An MILP based formulation for short-term hydro generation scheduling with analysis of the linearization effects on solution feasibility

Mixed integer linear programming (MILP) based formulations and solution methods for short-term hydro generation scheduling (HGS) have been widely adopted by researchers, hydropower producers, and system operators in recent years. This approach calls for the nonlinear forebay level, tailrace level, penstock loss, and hydropower production functions to be replaced with their piecewise linear approximations. However, the effects of the linearization of the nonlinear functions and related constraints on solution feasibility have not been fully discussed in the literature. In this paper, the issues concerning solution feasibility are discussed in detail and a method is presented to ensure that the solution obtained based on the approximated MILP formulation remains feasible for the original nonlinear formulation. Furthermore, it is found that the real number water delay can be handled in the formulation without destroying the linear structure of the water balance constraints. Numerical testing results show that the method presented in this paper is effective.