Decomposition approaches for block-structured chance-constrained programs with application to hydro-thermal unit commitment

The unit commitment problem, aims at computing the production schedule that satisfies the offer-demand equilibrium at minimal cost. Often such problems are considered in a deterministic framework. However uncertainty is present and non-negligible. Robustness of the production schedule is therefore a...

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Bibliographic Details
Published in:Mathematical methods of operations research (Heidelberg, Germany) Germany), 2014-12, Vol.80 (3), p.227-253
Main Author: van Ackooij, Wim
Format: Article
Language:English
Subjects:
Business and Management
Calculus of Variations and Optimal Control
Optimization
Decomposition
Energy management
Equilibrium
Heuristic
Investigations
Mathematical models
Mathematics
Mathematics and Statistics
Operations research
Operations Research/Decision Theory
Optimization
Original Article
Robustness
Schedules
Simplification
Studies
Uncertainty
Unit commitment
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Summary:The unit commitment problem, aims at computing the production schedule that satisfies the offer-demand equilibrium at minimal cost. Often such problems are considered in a deterministic framework. However uncertainty is present and non-negligible. Robustness of the production schedule is therefore a key question. In this paper, we will investigate this robustness when hydro valleys are made robust against uncertainty on inflows and the global schedule is robust against uncertainty on customer load. Both robustness requirements will be modelled by using bilateral joint chance constraints. Since this is a fairly large model, we will investigate several decomposition procedures and compare these on several typical numerical instances. The latter decomposition procedures are clearly a prerequisite if robust unit commitment is ever to be used in practice. We will show that an efficient decomposition procedure exists and can be used to derive a robust production schedule. The obtained results are illustrated on a convex simplification of a unit commitment problem in order to avoid the use of heuristics. The investigated decomposition approaches can be applied trivially to a non-convex setting, but will need to be followed by appropriate heuristics. How this may work in practice is also illustrated.
ISSN:1432-2994
1432-5217
DOI:10.1007/s00186-014-0478-5