Convex Relaxations of the Short-Term Hydrothermal Scheduling Problem

This paper concerns the assessment of two methods for convex relaxation of the short-term hydrothermal scheduling problem. The problem is originally formulated as a mixed integer programming problem, and then approximated using both Lagrangian and Linear relaxation. The two relaxation methods are qu...

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Bibliographic Details
Published in:IEEE transactions on power systems 2021-07, Vol.36 (4), p.3293-3304
Main Authors: Helseth, Arild, Jaehnert, Stefan, Diniz, Andre Luiz
Format: Article
Language:English
Subjects:
Electric power systems
Hydroelectric power generation
Integer programming
Linear programming
Mixed integer
Operating costs
Power generation economics
Predictive models
Relaxation methods
Reserve capacity
Scheduling
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Summary:This paper concerns the assessment of two methods for convex relaxation of the short-term hydrothermal scheduling problem. The problem is originally formulated as a mixed integer programming problem, and then approximated using both Lagrangian and Linear relaxation. The two relaxation methods are quantitatively compared using a realistic data description of the Northern European power system, considering a set of representative days. We find that the Lagrangian relaxation approximates system operational costs in the range 55-81% closer to the mixed integer programming problem solution than the Linear relaxation. We show how these cost gaps vary with season and climatic conditions. Conversely, the differences in both marginal cost of electricity and reserve capacity provided by the Lagrangian and Linear relaxation are muted.
ISSN:0885-8950
1558-0679
DOI:10.1109/TPWRS.2020.3047346