Inexact convex relaxations for AC optimal power flow: Towards AC feasibility
Abstract
Convex relaxations of AC optimal power flow (AC-OPF) problems have attracted significant interest as in several instances they provably yield the global optimum to the original non-convex problem. If, however, the relaxation is inexact, the obtained solution is not AC-feasible. The quality of the obtained solution is essential for several practical applications of AC-OPF, but detailed analyses are lacking in existing literature. Here, this paper aims to cover this gap. We provide an in-depth investigation of the solution characteristics when convex relaxations are inexact, we assess the most promising AC feasibility recovery methods for large-scale systems, and we propose two new metrics that lead to a better understanding of the quality of the identified solutions. We perform a comprehensive assessment on 96 different test cases, ranging from 14 to 3120 buses, and we show the following: (i) Despite an optimality gap of less than 1%, several test cases still exhibit substantial distances to both AC feasibility and local optimality and the newly proposed metrics characterize these deviations. (ii) Penalization methods fail to recover an AC-feasible solution in 15 out of 45 test cases. (iii) The computational benefits of warm-starting non-convex solvers have significant variation, but a computational speedup exists inmore »
- Authors:
-
[1];
- Technical Univ of Denmark, Lyngby (Denmark)
- Georgia Inst. of Technology, Atlanta, GA (United States); Argonne National Lab. (ANL), Lemont, IL (United States)
- Publication Date:
- Research Org.:
- Argonne National Laboratory (ANL), Argonne, IL (United States)
- Sponsoring Org.:
- USDOE Office of Electricity (OE)
- OSTI Identifier:
- 1829268
- Alternate Identifier(s):
- OSTI ID: 1634274
- Grant/Contract Number:
- AC02-06CH11357
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Electric Power Systems Research
- Additional Journal Information:
- Journal Volume: 187; Journal ID: ISSN 0378-7796
- Publisher:
- Elsevier
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 24 POWER TRANSMISSION AND DISTRIBUTION; Convex quadratic optimization; Nonlinear programming; Optimal power flow; Semidefinite programming
Citation Formats
Venzke, Andreas, Chatzivasileiadis, Spyros, and Molzahn, Daniel K. Inexact convex relaxations for AC optimal power flow: Towards AC feasibility. United States: N. p., 2020.
Web. doi:10.1016/j.epsr.2020.106480.
Venzke, Andreas, Chatzivasileiadis, Spyros, & Molzahn, Daniel K. Inexact convex relaxations for AC optimal power flow: Towards AC feasibility. United States. https://doi.org/10.1016/j.epsr.2020.106480
Venzke, Andreas, Chatzivasileiadis, Spyros, and Molzahn, Daniel K. Tue .
"Inexact convex relaxations for AC optimal power flow: Towards AC feasibility". United States. https://doi.org/10.1016/j.epsr.2020.106480. https://www.osti.gov/servlets/purl/1829268.
@article{osti_1829268,
title = {Inexact convex relaxations for AC optimal power flow: Towards AC feasibility},
author = {Venzke, Andreas and Chatzivasileiadis, Spyros and Molzahn, Daniel K.},
abstractNote = {Convex relaxations of AC optimal power flow (AC-OPF) problems have attracted significant interest as in several instances they provably yield the global optimum to the original non-convex problem. If, however, the relaxation is inexact, the obtained solution is not AC-feasible. The quality of the obtained solution is essential for several practical applications of AC-OPF, but detailed analyses are lacking in existing literature. Here, this paper aims to cover this gap. We provide an in-depth investigation of the solution characteristics when convex relaxations are inexact, we assess the most promising AC feasibility recovery methods for large-scale systems, and we propose two new metrics that lead to a better understanding of the quality of the identified solutions. We perform a comprehensive assessment on 96 different test cases, ranging from 14 to 3120 buses, and we show the following: (i) Despite an optimality gap of less than 1%, several test cases still exhibit substantial distances to both AC feasibility and local optimality and the newly proposed metrics characterize these deviations. (ii) Penalization methods fail to recover an AC-feasible solution in 15 out of 45 test cases. (iii) The computational benefits of warm-starting non-convex solvers have significant variation, but a computational speedup exists in over 75% of cases.},
doi = {10.1016/j.epsr.2020.106480},
journal = {Electric Power Systems Research},
number = ,
volume = 187,
place = {United States},
year = {Tue Jun 23 00:00:00 EDT 2020},
month = {Tue Jun 23 00:00:00 EDT 2020}
}
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