Under-relaxed iterative procedure for feasible short-term scheduling of a hydro chain

This paper presents a method for short-term hydro scheduling. The objective is to determine a feasible operation of a set of coupled hydro units, fulfilling the aggregate requirements obtained from a higher-level hydrothermal coordination tool. In order to take into account the nonlinear relationship among the electrical power, the net head and the turbine water discharge, an under-relaxed iterative procedure is proposed. The performance of this algorithm enhances previous research works as possible diverging oscillations are damped in order to reach the convergence. Therefore, the net heads used to build the power/discharge curves of the head dependent units are determined using previous iterations results. This way, each stage can be solved by means of a MILP optimization problem where binary variables allow modeling the discrete hydro unit-commitment decisions. The process finishes when the maximum gap between the reservoir levels of two consecutive iterations satisfies the convergence tolerance. A case study is also presented to show its application to a real size hydro chain.