Convex relaxations for gas expansion planning

doi:10.1287/ijoc.2016.0697

Title: Convex relaxations for gas expansion planning

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Abstract

Expansion of natural gas networks is a critical process involving substantial capital expenditures with complex decision-support requirements. Here, given the non-convex nature of gas transmission constraints, global optimality and infeasibility guarantees can only be offered by global optimisation approaches. Unfortunately, state-of-the-art global optimisation solvers are unable to scale up to real-world size instances. In this study, we present a convex mixed-integer second-order cone relaxation for the gas expansion planning problem under steady-state 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 high-quality 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 high-quality solution

Authors:

Borraz-Sanchez, Conrado ^[1]; Bent, Russell Whitford ^[1]; Backhaus, Scott N. ^[1]; Hijazi, Hassan ^[2]; Van Hentenryck, Pascal ^[2]

Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
NICTA and ANU, Canberra (Australia)

Publication Date:: 2016-01-01

Research Org.:: Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

Sponsoring Org.:: USDOE

OSTI Identifier:: 1296664

Report Number(s):: LA-UR-15-24636
Journal ID: ISSN 1091-9856

Grant/Contract Number:: AC52-06NA25396

Resource Type:: Accepted Manuscript

Journal Name:: INFORMS Journal on Computing

Additional Journal Information:: Journal Volume: 28; Journal Issue: 4; Journal ID: ISSN 1091-9856

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


                    Borraz-Sanchez, 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.

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                    Borraz-Sanchez, 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.

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                    Borraz-Sanchez, 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.

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@article{osti_1296664,

  title        = {Convex relaxations for gas expansion planning},

  author       = {Borraz-Sanchez, 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 decision-support requirements. Here, given the non-convex nature of gas transmission constraints, global optimality and infeasibility guarantees can only be offered by global optimisation approaches. Unfortunately, state-of-the-art global optimisation solvers are unable to scale up to real-world size instances. In this study, we present a convex mixed-integer second-order cone relaxation for the gas expansion planning problem under steady-state 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 high-quality 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 high-quality solution},

  doi          = {10.1287/ijoc.2016.0697},

  journal      = {INFORMS Journal on Computing},

  number       = 4,

  volume       = 28,

  place        = {United States},

  year         = {2016},

  month        = {1}

}

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