Monotonicity of dissipative flow networks renders robust maximum profit problem tractable: General analysis and application to natural gas flows
Monotonicity of dissipative flow networks renders robust maximum profit problem tractable: General analysis and application to natural gas flows
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耗散流网络的单调性使得稳健的最大利润问题变得易于处理：天然气流的一般分析和应用
DOI：
10.1109/cdc.2015.7402933
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发表时间：
2015
期刊：
影响因子：
--
通讯作者：
M. Chertkov
中科院分区：
文献类型：
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作者：
Marc Vuffray;Sidhant Misra;M. Chertkov
我们考虑一般的，稳定的，平衡的商品流在网络中的网络流的一个实例的特点是边缘流和节点的潜力。假设进出节点的边流是守恒的，从而表示标准的网络流关系。剩余的自由度在网络上的流量分布的限制，使在头部和尾部的边缘的电位差表示为边缘流的非线性函数的潜力。我们认为网络的节点分为三类：源注入流到网络中的一定的成本，终端购买流在一个固定的价格，和“内部”客户每个提取不确定的流量，有一个优先级，因此它是不定价的。我们的目标是运营网络，使利润最大化，即出售给终端的流量减去注入成本，同时将潜力保持在规定的范围内。我们还要求该操作点对于内部客户退出的不确定性是稳健的。在这种情况下，我们证明了潜在的单调功能的提款。这一观察使我们能够在最大利润优化中替换无限多个节点约束，每个节点约束代表一个特定的提取不确定性值，只有两个约束代表所有不确定性节点分别消耗其最小和最大量的情况。我们说明了这个一般结果的天然气输送网络的一个例子。在该使能示例中，假设内部客户的气体抽取是不确定的，势是气体压力的平方，势降函数在流量及其强度中是双线性的，其中添加了表示压缩的可调因子。
We consider general, steady, balanced flows of a commodity over a network where an instance of the network flow is characterized by edge flows and nodal potentials. Edge flows in and out of a node are assumed to be conserved, thus representing standard network flow relations. The remaining freedom in the flow distribution over the network is constrained by potentials so that the difference of potentials at the head and the tail of an edge is expressed as a nonlinear function of the edge flow. We consider networks with nodes divided into three categories: sources that inject flows into the network for a certain cost, terminals which buy the flow at a fixed price, and “internal” customers each withdrawing an uncertain amount of flow, which has a priority and thus it is not priced. Our aim is to operate the network such that the profit, i.e. amount of flow sold to terminals minus cost of injection, is maximized, while maintaining the potentials within prescribed bounds. We also require that the operating point is robust with respect to the uncertainty of internal customers' withdrawal. In this setting we prove that potentials are monotonic functions of the withdrawals. This observation enables us to replace in the maximum profit optimization infinitely many nodal constraints, each representing a particular value of withdrawal uncertainty, by only two constraints representing the cases where all nodes with uncertainty consume their minimum and maximum amounts respectively. We illustrate this general result on an example of the natural gas transmission network. In this enabling example, gas withdrawals by internal customers are assumed uncertain, the potentials are gas pressures squared, the potential drop functions are bilinear in the flow and its intensity with an added tunable factor representing compression.