1515
eng
reportzib
0
2012-04-24
2012-04-24
--
The set of solutions to nomination validation in passive gas transportation networks with a generalized flow formula
In this paper we give an analytical description on the structure of
solutions to the gas nomination validation problem in gas
transportation networks. These networks are assumed to contain no
active devices, only certain hypothetical pipelines, where the flow
of gas is modeled by a generalized version of the quadratic
Weymouth's equation. The purpose of considering generalized flow
formulas is to be able to adapt our results to various gas network
optimization problems involving gas flow formulas beyond Weymouth's
equation. Such formulas can appear in leaves of branch and bound
trees, or they can stem from discretization and linearization
carried out at active devices. We call a balanced supply-demand
vector a nomination, and the passive nomination validation problem
is to decide whether there exist pressures at the nodes generating a
given nomination. We prove that in our setup the pressure square
vectors generating a given nomination form a one-dimensional
connected and continuous curve in the pressure square space, and
this curve is a line for the classical Weymouth's equation. We also
present a visual approach for the easy comprehension of how this
solution curve arises; we give a short investigation of the set of
feasible nominations; and finally we give a proof that the
nomination validation problem in gas networks with active devices is
NP-complete.
1438-0064
urn:nbn:de:0297-zib-15151
Jácint Szabó
Benjamin Hiller
ZIB-Report
11-44
eng
uncontrolled
pressure drop equation
eng
uncontrolled
gas networks
eng
uncontrolled
generalized flow formula
Mathematics of Computing
OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING
Mathematical Optimization
MODAL-GasLab
ForNe
MODAL-Gesamt
https://opus4.kobv.de/opus4-zib/files/1515/ZR-11-44.pdf