On the quantification of nomination feasibility in stationary gas networks with random load

Claudia Gotzes (), Holger Heitsch (), René Henrion () and Rüdiger Schultz ()
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Claudia Gotzes: University of Duisburg-Essen
Holger Heitsch: Weierstrass Institute
René Henrion: Weierstrass Institute
Rüdiger Schultz: University of Duisburg-Essen

Mathematical Methods of Operations Research, 2016, vol. 84, issue 2, No 8, 427-457

Abstract: Abstract The paper considers the computation of the probability of feasible load constellations in a stationary gas network with uncertain demand. More precisely, a network with a single entry and several exits with uncertain loads is studied. Feasibility of a load constellation is understood in the sense of an existing flow meeting these loads along with given pressure bounds in the pipes. In a first step, feasibility of deterministic exit loads is characterized algebraically and these general conditions are specified to networks involving at most one cycle. This prerequisite is essential for determining probabilities in a stochastic setting when exit loads are assumed to follow some (joint) Gaussian distribution when modeling uncertain customer demand. The key of our approach is the application of the spheric-radial decomposition of Gaussian random vectors coupled with Quasi Monte-Carlo sampling. This approach requires an efficient algorithmic treatment of the mentioned algebraic relations moreover depending on a scalar parameter. Numerical results are illustrated for different network examples and demonstrate a clear superiority in terms of precision over simple generic Monte-Carlo sampling. They lead to fairly accurate probability values even for moderate sample size.

Keywords: Mathematical models for gas pipelines; Nomination validation; Gas network capacity; Uncertainty quantifcation; Optimization under stochastic uncertainty; Spheric-radial decomposition; 62P30; 90B15; 90C15; 90C31 (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (11)

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DOI: 10.1007/s00186-016-0564-y

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