Download A Scenario Tree-Based Decomposition for Solving Multistage by Debora Mahlke PDF

By Debora Mahlke

ISBN-10: 3834814091

ISBN-13: 9783834814098

Optimization difficulties related to doubtful info come up in lots of components of business and monetary functions. Stochastic programming offers an invaluable framework for modeling and fixing optimization difficulties for which a chance distribution of the unknown parameters is available.
stimulated through useful optimization difficulties taking place in power structures with regenerative power offer, Debora Mahlke formulates and analyzes multistage stochastic mixed-integer types. for his or her resolution, the writer proposes a singular decomposition technique which depends upon the concept that of splitting the underlying state of affairs tree into subtrees. according to the formulated types from strength construction, the set of rules is computationally investigated and the numerical effects are discussed.

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

Optimization difficulties related to doubtful information come up in lots of parts of business and fiscal purposes. Stochastic programming presents an invaluable framework for modeling and fixing optimization difficulties for which a likelihood distribution of the unknown parameters is out there. stimulated through sensible optimization difficulties taking place in power platforms with regenerative power provide, Debora Mahlke formulates and analyzes multistage stochastic mixed-integer versions.

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

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For the next l consecutive nodes on Ns the plant is not operating and then switched on again. The xk variable of all other nodes is set to one or down variable equals one, as explained to zero such that no further xup k or xk above. Further on, we choose the N − T points fns,l , where the power plant is switched on in node n ∈ N \Ns , which means xup n = 1. If t(n) − 1 ≤ l the power plant is not operating on the path(p(n)). Additionally, it is turned off on the path(vt(n)−1 ) with xup vt(n) = 1.

25) over the complete planning horizon, we obtain: ⎛ ⎞ ⎝ min t∈T \{1} ⎠. 26) j∈J This completes the description of the MINLP formulation of the deterministic model. 1. 5 Linearization of the Nonlinear Functions In this section, we present the approximation of the nonlinear efficiency terms occurring within the description of power plants as well as in the description of energy storages. As the efficiency of a machine significantly depends on the current operation level, these functions are indispensable for a realistic problem description.

Basically, it expresses the ratio between the power input and the useful power output. As already mentioned, the efficiency of a power conversion machine depends on the current production level, in general showing a nonlinear behavior. 1, the efficiency typically grows with increasing production. For a power plant i ∈ I, we represent the efficiency by the function ηi (pit ), depending on the produced power pit . Here, the efficiency is associated with the ratio of the consumed power and the produced power pit .

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