天然气扩建规划的凸松弛法
Convex Relaxations for Gas Expansion Planning
摘要：
天然气管网的扩建是一个关键过程，涉及大量资本支出和复杂的决策支持要求。考虑到输气约束的非凸性，全局最优性和不可行性保证只能通过全局优化方法来提供。不幸的是，最先进的全局优化求解器无法扩展到现实世界的大小实例。在这项研究中，我们提出了一个凸混合整数二阶锥松弛的气体扩张规划问题在稳态条件下。底层模型提供了严格的下限与高计算效率。此外，松弛的最优解通常可以用于导出原始问题的高质量解决方案，从而导致可证明的紧密最优性差距，并且在某些情况下，全局最优解。凸松弛是基于几个关键的想法，包括引入通量方向变量，确切的麦考密克松弛，开/关约束，和整数切割。在传统的比利时天然气网络以及其他实际的大型网络上进行了数值实验。结果表明的精度和计算速度的松弛和它的能力，以产生高质量的解决方案。
英文摘要：
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 soluutions. 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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