I am solving a Hydro power system optimization and faced a conditional constraint equation of the form below. have a look and send me your ideas.
it is as follows:
I have a Conditional spillage constraint equation of the form:
- S(r,t) = V(r,t) - Vrmax *
Where V(r,t) = the reservoir level (volume) in time period t, S(r,t) = spill in time period t and Vrmax is the maximum reservoir volume.
Both V(r,t) and S(r,t) are variables whereas Vrmax is a parameter which i already have the data.
The Condition is:
if S(r,t) >= 0
then V(r,t) = Vrmax (that means V(r,t) takes the value of Vrmax)
and s(r,t) = s(r,t) (that means S(r,t) takes its own value)
else If s(r,t) < 0
then V(r,t) = V(r,t) (that means V(r,t) takes its own value)
and s(r,t) =0 (that s(r,t) takes a value of zero)
In addition there are two upper and lower bound equations for the above variables (V and S):
- V(r,t) <= Vrmax *
- S(r,t) >=0 *
my questions are:
1. I was attempting to use the function Linprog to solve the equation. But linprog accepts only coefficients of equation in matrix form which makes it difficult for the above equation since it is conditional. Is there any way I can represent such function in MATLAB linear programming platform using matrix? IF not what else can I do?
2. The three equations inside double asterics are standard equations used in water reservioir simulation. but it is clear that the first equation cant hold true if both the second and third holds true. how can this be managed?
Regards Ashenafi
