Problem turns infeasible out of nowhere

[Jasper Meyer]

Hi,

after the basic obstacle of my problem had been solved (https://groups.google.com/forum/#!topic/yalmip/b7IFBqMau9s) I proceeded in implementing more details I thought it would work now. But unfortunately after changing the problem slightly it becomes infeasible. I attach all the files needed as the code became quite long (as I couldn't figure out, where the problem is, I wasn't able to simplify it any further, sorry).

I am still modeling a storage with a given demand over time. When this demand was created randomly, everything worked out fine no matter how different the demand was. I attached one randomly created demand, that worked (file: Demand_rand). But now I changed the demand (file Demand_real) and my problem became infeasible and I can't figure out why. It seems like the installed discharging power is the problem.

s(1).mod(2).cap = 100; %discharging power capacity [MW] 

After hours of testing, I found out, that the problem works for values between 0 and 8.5574. As soon as it is raised above that level, the problem becomes infeasible.

I would be so grateful if you can give me a hint why this is happening.

Thank you in advance and best regards

Jasper

[Johan Löfberg]

You will have to sort that out by removing constraints, adding slacks etc.

For instance, if I add a slack on the last constraint

slack = sdpvar(T,1)

...
constraints = [constraints, CE_ex_out(t,1) == min(E_dem_out(t,1), E_out_cap(t,1))+slack(t)];

and minimize the 1-norm of that slack, it reveals some significant non-zero slacks required at some time instants

 solvesdp(constraints,norm(slack,1))

         0
    0.0000
    0.0000
    0.0000
    0.0000
    0.0000
    0.0000
    0.0000
    0.0000
    0.0000
    0.0000
   -0.0000
   -0.0000
   -0.0000
   -0.0000
   -0.0000
   -0.0000
    0.0000
   -0.0000
   -0.0000
   -0.0000
   -0.0000
   -0.0000
    0.0000
    0.0000
   -2.5193
   -1.2597
   -0.6298
   -0.3149
   -0.1575
   -0.0787
   -0.0394
   -0.0197
    0.0000
   -0.0000
   -0.0000
   -0.0000
   -0.0000
    0.0000
   -0.0000
   -0.0000
    0.0000
    0.0000
    0.0000
    0.0000
    0.0000
    0.0000
    0.0000
    0.0000
    0.0000

BTW, I hope you realize that a model with blabla=min(decisionvariables) leads to MILP reformulations. If possible, you should avoid the equality. Perhaps it is possible to reformulate something as blabla <= min(decisionvariales), which is a convex set, based on argument that the optimal solution will satisfy equality

[Jasper Meyer]

Thank you very much. I will try to work it out following your hints.