期刊
INFORMS JOURNAL ON COMPUTING
卷 28, 期 4, 页码 645-656出版社
INFORMS
DOI: 10.1287/ijoc.2016.0697
关键词
natural gas; convex relaxations; network design; mixed-integer programming; second-order cone programming
资金
- Advanced Grid Modeling Program in the Office of Electricity in the U.S. Department of Energy
- National Nuclear Security Administration of the U.S. Department of Energy at Los Alamos National Laboratory [DE-AC52-06NA25396]
- NICTA's Optimization Research Group as part of the Future Energy Systems project
- Australian Government through the Department of Communications
- Australian Research Council through the ICT Centre of Excellence Program
Expansion of natural gas networks is a critical process involving substantial capital expenditures with complex decision-support requirements. Given the nonconvex 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.
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