THe problem is that ga() does not support the combination of integer constraints and nonlinear equality constraints. That is because the mechanism that ga() uses for integer constraints is to hook into the nonlinear constraints.
You can rewrite your code to eliminate discharge_status as being independent: it is just 1 minus charge_status.
But the power balance still remains, and Problem Based Optimization does not know how to construct the parameters for ga in a way that will work.
If you examine your powerbalance equation you will see that the charge or discharge status is multiplied by the charge or discharge -- you are selecting one or the other. But as far as ga is concerned, that means you are multiplying two inputs together... which is a nonlinear operation. So you cannot convert it to a linear inequality or equality.
The easiest way to handle this, for a modest number of indicator variables, is to iterate through all the possible combination of indicator variable values, invoking optimization for each one, recording all the results, and picking the best of them at the end.
%test economic disptach with 2 genertors and one battery
Load=[350; 607; 380; 605];%hourly load level, only study 4 hours
n = length(Load); %use load's demension to define the size
basegen_cost=[10; 10; 10; 10];%base load generator is cheap, cost is 10$/MW for all the hours
peakergen_cost=[50; 50; 50; 50];%peaker load generator is more expensive, 50$/MW for all the hours
discharge_cost=[0; 0; 0; 0]; %assuming no cost to discharge
charge_cost=[0; 0; 0; 0]; %assuming no cost to charge
dispatch = optimproblem;
ini_SOC=0;%battery initial State of charge is 0, empty.
soclevel = optimexpr(n,1);%optimization expression for soc level,since it's related to other variables.
charge_status = optimvar('charge_status',n,'Type','integer','LowerBound',0,'UpperBound',1); %charging status 0 /1
%discharge_status=optimvar('discharge_status',n,'Type','integer','LowerBound',0,'UpperBound',1); %discharging status 0/1
discharge_status = 1 - charge_status;
charge = optimvar('charge',n,'LowerBound',0,'UpperBound',10); %charging MW,including limit;
discharge=optimvar('discharge',n,'LowerBound',0,'UpperBound',10); %discharging MW, including limits;
basegen = optimvar('basegen',n,'LowerBound',0,'UpperBound',400); %base load generator's output limits;
peakergen = optimvar('peakergen',n,'LowerBound',0,'UpperBound',200); %peaker generator's output limits
total_cost=sum(discharge_status.*discharge.*discharge_cost+basegen.*basegen_cost+peakergen.*peakergen_cost-charge_status.*charge.*charge_cost); %production cost
total_gen=discharge_status.*discharge-charge_status.*charge+basegen+peakergen; %total generation from the battery and the two generators.
soclevel(1)=ini_SOC-discharge_status(1)*discharge(1)+charge_status(1)*charge(1); %SOC level at the end of the first hour
for i=2:4
soclevel(i)=soclevel(i-1)-discharge_status(i)*discharge(i)+charge_status(i)*charge(i); %SOC level for hour 2-4.
end
dispatch.Objective=total_cost; %objective is to minimize the production cost
dispatch.Constraints.powerbalance=total_gen==Load; %total generation equal to total load
dispatch.Constraints.uppersoc=soclevel<=10; %SOC level upper limit;
dispatch.Constraints.lowersoc=soclevel>=0; %SOC level lower limit;
show(dispatch);
solution = solve(dispatch)
