Abstract
The short-term cost-optimal dispatch of electric power in a generation system under uncertain electricity demand is considered. The system comprises thermal and pumped-storage hydro units. An operation model is developed which represents a multistage mixed-integer stochastic program and a conceptual solution method using Lagrangian relaxation is sketched. For fixed start-up and shut-down decisions an efficient algorithm for solving the multistage stochastic program is described and numerical results are reported.
This research is supported by the Schwerpunktprogramm “Echtzeit-Optimierung großer Systeme” of the Deutsche Forschungsgemeinschaft (DFG)
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
D.P. Bertsekas, G.S. Lauer, N.R. Sandell, and T.A. Posbergh. Optimal short-term scheduling of large-scale power systems. IEEE Transactions on Automatic Control,28(1983)1–11.
CPLEX Optimization, Inc. Using the CPLEX Callable Library,1989–1995.
D. Dentcheva and W. Römisch. Optimal power generation under uncertainty via stochastic programming. Preprint Nr. 96–35, Humboldt-Universität Berlin, Institut für Mathematik, 1996.
N. Gröwe, W. Römisch, and R. Schultz. A simple recourse model for power dispatch under uncertain demand. Annals of Operations Research,59(1995)135–164.
J. Jacobs, G. Freeman, J. Grygier, D. Morton, G. Schultz, K. Staschus, and J. Stedinger. SOCRATES: A system for scheduling hydroelectric generation under uncertainty. Annals of Operations Research,59(1995)99–133.
K.C. Kiwiel. Proximity control in bundle methods for convex nondifferentiable minimization. Mathematical Programming,46(1990)105–122.
C. Lemarechal. Lagrangian decomposition and nonsmooth optimization: bundle algorithm, prox iteration, augmented lagrangian. In: F. Gianessi (Ed.) Nonsmooth Optimization Methods and Applications, Gordon and Breach 1992, 201–216.
M.P. Nowak. A fast descent method for the hydro storage subproblem in power generation. Working Paper 96–109, International Institute for Applied Systems Analysis, September 1996.
M.V.F Pereira and L.M.V.G. Pinto. Multi-stage stochastic optimization applied to energy planning. Mathematical Programming,52(1991)359–375.
G.B. Sheble and G.N. Fand. Unit commitment literature synopsis. IEEE Transactions on Power Systems,9(1994)128–135.
S. Takriti, J.R. Birge, and E. Long. A stochastic model for the unit commitment problem. IEEE Transactions on Power Systems,11(1996)1397–1506.
F. Zhuang and F.D. Galiana. Towards a more rigorous and practical unit commitment by lagrangian relaxation. IEEE Transactions on Power Systems,3(1988)763–773.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1997 B. G. Teubner Stuttgart
About this chapter
Cite this chapter
Nowak, M.P., Römisch, W. (1997). Optimal Power Dispatch via Multistage Stochastic Programming. In: Brøns, M., Bendsøe, M.P., Sørensen, M.P. (eds) Progress in Industrial Mathematics at ECMI 96. European Consortium for Mathematics in Industry, vol 9. Vieweg+Teubner Verlag, Wiesbaden. https://doi.org/10.1007/978-3-322-96688-9_37
Download citation
DOI: https://doi.org/10.1007/978-3-322-96688-9_37
Publisher Name: Vieweg+Teubner Verlag, Wiesbaden
Print ISBN: 978-3-322-96689-6
Online ISBN: 978-3-322-96688-9
eBook Packages: Springer Book Archive