will be happier and more successful if you choose just one approach rather than a hybrid.

For documentation of the problem-based approach, see Problem-Based Optimization Workflow. For a simple example, see Solve a Constrained Nonlinear Problem, Problem-Based. For an example related to your application, see Optimal Dispatch of Power Generators: Problem-Based.

Good luck,

Alan Weiss

MATLAB mathematical toolbox documentation

[hussain askar]

Thanks Alan, yes I already changed everything to a Problem-Based approach and everything is working great now with no errors and by default, the optimization was solved using quadprog instead of fmincon and it seems that I can not change it to fmincon. I tried adding some options to specify that i want to solve using fmincon algorithm but it ignored that when I ran it and solved using quadprog.

[values,Cost,exitflag] = solve(prob);

when i use this line, does it solve the optimization by choosing the best function for it? Also, why did it choose quadprog over fmincon?

[Alan Weiss]

solve chooses quadprog because your problem is a quadratic programming problem, and quadprog is the most appropriate solver. However, if you want to use fmincon for some reason (even though it is an inferior solver for this problem), then you must create an initial point structure x0 with fields for all of your optimizaton variables, and call solve like this:

[values,Cost,exitflag] = solve(prob,x0,"Solver","fmincon");

See the solve reference page.

Alan Weiss

MATLAB mathematical toolbox documentation

[hussain askar]

hey Alan,

Can you help me with this issue:

Pmin = -100; % Max Discharge Rate [W]

Pmax = 100; % Max Charge Rate [W]

PbattV = optimvar('PbattV',N,'LowerBound',Pmin,'UpperBound',Pmax);

I would like to introduce a new cost term in my objective function (cost function) so that when PbattV is positive (charging) between t=8:20 then there will be a cost.

I tried this:

for t = 8:20

if PbattV(t) >= 0

c5 = c5 + 300 * PbattV(t);

else

c5 = c5 + 0 * PbattV(t);

end

end

but i'm getting this error " Conversion to logical from optim.problemdef.OptimizationInequality is not possible." How can I solve this?

[Alan Weiss]

Sorry, you are going to have to reformulate your if statements along the lines of Integer and Logical Modeling. This requires you to create binary variables and link them to your optimization variables. It takes some thought and possibly experimentation. Take it one step at a time, you'll be pleased with the results.

Alan Weiss

MATLAB mathematical toolbox documentation