Solving the unit commitment problem of hydropower plants via Lagrangian Relaxation and Sequential Quadratic Programming

We consider the optimal scheduling of hydropower plants in a hydrothermal inter- connected system. This problem, of outmost importance for large-scale power systems with a high proportion of hydraulic generation, requires a detailed description of the so-called hydro unit production function. In our model, we relate the amount of generated hydropower to nonlinear tailrace levels; we also take into account hydraulic losses, turbine-generator efficiencies, as well as multiple 0-1 states associated with forbidden operation zones. Forbidden zones are crucial to avoid nasty phenomena such as mechanical vibrations in the turbine, cavitation, and low efficiency levels. The minimization of operating costs subject to such detailed constraints results in a large-scale mixed-integer nonlinear programming problem. By means of Lagrangian Relaxation, the original problem is split into a sequence of smaller and easy-to-solve subproblems, coordinated by a dual master program. In order to deal better with the combinatorial aspect introduced by the forbidden zones, we derive three different decomposition strategies, applicable to various configurations of hydro plants (with few or many units, which can be identical or different). We use a Sequential Quadratic Programming algorithm to solve nonlinear subproblems. We assess our approach on a real-life hydroelectric configuration extracted from the south sub region of the Brazilian hydrothermal power system.