A Scenario Tree-Based Decomposition for Solving Multistage - download pdf or read online

By Debora Mahlke

ISBN-10: 3834814091

ISBN-13: 9783834814098

ISBN-10: 3834898295

ISBN-13: 9783834898296

Optimization difficulties regarding doubtful info come up in lots of parts of commercial and monetary purposes. Stochastic programming presents an invaluable framework for modeling and fixing optimization difficulties for which a likelihood distribution of the unknown parameters is available.
prompted by way of functional optimization difficulties happening in power platforms with regenerative strength offer, Debora Mahlke formulates and analyzes multistage stochastic mixed-integer types. for his or her answer, the writer proposes a singular decomposition process which is determined by the idea that of splitting the underlying state of affairs tree into subtrees. in accordance with the formulated types from power construction, the set of rules is computationally investigated and the numerical effects are discussed.

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Additional info for A Scenario Tree-Based Decomposition for Solving Multistage Stochastic Programs: With Application in Energy Production

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Among others mainly load profiles, electricity prices, and the power supply by regenerative energy are affected. In this thesis, we focus on the optimization under uncertain wind power generation, resulting from its meteorological dependence and uncertain prices for electricity. Regarding the fluctuations of the consumers’ demand, we assume the corresponding load to be deterministic, as a reliable forecast of the load of one day or even one week can be given by schedulers. 1 Basic Concepts in Stochastic Programming The following introduction to the basic concepts in stochastic programming and the notation used in this thesis are based on [RS01], [BL97] and [KM05].

23) The fuel costs are computed with respect to the efficiency ηi (pit ), as they depend on the energy which is actually consumed by the plant. In contrast, the variable costs are expressed in dependence of the produced energy pτit in period t. Note that the number of time steps per hour, denoted by τ , appears in the formulation. of an energy storage j ∈ J in step t ∈ T \ {1} can be The costs cstor jt expressed as cstor jt γjf uel = τ sout lt + ext ηj (sout lt ) k∈Kj l∈Lj in,up γjin,up zkt + out,up γjout,up zlt .

T } taking values in R2 . In our case, ωt represents the wind power available in period t and γtimp the price for electricity in t. At the beginning of the planning horizon only the data for time step t = 1 is known, which means that ξ1 is deterministic. For data of future periods only the probability distribution is given. Nevertheless, decisions on how to operate the facilities have to be made without complete knowledge of the wind power production or electricity prices during the planning horizon.

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A Scenario Tree-Based Decomposition for Solving Multistage Stochastic Programs: With Application in Energy Production by Debora Mahlke

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