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A mixed-integer stochastic nonlinear optimization problem with joint probabilistic constraints. (English) Zbl 1294.90014
Summary: We illustrate the solution of a mixed-integer stochastic nonlinear optimization problem in an application of power management. In this application, a coupled system consisting of a hydro power station and a wind farm is considered. The objective is to satisfy the local energy demand and sell any surplus energy on a spot market for a short time horizon. Generation of wind energy is assumed to be random, so that demand satisfaction is modeled by a joint probabilistic constraint taking into account the multivariate distribution.
The turbine is forced to either operate between given positive limits or to he shut down. This introduces additional binary decisions. The numerical solution procedure is presented and results are illustrated.

MSC:
90B05 Inventory, storage, reservoirs
90C15 Stochastic programming
90C10 Integer programming
Software:
SCIP
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