Optimal Power Generation under Uncertainty via Stochastic Programming

A power generation system comprising thermal and pumped storage hy dro plants is considered Two kinds of models for the cost optimal generation of electric power under uncertain load are introduced i a dynamic model for the short term operation and ii a power production planning model In both cases the presence of stochastic data in the optimization model leads to multi stage and two stage stochastic programs respectively Both stochastic programming problems involve a large number of mixed integer stochastic de cisions but their constraints are loosely coupled across operating power units This is used to design Lagrangian relaxation methods for both models which lead to a decomposition into stochastic single unit subproblems For the dy namic model a Lagrangian decomposition based algorithm is described in more detail Special emphasis is put on a discussion of the duality gap the e cient solution of the multi stage single unit subproblems and on solving the dual problem by bundle methods for convex nondi erentiable optimization