Convex Relaxations and Approximations of Chance-Constrained AC-OPF Problems

Lejla Halilbasic*, Pierre Pinson, Spyros Chatzivasileiadis

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review

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Abstract

This paper deals with the impact of linear approximations for the unknown nonconvex confidence region of chance-constrained AC optimal power flow problems. Such approximations are required for the formulation of tractable chance constraints. In this context, we introduce the first formulation of a chance-constrained second-order cone (SOC) OPF. The proposed formulation provides convergence guarantees due to its convexity, while it demonstrates high computational efficiency. Combined with an AC feasibility recovery, it is able to identify better solutions than chance-constrained nonconvex AC-OPF formulations. To the best of our knowledge, this paper is the first to perform a rigorous analysis of the AC feasibility recovery procedures for robust SOC-OPF problems. We identify the issues that arise from the linear approximations, and by using a reformulation of the quadratic chance constraints, we introduce new parameters able to reshape the approximation of the confidence region. We demonstrate our method on the IEEE 118-bus system.
Original languageEnglish
JournalIEEE Transactions on Power Systems
Volume34
Issue number2
Pages (from-to)1459 - 1470
ISSN0885-8950
DOIs
Publication statusPublished - 2018

Keywords

  • Robustness
  • Uncertainty
  • Optimization
  • Mathematical model
  • Convergence
  • Taylor series
  • Generators
  • Chance-constrained AC-OPF
  • convex relaxations
  • second order cone programming
  • AC feasibility recovery

Cite this

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title = "Convex Relaxations and Approximations of Chance-Constrained AC-OPF Problems",
abstract = "This paper deals with the impact of linear approximations for the unknown nonconvex confidence region of chance-constrained AC optimal power flow problems. Such approximations are required for the formulation of tractable chance constraints. In this context, we introduce the first formulation of a chance-constrained second-order cone (SOC) OPF. The proposed formulation provides convergence guarantees due to its convexity, while it demonstrates high computational efficiency. Combined with an AC feasibility recovery, it is able to identify better solutions than chance-constrained nonconvex AC-OPF formulations. To the best of our knowledge, this paper is the first to perform a rigorous analysis of the AC feasibility recovery procedures for robust SOC-OPF problems. We identify the issues that arise from the linear approximations, and by using a reformulation of the quadratic chance constraints, we introduce new parameters able to reshape the approximation of the confidence region. We demonstrate our method on the IEEE 118-bus system.",
keywords = "Robustness, Uncertainty, Optimization, Mathematical model, Convergence, Taylor series, Generators, Chance-constrained AC-OPF, convex relaxations, second order cone programming, AC feasibility recovery",
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year = "2018",
doi = "10.1109/TPWRS.2018.2874072",
language = "English",
volume = "34",
pages = "1459 -- 1470",
journal = "I E E E Transactions on Power Systems",
issn = "0885-8950",
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Convex Relaxations and Approximations of Chance-Constrained AC-OPF Problems. / Halilbasic, Lejla; Pinson, Pierre; Chatzivasileiadis, Spyros.

In: IEEE Transactions on Power Systems, Vol. 34, No. 2, 2018, p. 1459 - 1470.

Research output: Contribution to journalJournal articleResearchpeer-review

TY - JOUR

T1 - Convex Relaxations and Approximations of Chance-Constrained AC-OPF Problems

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AU - Pinson, Pierre

AU - Chatzivasileiadis, Spyros

PY - 2018

Y1 - 2018

N2 - This paper deals with the impact of linear approximations for the unknown nonconvex confidence region of chance-constrained AC optimal power flow problems. Such approximations are required for the formulation of tractable chance constraints. In this context, we introduce the first formulation of a chance-constrained second-order cone (SOC) OPF. The proposed formulation provides convergence guarantees due to its convexity, while it demonstrates high computational efficiency. Combined with an AC feasibility recovery, it is able to identify better solutions than chance-constrained nonconvex AC-OPF formulations. To the best of our knowledge, this paper is the first to perform a rigorous analysis of the AC feasibility recovery procedures for robust SOC-OPF problems. We identify the issues that arise from the linear approximations, and by using a reformulation of the quadratic chance constraints, we introduce new parameters able to reshape the approximation of the confidence region. We demonstrate our method on the IEEE 118-bus system.

AB - This paper deals with the impact of linear approximations for the unknown nonconvex confidence region of chance-constrained AC optimal power flow problems. Such approximations are required for the formulation of tractable chance constraints. In this context, we introduce the first formulation of a chance-constrained second-order cone (SOC) OPF. The proposed formulation provides convergence guarantees due to its convexity, while it demonstrates high computational efficiency. Combined with an AC feasibility recovery, it is able to identify better solutions than chance-constrained nonconvex AC-OPF formulations. To the best of our knowledge, this paper is the first to perform a rigorous analysis of the AC feasibility recovery procedures for robust SOC-OPF problems. We identify the issues that arise from the linear approximations, and by using a reformulation of the quadratic chance constraints, we introduce new parameters able to reshape the approximation of the confidence region. We demonstrate our method on the IEEE 118-bus system.

KW - Robustness

KW - Uncertainty

KW - Optimization

KW - Mathematical model

KW - Convergence

KW - Taylor series

KW - Generators

KW - Chance-constrained AC-OPF

KW - convex relaxations

KW - second order cone programming

KW - AC feasibility recovery

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JO - I E E E Transactions on Power Systems

JF - I E E E Transactions on Power Systems

SN - 0885-8950

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