Division of Optimization and Systems Theory,
Department of Mathematics,
In this talk, I will summarize my thesis, titled "On optimization of power production". It treats some large-scale, non-convex optimization problems that appear in short-term production planning of power. For systems with thermal generation (oil, coal, gas, nuclear), a basic problem is when to start and stop units to minimize operational costs, the unit commitment problem. It contains the convex problem of optimally allocate an electric load among units, optimal dispatch, as a subproblem. We describe algorithms for these problems which are based on Lagrangian relaxation and solution of the corresponding dual problem. For hydro power systems we study a model which explicitly includes the dependency of dam elevation on power output. The resulting optimization problem has bilinear objective and structured network constraints. We use a certain concavity property to show that any local optimum is an extreme point of the feasible set. This property motivates a simplex-type algorithm for computing local optima. Explicit convexification of the terms in the objective function gives a family of convex problems, which underestimate the original problem, and provides feasible solutions. A branch-and-bound strategy is then employed to compute global optima. Finally, the problem of cogeneration is treated. Some power systems has the capability to use exhaust heat from the electricity production for district heating or for distillation of water. Since heat or water may be stored, an inventory balance now couples the production between time periods. The approach for this problem is again Lagrangian relaxation, coupled with a certain restrification to cope with the complexity of the subproblems. For all problems considered, computational results for real or realistic problems will be presented.