Using Semidefinite Relaxation to Solve the Day-Ahead Hydro Unit Commitment Problem

In this paper, we present a mixed-integer formulation with nonlinear production functions of the day-ahead hydro unit commitment problem for hydro-dominant power systems. The objective is to minimize unit startup and shutdown costs and maximize water use efficiency in the daily operation of multiple hydro plants. Determination of hourly generation dispatches and unit configurations is subject to reservoir dynamics, power balance, as well as target constraints coupling short-term generation with long-term reservoir operation goals. In addition, ac power flow constraints are considered. An equivalent quadratically-constrained quadratic formulation is approximated by successive convex semidefinite programming relaxations in a branch-and-bound algorithm for optimal solutions. Numerical case studies for several system configurations are presented to illustrate the effectiveness of the relaxation algorithm.