Solving the natural gas flow problem using semidefinite program relaxation
Solving the natural gas flow problem using semidefinite program relaxation
复制标题
使用半定规划松弛求解天然气流动问题
DOI：
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
R. Baldick
中科院分区：
文献类型：
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作者：
Abhishek Ojha;V. Kekatos;R. Baldick
天然气价格的下降和对快速反应发电机的迫切需求正在改变天然气网络。燃气发电厂为平衡风能发电而间歇性地运行，造成了天然气需求量增加的时空波动。天然气管网建模、监测和控制的核心是一组将节点气体注入和压力与管道流量相关联的非线性方程。给定网络中所有点的天然气需求，气体流量任务旨在找到所涉及的其余物理量。对于树状网络，该问题具有封闭形式的解;然而，求解实际网状网络的方程是不平凡的。这个问题在这里提出了一个可行性问题，涉及二次等式和不等式，并进一步放宽到凸半定规划（SDP）的最小化。绘制平行的功率流问题，放松被证明是准确的，如果成本函数是明智的设计使用一组频繁发生的网络状态。比利时网络上的数值试验证实了新方法的优越性，在恢复实际的气体系统状态的牛顿-拉夫逊求解器。
Decreasing gas prices and the pressing need for fast-responding electric power generators are currently transforming natural gas networks. The intermittent operation of gas-fired power plants to balance wind energy generation introduces spatiotemporal fluctuations of increasing volumes in gas demand. At the heart of modeling, monitoring, and control of gas networks is a set of nonlinear equations relating nodal gas injections and pressures to flows over pipelines. Given gas demands at all points of the network, the gas flow task aims at finding the rest of the physical quantities involved. For a tree-like network, the problem enjoys a closed-form solution; yet solving the equations for practical meshed networks is non-trivial. This problem is posed here as a feasibility problem involving quadratic equalities and inequalities, and is further relaxed to a convex semidefinite program (SDP) minimization. Drawing parallels to the power flow problem, the relaxation is shown to be exact if the cost function is judiciously designed using a set of frequently occurring network states. Numerical tests on a Belgian network corroborate the superiority of the novel method in recovering the actual gas system state over a Newton-Raphson solver.