Monotonicity of dissipative flow networks renders robust maximum profit problem tractable: General analysis and application to natural gas flows

Marc Vuffray, Sidhant Misra, Michael Chertkov

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

18 Citations (Scopus)

Abstract

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.

Original languageEnglish
Title of host publication54rd IEEE Conference on Decision and Control,CDC 2015
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages4571-4578
Number of pages8
ISBN (Electronic)9781479978861
DOIs
Publication statusPublished - 8 Feb 2015
Externally publishedYes
Event54th IEEE Conference on Decision and Control, CDC 2015 - Osaka, Japan
Duration: 15 Dec 201518 Dec 2015

Publication series

NameProceedings of the IEEE Conference on Decision and Control
Volume54rd IEEE Conference on Decision and Control,CDC 2015
ISSN (Print)0743-1546

Conference

Conference54th IEEE Conference on Decision and Control, CDC 2015
Country/TerritoryJapan
CityOsaka
Period15/12/1518/12/15

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