Probability Statistics

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

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By Debora Mahlke

ISBN-10: 3834814091

ISBN-13: 9783834814098

ISBN-10: 3834898295

ISBN-13: 9783834898296

Optimization difficulties related to doubtful information 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 chance distribution of the unknown parameters is available.
inspired by means of sensible optimization difficulties happening in power platforms with regenerative power provide, Debora Mahlke formulates and analyzes multistage stochastic mixed-integer types. for his or her answer, the writer proposes a singular decomposition technique which is dependent upon the concept that of splitting the underlying state of affairs tree into subtrees. in response to the formulated types from strength creation, the set of rules is computationally investigated and the numerical effects are discussed.

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

Example text

25) = γtimp . 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.

These nonlinear functions appear as univariate nonlinear terms in the model, which have to be approximated in an adequate way. 5, we present a piecewise linear approximation of each nonlinear term, yielding a mixed-integer linear problem. 3 Constraints In the following section the constraints describing the problem are modeled explicitly. We start with the major restriction, concerning the demand satisfaction. In each time step t ∈ T the demand δt has to be covered by the produced power pit of the plants i ∈ I, the imported power xt , and the available wind power supply ωt .

N, k ∈ Ns . We know that the system of constraints restricted to Γs corresponds to the deterministic case. 2) for n, k ∈ Ns is redundant. 2) for n, k ∈ Ns is also redundant in the complete system. 5) can be handled analogously. ✷ Subsequently, we present the main result of this section, which is the complete description of PΓ,L,l by linear inequalities. 4 Let Γ be a scenario tree with the node set N = {1, . . , N }. 12) provide a complete linear description of PΓ,L,l . Proof. 12)}. 50 Chapter 4.

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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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