Computing the Feasible Spaces of Optimal Power Flow Problems
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.
- Publication Date:
- Grant/Contract Number:
- AC02-06CH11357
- Type:
- 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
- Research Org:
- Argonne National Lab. (ANL), Argonne, IL (United States)
- Sponsoring Org:
- USDOE Advanced Research Projects Agency - Energy (ARPA-E)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 24 POWER TRANSMISSION AND DISTRIBUTION; Convex optimization; Feasible space; Global solution; Optimal power flow (OPF)
- OSTI Identifier:
- 1401986
Molzahn, Daniel K. Computing the Feasible Spaces of Optimal Power Flow Problems. United States: N. p.,
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. 2017.
"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},
number = 6,
volume = 32,
place = {United States},
year = {2017},
month = {3}
}