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

Xu Ma; Umesh Vaidya; Nicola Elia

doi:10.1109/CDC.2018.8619620

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

Xu Ma, Umesh Vaidya, Nicola Elia

Electrical and Computer Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference 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 language	English (US)
Title of host publication	2018 IEEE Conference on Decision and Control, CDC 2018
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	6532-6537
Number of pages	6
ISBN (Electronic)	9781538613955
DOIs	https://doi.org/10.1109/CDC.2018.8619620
State	Published - Jul 2 2018
Event	57th IEEE Conference on Decision and Control, CDC 2018 - Miami, United States Duration: Dec 17 2018 → Dec 19 2018

Publication series

Name	Proceedings of the IEEE Conference on Decision and Control
Volume	2018-December
ISSN (Print)	0743-1546
ISSN (Electronic)	2576-2370

Conference

Conference	57th IEEE Conference on Decision and Control, CDC 2018
Country/Territory	United States
City	Miami
Period	12/17/18 → 12/19/18

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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10.1109/CDC.2018.8619620

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Ma, X., Vaidya, U., & Elia, N. (2018). The Primal-Dual Gradient Method for Non-Convex Robust Optimization with an Application to the Robust AC-OPF. In 2018 IEEE Conference on Decision and Control, CDC 2018 (pp. 6532-6537). Article 8619620 (Proceedings of the IEEE Conference on Decision and Control; Vol. 2018-December). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2018.8619620

The Primal-Dual Gradient Method for Non-Convex Robust Optimization with an Application to the Robust AC-OPF. / Ma, Xu; Vaidya, Umesh; Elia, Nicola.
2018 IEEE Conference on Decision and Control, CDC 2018. Institute of Electrical and Electronics Engineers Inc., 2018. p. 6532-6537 8619620 (Proceedings of the IEEE Conference on Decision and Control; Vol. 2018-December).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Ma, X, Vaidya, U & Elia, N 2018, The Primal-Dual Gradient Method for Non-Convex Robust Optimization with an Application to the Robust AC-OPF. in 2018 IEEE Conference on Decision and Control, CDC 2018., 8619620, Proceedings of the IEEE Conference on Decision and Control, vol. 2018-December, Institute of Electrical and Electronics Engineers Inc., pp. 6532-6537, 57th IEEE Conference on Decision and Control, CDC 2018, Miami, United States, 12/17/18. https://doi.org/10.1109/CDC.2018.8619620

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N2 - 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.

AB - 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.

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

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