Stochastic Lagrangian Relaxation applied to Power Scheduling in a Hydro-Thermal System under Uncertainty
dc.contributor.author | Nowak, Matthias Peter | |
dc.contributor.author | Römisch, Werner | |
dc.date.accessioned | 2017-06-15T17:59:25Z | |
dc.date.available | 2017-06-15T17:59:25Z | |
dc.date.created | 2005-11-15 | |
dc.date.issued | 2005-11-15 | |
dc.identifier.issn | 0863-0976 | |
dc.identifier.uri | http://edoc.hu-berlin.de/18452/3342 | |
dc.description.abstract | A dynamic (multi-stage) stochastic programming model for the weekly cost-optimal generation of electric power in a hydro-thermal generation system under uncertain load is developed. The model involves a large number of mixed-integer (stochastic) decision variables and constraints linking time periods and operating power units. A stochastic Lagrangian relaxation scheme is designed by assigning (stochastic) multipliers to all constraints coupling power units. It is assumed that the stochastic load process is given (or approximated) by a finite number of realizations (scenarios) in scenario tree form. Solving the dual by a bundle subgradient method leads to a successive decomposition into stochastic single (thermal or hydro) unit subproblems. The stochastic thermal and hydro subproblems are solved by a stochastic dynamic programming technique and by a specific descent algorithm, respectively. A Lagrangian heuristics that provides approximate solutions for the first stage (primal) decisions starting from the optimal (stochastic) multipliers is developed. Numerical results are presented for realistic data from a German power utility and for numbers of scenarios ranging from 5 to 100 and a time horizon from 7 to 9 days. The sizes of the corresponding optimization problems go up to 200.000 binary and 350.000 continuous variables, and more than 500.000 constraints. | eng |
dc.language.iso | eng | |
dc.publisher | Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, Institut für Mathematik | |
dc.rights.uri | http://rightsstatements.org/vocab/InC/1.0/ | |
dc.subject | uncertain load | eng |
dc.subject | mixed-integer | eng |
dc.subject | Multi-stage stochastic program | eng |
dc.subject | stochastic Lagrangian relaxation | eng |
dc.subject | power generation | eng |
dc.subject | hydro-thermal system | eng |
dc.subject.ddc | 510 Mathematik | |
dc.title | Stochastic Lagrangian Relaxation applied to Power Scheduling in a Hydro-Thermal System under Uncertainty | |
dc.type | book | |
dc.identifier.urn | urn:nbn:de:kobv:11-10053645 | |
dc.identifier.doi | http://dx.doi.org/10.18452/2690 | |
local.edoc.pages | 25 | |
local.edoc.type-name | Buch | |
local.edoc.container-type | series | |
local.edoc.container-type-name | Schriftenreihe | |
local.edoc.container-year | 1998 | |
dc.identifier.zdb | 2075199-0 | |
bua.series.name | Preprints aus dem Institut für Mathematik | |
bua.series.issuenumber | 1998,24 |