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2000-01-20Buch DOI: 10.18452/8228
Power management in a hydro-thermal system under uncertainty by Lagrangian relaxation
dc.contributor.authorGröwe-Kuska, Nicole
dc.contributor.authorKiwiel, Krzysztof C.
dc.contributor.authorNowak, Matthias Peter
dc.contributor.authorRömisch, Werner
dc.contributor.authorWegner, Isabel
dc.contributor.editorHigle, Julie L.
dc.contributor.editorRömisch, Werner
dc.contributor.editorSen, Surrajeet
dc.date.accessioned2017-06-16T19:37:06Z
dc.date.available2017-06-16T19:37:06Z
dc.date.created2006-02-07
dc.date.issued2000-01-20
dc.date.submitted2000-01-10
dc.identifier.urihttp://edoc.hu-berlin.de/18452/8880
dc.description.abstractWe present a dynamic multistage stochastic programming model for the cost-optimal generation of electric power in a hydro-thermal system under uncertainty in load, inflow to reservoirs and prices for fuel and delivery contracts. The stochastic load process is approximated by a scenario tree obtained by adapting a SARIMA model to historical data, using empirical means and variances of simulated scenarios to construct an initial tree, and reducing it by a scenario deletion procedure based on a suitable probability distance. Our model involves many mixed-integer variables and individual power unit constraints, but relatively few coupling constraints. Hence we employ stochastic Lagrangian relaxation that assigns stochastic multipliers to the coupling constraints. Solving the Lagarangian dual by a proximal bundle method leads to successive decomposition into single thermal and hydro unit subproblems that are solved by dynamic programming and a specialized descent algorithm, respectively. The optimal stochastic multipliers are used in Lagrangian heuristics to construct approximately optimal first stage decisions. Numerical results are presented for realistic data from a German power utility, with a time horizon of one week and scenario numbers ranging from 5 to 100. The corresponding optimization problems have up to 200,000 binary and 350,000 continuous variables, and more than 500,000 constraints.eng
dc.language.isoeng
dc.publisherHumboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, Institut für Mathematik
dc.subjectLagrangian relaxationeng
dc.subjectStochastic programmingeng
dc.subjectbundle methodseng
dc.subjectunit commitmenteng
dc.subjectscenario generationeng
dc.subject.ddc510 Mathematik
dc.titlePower management in a hydro-thermal system under uncertainty by Lagrangian relaxation
dc.typebook
dc.identifier.urnurn:nbn:de:kobv:11-110-18452/8880-5
dc.identifier.doihttp://dx.doi.org/10.18452/8228
local.edoc.container-titleStochastic Programming E-Print Series
local.edoc.type-nameBuch
local.edoc.container-typeseries
local.edoc.container-type-nameSchriftenreihe
local.edoc.container-publisher-nameSpringer
local.edoc.container-publisher-placeNew York [u.a.]
local.edoc.container-volume2000
local.edoc.container-issue1
local.edoc.container-year2002
local.edoc.container-erstkatid2936317-2

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