Tight and Compact Sample Average Approximation for Joint Chance-Constrained Problems with Applications to Optimal Power Flow

Álvaro Porras (), Concepción Domínguez (), Juan Miguel Morales () and Salvador Pineda ()
Additional contact information
Álvaro Porras: OASYS Research Group, University of Málaga, 29071 Málaga, Spain
Concepción Domínguez: OASYS Research Group, University of Málaga, 29071 Málaga, Spain
Juan Miguel Morales: OASYS Research Group, University of Málaga, 29071 Málaga, Spain
Salvador Pineda: OASYS Research Group, University of Málaga, 29071 Málaga, Spain

INFORMS Journal on Computing, 2023, vol. 35, issue 6, 1454-1469

Abstract: In this paper, we tackle the resolution of chance-constrained problems reformulated via sample average approximation. The resulting data-driven deterministic reformulation takes the form of a large-scale mixed-integer program (MIP) cursed with Big-Ms. We introduce an exact resolution method for the MIP that combines the addition of a set of valid inequalities to tighten the linear relaxation bound with coefficient strengthening and constraint screening algorithms to improve its Big-Ms and considerably reduce its size. The proposed valid inequalities are based on the notion of k -envelopes and can be computed off-line using polynomial-time algorithms and added to the MIP program all at once. Furthermore, they are equally useful to boost the strengthening of the Big-Ms and the screening rate of superfluous constraints. We apply our procedures to a probabilistically constrained version of the DC optimal power flow problem with uncertain demand. The chance constraint requires that the probability of violating any of the power system’s constraints be lower than some positive threshold. In a series of numerical experiments that involve five power systems of different size, we show the efficiency of the proposed methodology and compare it with some of the best performing convex inner approximations currently available in the literature.

Keywords: chance constraints; probabilistic constraints; k -violation problems; combinatorial optimization; mixed-integer programming; valid inequalities; optimal power flow (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://dx.doi.org/10.1287/ijoc.2022.0302 (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:inm:orijoc:v:35:y:2023:i:6:p:1454-1469

Access Statistics for this article

More articles in INFORMS Journal on Computing from INFORMS Contact information at EDIRC.
Bibliographic data for series maintained by Chris Asher ().