How can I change a real variable by comparing sdpvar variables with real variables?

[Abersa]

Hi~
There is a array about price, just like:

Price.Tables(1,96) = [0.365 0.365 0.365 0.365 0.365 0.365 0.365 0.365 0.365 0.365 0.365 0.365 0.365 0.365 0.365 0.365 0.365 0.365 0.365 0.365 0.365 0.365 0.365 0.365 0.365 0.365 0.365 0.365 0.365 0.365 0.365 0.365 0.869 0.869 0.869 0.869 0.869 0.869 0.869 0.869 0.869 0.869 0.869 0.869 0.869 0.869 0.869 0.869 0.687 0.687 0.687 0.687 0.687 0.687 0.687 0.687 0.687 0.687 0.687 0.687 0.687 0.687 0.687 0.687 0.687 0.687 0.687 0.869 0.869 0.869 0.869 0.869 0.869 0.869 0.869 0.869 0.869 0.869 0.869 0.869 0.869 0.869 0.869 0.869 0.687 0.687 0.687 0.687 0.687 0.687 0.687 0.687 0.687 0.687 0.687 0.687];

Then, there is a sdpvar : eRE(1,96).
I want to turn Price.table(1,t) into 0.3 (Price.Disc), when eRE(1,t)<0.
Its my code:

evElectionPrice = sdpvar(1,96,'full');     % Set the price as  sdpvar variable 
evElectionPriceMAX(1,1:96) = Price.Disc; % Price.Disc = 0.3. evElectionPriceMAX is maximum of price.
evElectionPriceMIN(1,1:96) = Price.Disc;  % evElectionPriceMIN is minimum of price.
% c is constraints
c = [c,evElectionPrice<=evElectionPriceMAX];  % I  want to change evElectionPriceMAX(1,t) and the evElectionPriceMIN(1,t) to fit eRE(1,t)
c = [c,evElectionPrice>=evElectionPriceMIN];
d = binvar(2,1);
for t = 1 : 96 % I cant  use the implies well
    d = binvar(4,1);
    c = [c,sum(d) == 1,
        implies(d(1),[eRE(1,t) > 0,evElectionPriceMAX(1,t) == Price.Table1(1,t)]);
        implies(d(2),[eRE(1,t) > 0,evElectionPriceMIN(1,t) == Price.Table1(21t)]);
        implies(d(3),[eRE(1,t) <= 0,evElectionPriceMIN(1,t) == Price.Disc]);
        implies(d(4),[eRE(1,t) <= 0,evElectionPriceMAX(1,t) == Price.Disc])];
end
objective = sum(evElectionPrice.*abs(eRE));

Obviously, It cant run, but I cant revise code and dont know how to use implies.
Could u help?

[mrkento11]

I just read your code, and I don't know what it does, so it is very difficult to try to understand your reasoning. Moreover, don't know what the variables do.

However, my comments would be:

1. the variable d does not have the dimension of the amount of cases you have. it should be d = binvar(4,1). You also declared d = binvar() twice. Once outside the for loop and once inside.
2. Both the variable evElectionPriceMAX and evElectionPriceMIN, are the same (Price.Disc). This implies ElectionPrice is bounded up and down by the same number.
3. Your for loop seem to use d as a binvar, but then after every loop you overwrite this variable. I truly don't fully understand what you want to achieve, but it seems that you want to have four cases for 96 instances, so it seems that you need to declare d = binvar(4,96);
4. You have some warning because you use strict inequalities. Yalmip is gentle enough to try to correct your mistake, but they are not supported since a while ago. For example: {eRE(1,t) > 0 -> eRE(1,t) >= 0}. Refer to: https://yalmip.github.io/inside/strictinequalities/

Try to formulate the question again to give us better clues to help you out.

[johanlofberg]

Yes, that is basically the manual representation of the absolute value/max operator in max(a*x,-b*x)

[Abersa]

Thank u, I think I am trapped in a strange circle of thinking. I should regard electricity price as a function. Another question: Why does the calculation of the objective function become slow after using the absolute value？How to calculate variance in Yalmip？

[johanlofberg]

Why are you trapped. I gave you the model, and it is very basic as it is just a matter of a two implies

Not sure what you mean with slow when adding abs. How abs enters the model can create vastly different models, depending on convexity (as YALMIP has to use a MILP representation if you use abs in a nonconvex way). However, I gave you a model which doesn't require any abs

[johanlofberg]

This thoughevElectionPrice.*abs(eRE)will be extremely bad, as both evElectionPrice and eRE are decision variables, so you end up with a bilinear expression (and an absolute value operator), and a much much harder problem

[Abersa]

I think I understand what you mean。Thanks