Hydro-thermal coordination problem using improved direct and indirect methods

Hydro thermal coordination (HTC) is one of the subjects where numerical optimization has been extensively applied as the permanent quest of improving existing general techniques for such large scale combinatorial problems. The solution of HTC is used in vertical market structures and deregulated environments based on central cost minimization.; In this thesis, three different stand alone compiled applications are implemented on the same platform in order to solve the HTC problem, namely. Interior Point Methods (IPMs). Lagrangian Relaxation (LR) and Semidefinite Programming (SDP). A direct solution approach based on Interior Point Methods (IPMs) requires a linear programming formulation of the problem. Although IPMs have been successfully applied to the HTC problem, the implementations are based on interpreted programming languages or commercial solvers; thus, there is no quantitative assessment on the performance of predictor corrector methods versus standard methods or other decomposition or direct solution techniques.; A decomposition technique based on an improved Lagrangian Relaxation (LR) algorithm is presented. Former solution techniques used in the maximization of the dual function of the HTC problem are based on the subgradient technique, or in the maximization of the outer approximation of the dual function constructed by cutting planes; these techniques have problem dependent parameters that have to be tuned. We implement a new technique for HTC based on computing the analytic center of the polytope defined by the polyhedral approximation of the dual function and bounds on the dual variables. The polytope shrinks its size until enclosing the dual optimum. The algorithm used in the dual function maximization does not suffer from problem dependent parameter tuning.; Additionally, a new direct solution approach based on Semidefinite Programming (SDP) is successfully implemented on a convex quadratic formulation of the HTC problem. Semidefinite programming is linear programming over the cone of positive definite matrices, and, therefore, it can be solved efficiently with IPMs.; The result of this study shows that, at the moment, for most realistic sized problems, decomposition is the best alternative. However, SDP has provided very promising results and its implementation can be further improved considering the special structure of the HTC problem. Numerical examples ranging up to 60 thermal plants and 32 hydro plants are presented.