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SPEPS Preprint

Author(s): Nicole Gröwe-Kuska, Humboldt-University Berlin
Krzysztof C. Kiwiel, Systems Research Institute, Warsaw
Matthias Peter Nowak, Humboldt-University Berlin
Werner Römisch, Humboldt-University Berlin
Isabel Wegner, Humboldt-University Berlin
Title: Power management in a hydro-thermal system under uncertainty by Lagrangian relaxation
Date of Acceptance: 20.01.2000
Submission Date: 10.01.2000
Series Title: Stochastic Programming E-Print Series
(SPEPS)
Editors: Julie L. Higle; Werner Römisch; Surrajeet Sen
Keywords (eng): Lagrangian relaxation, Stochastic programming, bundle methods, unit commitment, scenario generation
Appeared in: The IMA volumes in mathematics and its applications (Vol. 128, 2002)
Springer (New York [u.a.])
Metadata export: To export the complete metadata set as Endote or Bibtex format please click to the appropriate link. Endnote   Bibtex  

Abstract (eng):
We 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.
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