Natural gas consumption by users of pipeline networks is subject to increasing uncertainty that originates from the intermittent nature of electric power loads serviced by gas-fired generators. To enable computationally efficient optimization of gas network flows subject to uncertainty, we develop a finite volume representation of stochastic solutions of hyperbolic partial differential equation (PDE) systems on graph-connected domains with nodal coupling and boundary conditions. The representation is used to express the physical constraints in stochastic optimization problems for gas flow allocation subject to uncertain parameters. The method is based on the stochastic finite volume approach that was recently developed for uncertainty quantification in transient flows represented by hyperbolic PDEs on graphs. In this study, we develop optimization formulations for steady-state gas flow over actuated transport networks subject to probabilistic constraints. In addition to the distributions for the physical solutions, we examine the dual variables that are produced by way of the optimization, and interpret them as price distributions that quantify the financial volatility that arises through demand uncertainty modeled in an optimization-driven gas market mechanism. We demonstrate the computation and distributional analysis using a single-pipe example and a small test network.

翻译：燃气管网用户的天然气消费面临日益增长的不确定性，这种不确定性源于燃气发电机所服务的电力负荷的间歇性特征。为实现受不确定性影响的管网流量优化计算的高效性，我们开发了在具有节点耦合与边界条件的图连通域上双曲型偏微分方程系统随机解的有限体积表示。该表示用于表达含不确定参数的气体流量分配随机优化问题中的物理约束。该方法基于近期为图结构双曲型偏微分方程瞬态流不确定量化所发展的随机有限体积法。在本研究中，我们针对含概率约束的驱动输运网络稳态气体流量开发优化模型。除物理解的分布外，我们通过优化产生的对偶变量进行探究，将其解释为价格分布，用以量化由需求不确定性驱动的优化型天然气市场机制中产生的金融波动性。我们通过单管算例和一个小型测试网络演示计算过程与分布分析。