The Primal-Dual Gradient Method for Non-Convex Robust Optimization with an Application to the Robust AC-OPF

Xu Ma, Umesh Vaidya, Nicola Elia

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

The recent large-scale penetration of renewable energy in power networks has also introduced with it a risk of random variability. This new source of power uncertainty can fluctuate so substantially that the traditional base-point forecast and control scheme may fail to work. To address this challenge, we study the so-called robust AC optimal power flow (AC-OPF) so as to provide robust control solutions that can immunize the power system against the intermittent renewables. In this paper we generalize the continuous-time primal-dual gradient dynamics approach to solve the robust AC-OPF. One advantage of the proposed approach is that it does not require any convexity assumptions for the decision variables during the dynamical evolution. This paper first derives a stability analysis for the primal-dual dynamics associated with a generic robust optimization, and then applies the primal-dual dynamics to the robust AC-OPF problem. Simulation results are also provided to demonstrate the effectiveness of the proposed approach.

Original languageEnglish (US)
Title of host publication2018 IEEE Conference on Decision and Control, CDC 2018
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages6532-6537
Number of pages6
ISBN (Electronic)9781538613955
DOIs
StatePublished - Jan 18 2019
Externally publishedYes
Event57th IEEE Conference on Decision and Control, CDC 2018 - Miami, United States
Duration: Dec 17 2018Dec 19 2018

Publication series

NameProceedings of the IEEE Conference on Decision and Control
Volume2018-December
ISSN (Print)0743-1546

Conference

Conference57th IEEE Conference on Decision and Control, CDC 2018
Country/TerritoryUnited States
CityMiami
Period12/17/1812/19/18

Bibliographical note

Funding Information:
This research has been supported by the National Science Foundation grants CNS-1329915, ECCS-1150405, NSF CIF-1220643, and AFOSR AF FA-9550-15-1-0119.

Funding Information:
This research has been supported by the National Science Foundation grants CNS-1329915, ECCS-1150405, NSF CIF-1220643, and AFOSR AF FA- 9550-15-1-0119.

Publisher Copyright:
© 2018 IEEE.

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