Natural Gas Flow Solvers Using Convex Relaxation
Natural Gas Flow Solvers Using Convex Relaxation
复制标题
DOI：
10.1109/tcns.2020.2972593
复制
发表时间：
2019-06
影响因子：
4.2
通讯作者：
M. Singh;V. Kekatos
中科院分区：
文献类型：
--
作者：
M. Singh;V. Kekatos
庞大的基础设施发展，气体流动（GF）动态，以及天然气与电力网络的复杂相互依赖性，需要先进的计算工具。求解将气体注入与压力和管道流量相关的方程是天然气网络（NGN）操作的核心，然而需要仔细初始化和唯一性的现有求解器一直是一个悬而未决的问题。在这方面，本文认为非线性稳态版本的GF问题。它首先建立的GF问题的解决方案是唯一的任意NGN拓扑结构，压缩机类型，和规范集。对于在单个（参考）节点上指定压力并且压缩器不出现在循环中的GF设置，GF任务被设定为n凸最小化。为了处理更一般的设置，GF求解器依赖于一个混合整数二次约束二次规划（MI-QCQP）也被设计。该求解器可用于任何NGN的任何GF设置。它引入了二进制变量来捕捉流动方向，放松的压降方程的二次不等式约束，并使用一个精心选择的目标，以促进这种放松的准确性。松弛可能是准确的NGN与非重叠的周期和一个单一的固定压力节点。求解器通过McCormick线性化有效地处理所涉及的双线性项。数值试验验证了我们的说法，表明MI-QCQP求解器的规模很好，即使在充分条件被违反时，松弛是准确的，例如在NGN重叠周期和多个固定压力节点。
The vast infrastructure development, gas flow (GF) dynamics, and complex interdependence of gas with electric power networks call for advanced computational tools. Solving the equations relating gas injections to pressures and pipeline flows lies at the heart of natural gas network (NGN) operation, yet existing solvers that require careful initialization and uniqueness has been an open question. In this context, this article considers the nonlinear steady-state version of the GF problem. It first establishes that the solution to the GF problem is unique under arbitrary NGN topologies, compressor types, and sets of specifications. For GF setups where pressure is specified on a single (reference) node and compressors do not appear in cycles, the GF task is posed as n convex minimization. To handle more general setups, a GF solver relying on a mixed-integer quadratically constrained quadratic program (MI-QCQP) is also devised. This solver can be used for any GF setup at any NGN. It introduces binary variables to capture flow directions, relaxes the pressure drop equations to quadratic inequality constraints, and uses a carefully selected objective to promote the exactness of this relaxation. The relaxation is probably exact in NGNs with nonoverlapping cycles and a single fixed-pressure node. The solver handles efficiently the involved bilinear terms through McCormick linearization. Numerical tests validate our claims, demonstrate that the MI-QCQP solver scales well, and that the relaxation is exact even when the sufficient conditions are violated, such as in NGNs with overlapping cycles and multiple fixed-pressure nodes.