Stationary Gas Networks with Compressor Control and Random Loads: Optimization with Probabilistic Constraints

Abstract

We introduce a stationary model for gas flow based on simplified isothermal Euler equations in a non-cycled pipeline network. Especially the problem of the feasibility of a random load vector is analyzed. Feasibility in this context means the existence of a flow vector meeting these loads, which satisfies the physical conservation laws with box constraints for the pressure. An important aspect of the model is the support of compressor stations, which counteract the pressure loss caused by friction in the pipes. The network is assumed to have only one influx node; all other nodes are efflux nodes. With these assumptions the set of feasible loads can be characterized analytically. In addition we show the existence of optimal solutions for some optimization problems with probabilistic constraints. A numerical example based on real data completes this paper.

Convexity and starshapedness of feasible sets in stationary flow networks

“…Compressor stations counteract the pressure drop along the pipes caused by friction. The model in [12] supports these elements.…”

“…Especially the model in [9] is quite interesting, because it gives a new access to this topic with respect to uncertain boundary data. This model has also been studied and extended in [12]. The aim in these works is stochastic optimization resp.…”

“…Mathematical modeling. We will use the model introduced in [12], which is an extension of the model in [9]. The difference between these models is, that the model in [9] does not support compressor stations, which are an important element in gas transport.…”

“…Gas transport through a pipeline network has been the topic of many articles in the last years. These models are often based on the Euler equations (see [4]) or simplifications like the isothermal Euler equations (see [1,2,9,10,11,12,13]). An overview about existing models and the components of a gas network can be found in [5,16].…”

Modeling and simulation of gas networks coupled to power grids

“…Future work includes the investigation of optimal control problems for the coupled model as for example the control of compressor stations [14] or the inclusion of uncertain customer demands [10]. This will immediately lead to the class of nonlinear (stochastic) optimization problems and tailored solution techniques.…”