Short-term hydrothermal scheduling (STHS) is a non-convex and non-differentiable optimization problem that is difficult to solve efficiently. One of the most popular strategy is to reformulate the complicated STHS by various linearization techniques that makes the problem easy to solve. However, in this process, a large number of extra continuous variables, binary variables and constraints will be introduced, which may lead to a heavy computational burden, especially for a large-scale problem. In this paper, a logarithmic size mixed-integer linear programming (MILP) formulation is proposed for the STHS, i.e., only a logarithmic number of binary variables and constraints are required to piecewise linearize the nonlinear functions of STHS. Based on such an MILP formulation, a global optimal solution is therefore can be solved efficiently. To eliminate the linearization errors and cope with the transmission loss, a differentiable non-linear programming (NLP) formulation, which is equivalent to the original non-differentiable STHS is derived. By solving this NLP formulation via the powerful interior point method (IPM), where the previous global optimal solution of MILP formulation is used as the initial point, a high-quality feasible optimal solution to the STHS can thus be determined. Simulation results show that the proposed logarithmic size MILP formulation is more efficient than the generalized one and when it is incorporated into the solution procedure, our solution methodology is competitive with currently state-of-the-art approaches.
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