Stochastic Lagrangian relaxation applied to power scheduling in a hydro-thermal system under uncertainty

Stochastic Lagrangian relaxation applied to power scheduling in a hydro-thermal system under uncertainty

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Article ID: iaor2002260
Country: Netherlands
Volume: 100
Issue: 1
Start Page Number: 251
End Page Number: 272
Publication Date: Dec 2000
Journal: Annals of Operations Research
Authors: ,
Keywords: programming: probabilistic, programming: integer
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 demand (or 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 of 168 hours. The sizes of the corresponding optimization problems go up to 200,000 binary and 350,000 continuous variables, and more than 500,000 constraints.

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