Solution for short-term hydrothermal scheduling with a logarithmic size mixed-integer linear programming formulation

Abstract Short-term hydrothermal scheduling issue is usually hard to tackle on account of its highly non-convex and non-differentiable characteristics. A popular strategy for handling these difficulties is to reformulate the issue by various linearization techniques. However, in this process, a fairly large number of continuous/binary variables and constraints will be introduced, which may result in a heavy computational burden. In this study, a logarithmic size mixed-integer linear programming formulation is presented for this issue, that is, only a logarithmic size of binary variables and constraints will be required to piecewise linearize the nonlinear functions. Based on such a formulation, a global optimum is therefore can be solved efficiently. To remove the linearization errors and cope with the network loss, a derivable non-linear programming formulation is derived. By optimizing this formulation via the powerful interior point method, where the previous global solution of mixed-integer linear programming formulation is used as the starting point, a promising feasible solution is consequently attained. Numerical results show that the presented logarithmic size mixed-integer linear programming formulation is more efficient than the generalized one and when it is incorporated into the solution procedure, the proposed methodology is competitive with currently state-of-the-art approaches.