A power generation system comprising thermal and pumped-storage hydro plants is considered. Two kinds of models for the cost-optimal generation of electric power under uncertain load are introduced: (i) a dy-namic model for the short-term operation and (ii) a power production plan-ning 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) decisions, 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 dynamic model a Lagrangian decomposition based al-gorithm is described in more detail. Special emphasis is put on a discussion of the duality gap, the efficient solution of the multi-stage single unit sub-problems and on solving the dual problem by bundle methods for convex nondifferentiable optimization.
CITATION STYLE
Dentcheva, D., & Römisch, W. (1998). Optimal Power Generation under Uncertainty via Stochastic Programming (pp. 22–56). https://doi.org/10.1007/978-3-642-45767-8_2
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