I am working M.Sc. Thesis research on a load dispatch problem for Ethiopian power system that consists of mainly 15 hydroelectric power plants, 4 wind power plants, 5 geothermal plants and 2 solar power plants. The objective function bases itself on minimizing the power production cost. All types of power plants listed above have their own property and I have already formulated the model based on those properties.
Both the objective function as well as equality and non-equality constraints are all linear, discrete and deterministic. I am working for a year time with hourly resolution and using MATLAB platform to optimize the problem. The problem is already classified as large scale linear programming.
Given this information my problem is as follows:
I have a hydraulic continuity equation of the form:
V(t) =V(t-1) + In(t) – Q(t) –S(t)
Where V(t) = the reservoir level (volume) in time period t In(t),Q(t), S(t) = Inflow, Discharge and spill in time period t respectively In addition other equality and inequality constraints are included in the equation.
The decision (unknown) variables of the whole model are V, Q and S. 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 V(t) and V(t-1) can’t be differentiated as there is no time dimension. Is there any way I can represent such function in MATLAB linear programming platform? IF not what else can I do?
Regards Ashenafi
