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Convex Relaxations for Gas Expansion Planning

Conrado Borraz-Sanchez (conradob***at***lanl.gov)
Russell Bent (rbent***at***lanl.gov)
Scott Backhaus (backhaus***at***lanl.gov)
Hassan Hijazi (Hassan.Hijazi***at***anu.edu.au)
Pascal Van Hentenryck (pvanhent***at***umich.edu)

Abstract: Expansion of natural gas networks is a critical process involving substantial capital expenditures with complex decision-support requirements. 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 solutions.

Keywords: MINLP, MISOCP, Gas Expansion, Convex Relaxation

Category 1: Applications -- OR and Management Sciences

Category 2: Integer Programming ((Mixed) Integer Nonlinear Programming )

Category 3: Global Optimization (Applications )

Citation: @article{GEP:15, year={2015}, month={June}, journal={{NICTA} Technical Report}, institution={{NICTA, The Australian National University}}, title={Convex Relaxations for Gas Expansion Planning}, author={Borraz-S\'{a}nchez, C. and Bent, R. and Backhaus, S. and Hijazi, H. and Van Hentenryck, P.}, }

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Entry Submitted: 06/23/2015
Entry Accepted: 06/23/2015
Entry Last Modified: 06/23/2015

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