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Title: Computing the Feasible Spaces of Optimal Power Flow Problems

Abstract

The solution to an optimal power flow (OPF) problem provides a minimum cost operating point for an electric power system. The performance of OPF solution techniques strongly depends on the problem’s feasible space. This paper presents an algorithm that is guaranteed to compute the entire feasible spaces of small OPF problems to within a specified discretization tolerance. Specifically, the feasible space is computed by discretizing certain of the OPF problem’s inequality constraints to obtain a set of power flow equations. All solutions to the power flow equations at each discretization point are obtained using the Numerical Polynomial Homotopy Continuation (NPHC) algorithm. To improve computational tractability, “bound tightening” and “grid pruning” algorithms use convex relaxations to preclude consideration of many discretization points that are infeasible for the OPF problem. Here, the proposed algorithm is used to generate the feasible spaces of two small test cases.

Authors:
ORCiD logo [1]
  1. Argonne National Lab. (ANL), Argonne, IL (United States)
Publication Date:
Research Org.:
Argonne National Lab. (ANL), Argonne, IL (United States)
Sponsoring Org.:
USDOE Advanced Research Projects Agency - Energy (ARPA-E)
OSTI Identifier:
1401986
Grant/Contract Number:  
AC02-06CH11357
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
IEEE Transactions on Power Systems
Additional Journal Information:
Journal Volume: 32; Journal Issue: 6; Journal ID: ISSN 0885-8950
Publisher:
IEEE
Country of Publication:
United States
Language:
English
Subject:
24 POWER TRANSMISSION AND DISTRIBUTION; Convex optimization; Feasible space; Global solution; Optimal power flow (OPF)

Citation Formats

Molzahn, Daniel K. Computing the Feasible Spaces of Optimal Power Flow Problems. United States: N. p., 2017. Web. doi:10.1109/TPWRS.2017.2682058.
Molzahn, Daniel K. Computing the Feasible Spaces of Optimal Power Flow Problems. United States. doi:10.1109/TPWRS.2017.2682058.
Molzahn, Daniel K. Wed . "Computing the Feasible Spaces of Optimal Power Flow Problems". United States. doi:10.1109/TPWRS.2017.2682058. https://www.osti.gov/servlets/purl/1401986.
@article{osti_1401986,
title = {Computing the Feasible Spaces of Optimal Power Flow Problems},
author = {Molzahn, Daniel K.},
abstractNote = {The solution to an optimal power flow (OPF) problem provides a minimum cost operating point for an electric power system. The performance of OPF solution techniques strongly depends on the problem’s feasible space. This paper presents an algorithm that is guaranteed to compute the entire feasible spaces of small OPF problems to within a specified discretization tolerance. Specifically, the feasible space is computed by discretizing certain of the OPF problem’s inequality constraints to obtain a set of power flow equations. All solutions to the power flow equations at each discretization point are obtained using the Numerical Polynomial Homotopy Continuation (NPHC) algorithm. To improve computational tractability, “bound tightening” and “grid pruning” algorithms use convex relaxations to preclude consideration of many discretization points that are infeasible for the OPF problem. Here, the proposed algorithm is used to generate the feasible spaces of two small test cases.},
doi = {10.1109/TPWRS.2017.2682058},
journal = {IEEE Transactions on Power Systems},
issn = {0885-8950},
number = 6,
volume = 32,
place = {United States},
year = {2017},
month = {3}
}

Journal Article:
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Cited by: 7 works
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Works referencing / citing this record:

Solving large-scale reactive optimal power flow problems by a primal–dual $$\hbox {M}^{2}\hbox {BF}$$ M 2 BF approach
journal, July 2019

  • Pinheiro, Ricardo B. N. M.; Nepomuceno, Leonardo; Balbo, Antonio R.
  • Optimization and Engineering
  • DOI: 10.1007/s11081-019-09451-4