Economic dispatch (ED) problem considering valve-point effects (VPE), transmission loss and prohibited operating zones (POZ) is a very challenging issue due to its intrinsic non-convex, non-smooth and non-continuous natures. To achieve a near globally solution, a fully mixed-integer linear programming (FMILP) formulation is proposed for such an ED problem. Since the original loss function is highly coupled on n-dimensional spaces, it is usually hard to piecewise linearize entirely. To handle this difficulty, a reformulation trick is utilized, transforming it into a group of tractable quadratic constraints. By taking full advantage of the variables coupling relationships among univariate and bivariate functions, an FMILP formulation that requires as few binary variables and constraints as possible is consequently constructed for the ED with VPE and transmission loss. When the POZ restrictions are also considered, a distance-based technique is adopted to rebuild these constraints, making them compatible with the previous FMILP reformulation. With the help of a logarithmic size formulation technique, a further reduction can be made for the introduced binary variables and constraints. By solving such an FMILP formulation, a near globally solution is therefore gained efficiently. In order to search for a more excellent feasible solution, a non-linear programming (NLP) model for the ED will be given and solved based on the FMILP solution. The case study results show that the presented FMILP formulation is very effective in solving the ED problem that involves non-convex, non-smooth and non-continuous natures.
View A fully mixed-integer linear programming formulation for economic dispatch with valve-point effects, transmission loss and prohibited operating zones