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

The paper considers the computation of the probability of feasible load constellations in a stationary gas network with uncertain demand. More precisely, a networkwith a single entry and several exits with uncertain loads is studied. Feasibility of a load constellation is understood in the sense of an existing flowmeeting these loads alongwith 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 QuasiMonte-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 B René Henrion [email protected] Claudia Gotzes [email protected] Holger Heitsch [email protected] Rüdiger Schultz [email protected] 1 Faculty of Mathematics, University of Duisburg-Essen, Campus Essen, Thea-Leymann-Str. 9, 45127 Essen, Germany 2 Weierstrass Institute, Mohrenstraße 39, 10117 Berlin, Germany