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Learning Optimal Power Flow: Worst-Case Guarantees for Neural Networks

Venzke, Andreas and Qu, Guannan and Low, Steven and Chatzivasileiadis, Spyros (2020) Learning Optimal Power Flow: Worst-Case Guarantees for Neural Networks. In: 2020 IEEE International Conference on Communications, Control, and Computing Technologies for Smart Grids (SmartGridComm). IEEE , Piscataway, NJ, pp. 1-7. ISBN 9781728161273. https://resolver.caltech.edu/CaltechAUTHORS:20210113-163505813

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Abstract

This paper introduces for the first time a framework to obtain provable worst-case guarantees for neural network performance, using learning for optimal power flow (OPF) problems as a guiding example. Neural networks have the potential to substantially reduce the computing time of OPF solutions. However, the lack of guarantees for their worst-case performance remains a major barrier for their adoption in practice. This work aims to remove this barrier. We formulate mixed-integer linear programs to obtain worst-case guarantees for neural network predictions related to (i) maximum constraint violations, (ii) maximum distances between predicted and optimal decision variables, and (iii) maximum sub-optimality. We demonstrate our methods on a range of PGLib-OPF networks up to 300 buses. We show that the worst-case guarantees can be up to one order of magnitude larger than the empirical lower bounds calculated with conventional methods. More importantly, we show that the worst-case predictions appear at the boundaries of the training input domain, and we demonstrate how we can systematically reduce the worst-case guarantees by training on a larger input domain than the domain they are evaluated on.


Item Type:Book Section
Related URLs:
URLURL TypeDescription
https://doi.org/10.1109/smartgridcomm47815.2020.9302963DOIArticle
https://arxiv.org/abs/2006.11029arXivDiscussion Paper
https://doi.org/10.5281/zenodo.3871755Related ItemCode
ORCID:
AuthorORCID
Venzke, Andreas0000-0002-6101-6001
Qu, Guannan0000-0002-5466-3550
Low, Steven0000-0001-6476-3048
Additional Information:© 2020 IEEE. The work of A. Venzke was carried out while visiting the Department of Computing and Mathematical Sciences at the California Institute of Technology, Pasadena, CA 91125, USA. The work of A. Venzke and S. Chatzivasileiadis is supported by the multiDC project, funded by Innovation Fund Denmark, Grant Agreement No. 6154-00020.
Funders:
Funding AgencyGrant Number
Innovation Fund Denmark6154-00020
Record Number:CaltechAUTHORS:20210113-163505813
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20210113-163505813
Official Citation:A. Venzke, G. Qu, S. Low and S. Chatzivasileiadis, "Learning Optimal Power Flow: Worst-Case Guarantees for Neural Networks," 2020 IEEE International Conference on Communications, Control, and Computing Technologies for Smart Grids (SmartGridComm), Tempe, AZ, USA, 2020, pp. 1-7, doi: 10.1109/SmartGridComm47815.2020.9302963
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:107472
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:14 Jan 2021 18:11
Last Modified:14 Jan 2021 18:11

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