Two-stage distributionally robust optimal power flow with flexible loads

Yiling Zhang; Siqian Shen; Bowen Li; Johanna L. Mathieu

doi:10.1109/PTC.2017.7981202

Two-stage distributionally robust optimal power flow with flexible loads

Yiling Zhang, Siqian Shen, Bowen Li, Johanna L. Mathieu

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

7 Scopus citations

Abstract

In this paper, we formulate a two-stage distributionally robust (DR) model for the optimal power flow (OPF) problem in the presence of uncertainties from wind power generation and load-based reserves. Assuming ambiguous distributions of the random variables, we minimize the costs of generation, reserves, and the worst-case expected value of the penalty cost of violating constraints. We consider a lifted support and a distributional ambiguity set parameterized by empirical means and absolute deviations of the random variables. We adopt an enhanced linear decision rule (ELDR) to derive a quadratic programming reformulation of the DR-OPF model, and compare its performance to that of a DR chance-constrained OPF model. We study the optimal solution patterns of the two approaches, compare their performance in out-of-sample simulations, and also numerically justify the use of the ELDR.

Original language	English (US)
Title of host publication	2017 IEEE Manchester PowerTech, Powertech 2017
Publisher	Institute of Electrical and Electronics Engineers Inc.
ISBN (Electronic)	9781509042371
DOIs	https://doi.org/10.1109/PTC.2017.7981202
State	Published - Jul 13 2017
Externally published	Yes
Event	2017 IEEE Manchester PowerTech, Powertech 2017 - Manchester, United Kingdom Duration: Jun 18 2017 → Jun 22 2017

Publication series

Name	2017 IEEE Manchester PowerTech, Powertech 2017

Conference

Conference	2017 IEEE Manchester PowerTech, Powertech 2017
Country/Territory	United Kingdom
City	Manchester
Period	6/18/17 → 6/22/17

Bibliographical note

Funding Information:
This work was supported by NSF Grant #CCF-1442495.

Publisher Copyright:
© 2017 IEEE.

Keywords

distributionally robust optimization
enhanced linear decision rule
load control

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

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10.1109/PTC.2017.7981202

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Two-stage distributionally robust optimal power flow with flexible loads. / Zhang, Yiling; Shen, Siqian; Li, Bowen et al.
2017 IEEE Manchester PowerTech, Powertech 2017. Institute of Electrical and Electronics Engineers Inc., 2017. 7981202 (2017 IEEE Manchester PowerTech, Powertech 2017).

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

Zhang, Y, Shen, S, Li, B & Mathieu, JL 2017, Two-stage distributionally robust optimal power flow with flexible loads. in 2017 IEEE Manchester PowerTech, Powertech 2017., 7981202, 2017 IEEE Manchester PowerTech, Powertech 2017, Institute of Electrical and Electronics Engineers Inc., 2017 IEEE Manchester PowerTech, Powertech 2017, Manchester, United Kingdom, 6/18/17. https://doi.org/10.1109/PTC.2017.7981202

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title = "Two-stage distributionally robust optimal power flow with flexible loads",

abstract = "In this paper, we formulate a two-stage distributionally robust (DR) model for the optimal power flow (OPF) problem in the presence of uncertainties from wind power generation and load-based reserves. Assuming ambiguous distributions of the random variables, we minimize the costs of generation, reserves, and the worst-case expected value of the penalty cost of violating constraints. We consider a lifted support and a distributional ambiguity set parameterized by empirical means and absolute deviations of the random variables. We adopt an enhanced linear decision rule (ELDR) to derive a quadratic programming reformulation of the DR-OPF model, and compare its performance to that of a DR chance-constrained OPF model. We study the optimal solution patterns of the two approaches, compare their performance in out-of-sample simulations, and also numerically justify the use of the ELDR.",

keywords = "distributionally robust optimization, enhanced linear decision rule, load control",

author = "Yiling Zhang and Siqian Shen and Bowen Li and Mathieu, {Johanna L.}",

note = "Funding Information: This work was supported by NSF Grant #CCF-1442495. Publisher Copyright: {\textcopyright} 2017 IEEE.; 2017 IEEE Manchester PowerTech, Powertech 2017 ; Conference date: 18-06-2017 Through 22-06-2017",

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doi = "10.1109/PTC.2017.7981202",

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N2 - In this paper, we formulate a two-stage distributionally robust (DR) model for the optimal power flow (OPF) problem in the presence of uncertainties from wind power generation and load-based reserves. Assuming ambiguous distributions of the random variables, we minimize the costs of generation, reserves, and the worst-case expected value of the penalty cost of violating constraints. We consider a lifted support and a distributional ambiguity set parameterized by empirical means and absolute deviations of the random variables. We adopt an enhanced linear decision rule (ELDR) to derive a quadratic programming reformulation of the DR-OPF model, and compare its performance to that of a DR chance-constrained OPF model. We study the optimal solution patterns of the two approaches, compare their performance in out-of-sample simulations, and also numerically justify the use of the ELDR.

AB - In this paper, we formulate a two-stage distributionally robust (DR) model for the optimal power flow (OPF) problem in the presence of uncertainties from wind power generation and load-based reserves. Assuming ambiguous distributions of the random variables, we minimize the costs of generation, reserves, and the worst-case expected value of the penalty cost of violating constraints. We consider a lifted support and a distributional ambiguity set parameterized by empirical means and absolute deviations of the random variables. We adopt an enhanced linear decision rule (ELDR) to derive a quadratic programming reformulation of the DR-OPF model, and compare its performance to that of a DR chance-constrained OPF model. We study the optimal solution patterns of the two approaches, compare their performance in out-of-sample simulations, and also numerically justify the use of the ELDR.

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KW - load control

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Two-stage distributionally robust optimal power flow with flexible loads

Abstract

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Bibliographical note

Keywords

UN SDGs

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