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:

 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 (ARPAE)
 OSTI Identifier:
 1401986
 Grant/Contract Number:
 AC0206CH11357
 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 08858950
 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 = {08858950},
number = 6,
volume = 32,
place = {United States},
year = {2017},
month = {3}
}
Web of Science
Works referencing / citing this record:
Solving largescale 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