Optimization for a economic dispatch problem with a heat storage unit.

Hello,

I am trying to perform an optimization where I have a heat demand and a production unit together with a heat storage unit. The idea is that the heat should be stored so that when the demand is larger than the maximum available production the unit should have stored the possible excess heat from the previous time steps. I have been trying to implement this to intlinprog and linprog but haven't managed to implement the time aspect.

For example

    x=zeros(3,3);
    P_heat_max=110;
    P_demand=[100, 98, 118];
    [m n]=size(P_demand);
    P_heat_storage=zeros(1,3);
    P_heat_storage(1,1)=30;
    P_heat_storage(1,2)=P_heat_storage(1,1)-x(1,3); 
    P_heat_storage(1,3)=P_heat_storage(1,2)-x(2,3);
    cost=100; %SEK/mwh
    
    f = [cost;0;0];
    %[Demand, Charge, Discharge]    
    intcon=3;
    
    %Lower & Upper bounds
    lb=[0;0;0];
    ub=[P_heat_max;20;20];

    %linjära constraints
    A1=-[1,-1,1;1,-1,1;1,-1,1]; %Cover the demand
    B1=-P_demand; %Cover the demand
    
    A2=[0,0,1;0,0,1;0,0,1]; %To keep the minimum allowed energy content in the heat storage unit
    B2=(P_heat_storage-20);
    
    A=[A1;A2];
    B=[B1;B2];
    Aeq=[];
    Beq=[];
        
    x=intlinprog(f,intcon,A,B,Aeq,Beq,lb,ub);

How can make the system understand to produce extra heat in order to be able to satisfy future demands.

I am fairly new to MATLAB, any suggestion are highly appriciated.

Regards

A stressed Student