Convex relaxations for gas expansion planning
Abstract
Expansion of natural gas networks is a critical process involving substantial capital expenditures with complex decisionsupport requirements. Here, given the nonconvex nature of gas transmission constraints, global optimality and infeasibility guarantees can only be offered by global optimisation approaches. Unfortunately, stateoftheart global optimisation solvers are unable to scale up to realworld size instances. In this study, we present a convex mixedinteger secondorder cone relaxation for the gas expansion planning problem under steadystate conditions. The underlying model offers tight lower bounds with high computational efficiency. In addition, the optimal solution of the relaxation can often be used to derive highquality solutions to the original problem, leading to provably tight optimality gaps and, in some cases, global optimal solutions. The convex relaxation is based on a few key ideas, including the introduction of flux direction variables, exact McCormick relaxations, on/off constraints, and integer cuts. Numerical experiments are conducted on the traditional Belgian gas network, as well as other real larger networks. The results demonstrate both the accuracy and computational speed of the relaxation and its ability to produce highquality solution
 Authors:

 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 NICTA and ANU, Canberra (Australia)
 Publication Date:
 Research Org.:
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Sponsoring Org.:
 USDOE
 OSTI Identifier:
 1296664
 Report Number(s):
 LAUR1524636
Journal ID: ISSN 10919856
 Grant/Contract Number:
 AC5206NA25396
 Resource Type:
 Accepted Manuscript
 Journal Name:
 INFORMS Journal on Computing
 Additional Journal Information:
 Journal Volume: 28; Journal Issue: 4; Journal ID: ISSN 10919856
 Publisher:
 INFORMS
 Country of Publication:
 United States
 Language:
 English
 Subject:
 03 NATURAL GAS; Natural gas network; Expansion planning problem; MINLP problem; convex relaxations; Lower bound
Citation Formats
BorrazSanchez, Conrado, Bent, Russell Whitford, Backhaus, Scott N., Hijazi, Hassan, and Van Hentenryck, Pascal. Convex relaxations for gas expansion planning. United States: N. p., 2016.
Web. doi:10.1287/ijoc.2016.0697.
BorrazSanchez, Conrado, Bent, Russell Whitford, Backhaus, Scott N., Hijazi, Hassan, & Van Hentenryck, Pascal. Convex relaxations for gas expansion planning. United States. doi:10.1287/ijoc.2016.0697.
BorrazSanchez, Conrado, Bent, Russell Whitford, Backhaus, Scott N., Hijazi, Hassan, and Van Hentenryck, Pascal. Fri .
"Convex relaxations for gas expansion planning". United States. doi:10.1287/ijoc.2016.0697. https://www.osti.gov/servlets/purl/1296664.
@article{osti_1296664,
title = {Convex relaxations for gas expansion planning},
author = {BorrazSanchez, Conrado and Bent, Russell Whitford and Backhaus, Scott N. and Hijazi, Hassan and Van Hentenryck, Pascal},
abstractNote = {Expansion of natural gas networks is a critical process involving substantial capital expenditures with complex decisionsupport requirements. Here, given the nonconvex nature of gas transmission constraints, global optimality and infeasibility guarantees can only be offered by global optimisation approaches. Unfortunately, stateoftheart global optimisation solvers are unable to scale up to realworld size instances. In this study, we present a convex mixedinteger secondorder cone relaxation for the gas expansion planning problem under steadystate conditions. The underlying model offers tight lower bounds with high computational efficiency. In addition, the optimal solution of the relaxation can often be used to derive highquality solutions to the original problem, leading to provably tight optimality gaps and, in some cases, global optimal solutions. The convex relaxation is based on a few key ideas, including the introduction of flux direction variables, exact McCormick relaxations, on/off constraints, and integer cuts. Numerical experiments are conducted on the traditional Belgian gas network, as well as other real larger networks. The results demonstrate both the accuracy and computational speed of the relaxation and its ability to produce highquality solution},
doi = {10.1287/ijoc.2016.0697},
journal = {INFORMS Journal on Computing},
number = 4,
volume = 28,
place = {United States},
year = {2016},
month = {1}
}
Works referencing / citing this record:
GasLib—A Library of Gas Network Instances
journal, December 2017
 Schmidt, Martin; Aßmann, Denis; Burlacu, Robert
 Data, Vol. 2, Issue 4