Programming Shiftable Load Profile

I want to program a Shiftable Load (SL) profile demand as a MILP.

I have a SL demand that I want to be done once a day. The SL demand has two intervals, so it has to turn on before hour 23 because, otherwise, it wouldn't do all the intervals.

I have programed the SL lit in constraint C1 defining that x_S binary variable just must be 1 once a day.

Now, I need to assign the consumption in each interval.

You have my code below:

case1=optimproblem;

%% Sets
T=[1:24]'; %Time set [h]
L=[1:2]'; %Intervals of shiftable load profile set [h]

%% Parameters
C_Ip=[0.079 0.065 0.05 0.037 0.033 0.035 0.037 0.043 0.05 0.063 0.075 0.076 0.075 0.075 0.076 0.065 0.063 0.061 0.065 0.075 0.087 0.093 0.09 0]'; %Day-ahead purchase spot price [€/kWh]
D_S=[2.3 1.9]'; %Shiftable load demand [kWh]

%% Variables
x_S=optimvar('x_S',length(T),'Type','integer','LowerBound',0,'UpperBound',1); %Interval where shiftable load begins to be supplied
d_S=optimvar('d_S',length(T),'Type','continuous','LowerBound',0); %Shiftable load [kWh]
c_T=optimvar('c_T',length(T),'Type','continuous','LowerBound',0); %Total cost [€/h]

%% Constraints
case1.Constraints.C1=optimconstr(length(T));
for i=1:length(T)
    if T(i)>=1 &  T(i)<=23
        case1.Constraints.C1(i)=sum(x_S)==1;
    else
        case1.Constraints.C1(i)=sum(x_S(i))==0;
    end
end

%% Objective function
case1.Constraints.COF=optimconstr(length(T));
for i=1:length(T)
    case1.Constraints.COF(i)=c_T(i)==d_S(i).*C_Ip(i);
end

case1.Objective=sum(c_T);
options=optimoptions('intlinprog');
[solu,exitflag,output]=solve(case1,'Options',options);

Answer 1

[Pradnya Jadhav]

Hi

Dont understand your problem.

What is objective function.