Moment-SOS relaxation of the medium term hydrothermal dispatch problem

This paper analyzes the application of moment-SOS (sum of squares) relaxation to solve the medium term hydrothermal dispatch (MTHD) problem for predominantly hydro systems. The optimal dispatch is formulated as a two stage stochastic programming problem, which is nonconvex due to constraints that represent hydro power production, and may have multiple solutions. The size and conditioning of the problem pose challenges to the use of the semidefinite programming (SDP) techniques that are discussed in the text. The size of the problem restricts this study to first order moment relaxations. Therefore, to improve the quality of relaxed solutions, additional meaningful constraints are introduced in the SDP problems. Subsequently, the problem re-scalded to achieve numerical stability in SDP relaxation. Results obtained for different test systems, most of them being partitions of the Brazilian hydroelectric system, indicate that the procedures used to improve the quality of SDP solutions are effective.160