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This thesis is concerned with the optimal scheduling of hydro-thermal power generation systems. This problem, usually referred to as the unit commitment and economic dispatch problem, manifests itself as a large scale mixed integer programming problem. In the first instance a linear model is built and solved using branch-and-bound. This approach is, however, very expensive in terms of computational time. Using Lagrangian relaxation the original primal problem may be written in a dual formulation: the problem then admits decomposition into more tractable subproblems. Furthermore, the primal solution can be approximated closely from the dual solution using the duality gap as a termination criterion. A heuristic is used to construct nearly optimal solutions to the primal problem based on the information provided by the dual problem. The decomposition is such as to allow an implementation on a transputer array with significant reductions in the computational time. An investigation into the application of genetic algorithms to power scheduling shows that this approach is feasible although expensive in terms of computational time. Lagrangian relaxation is next used to solve a nonlinear model incorporating the purchasing and selling of electricity. The information provided by the Lagrange multipliers which can be interpreted as shadow prices, is used to determine the best strategy for the purchasing and selling of energy. Nonconvex programming problems such as this may exhibit a duality gap, that is a difference between the optimal solution of the primal and dual problems. An investigation of this problem for power scheduling linked the existence of this gap to the operating constraints of the system. |
