Inexact convex relaxations for AC optimal power flow: Towards AC feasibility

Venzke, Andreas; Chatzivasileiadis, Spyros; Molzahn, Daniel K.

doi:10.1016/j.epsr.2020.106480

Inexact convex relaxations for AC optimal power flow: Towards AC feasibility

Journal Article · Tue Jun 23 00:00:00 EDT 2020 · Electric Power Systems Research

DOI:https://doi.org/10.1016/j.epsr.2020.106480· OSTI ID:1829268

^[1]; Chatzivasileiadis, Spyros ^[1]; Molzahn, Daniel K. ^[2]

Technical Univ of Denmark, Lyngby (Denmark)
Georgia Inst. of Technology, Atlanta, GA (United States); Argonne National Lab. (ANL), Lemont, IL (United States)

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.

View Accepted Manuscript (DOE)

Research Organization:: Argonne National Laboratory (ANL), Argonne, IL (United States)

Sponsoring Organization:: USDOE Office of Electricity (OE)

Grant/Contract Number:: AC02-06CH11357

OSTI ID:: 1829268

Alternate ID(s):: OSTI ID: 1634274

Journal Information:: Electric Power Systems Research, Journal Name: Electric Power Systems Research Vol. 187; ISSN 0378-7796

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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