@article{ScheweSchmidtThuerauf2018, author = {Schewe, Lars and Schmidt, Martin and Th{\"u}rauf, Johannes}, title = {Structural Properties of Feasible Bookings in the European Entry-Exit Gas Market System}, series = {4OR}, journal = {4OR}, number = {18}, doi = {10.1007/s10288-019-00411-3}, pages = {197 -- 218}, year = {2018}, abstract = {In this work we analyze the structural properties of the set of feasible bookings in the European entry-exit gas market system. We present formal definitions of feasible bookings and then analyze properties that are important if one wants to optimize over them. Thus, we study whether the sets of feasible nominations and bookings are bounded, convex, connected, conic, and star-shaped. The results depend on the specific model of gas flow in a network. Here, we discuss a simple linear flow model with arc capacities as well as nonlinear and mixed-integer nonlinear models of passive and active networks, respectively. It turns out that the set of feasible bookings has some unintuitive properties. For instance, we show that the set is nonconvex even though only a simple linear flow model is used.}, language = {en} } @article{RobiniusScheweSchmidtetal.2018, author = {Robinius, Martin and Schewe, Lars and Schmidt, Martin and Stolten, Detlef and Th{\"u}rauf, Johannes and Welder, Lara}, title = {Robust Optimal Discrete Arc Sizing for Tree-Shaped Potential Networks}, series = {Computational Optimization and Applications}, journal = {Computational Optimization and Applications}, number = {73(3)}, doi = {10.1007/s10589-019-00085-x}, pages = {791 -- 819}, year = {2018}, abstract = {We consider the problem of discrete arc sizing for tree-shaped potential networks with respect to infinitely many demand scenarios. This means that the arc sizes need to be feasible for an infinite set of scenarios. The problem can be seen as a strictly robust counterpart of a single-scenario network design problem, which is shown to be NP-complete even on trees. In order to obtain a tractable problem, we introduce a method for generating a finite scenario set such that optimality of a sizing for this finite set implies the sizing's optimality for the originally given infinite set of scenarios. We further prove that the size of the finite scenario set is quadratically bounded above in the number of nodes of the underlying tree and that it can be computed in polynomial time. The resulting problem can then be solved as a standard mixed-integer linear optimization problem. Finally, we show the applicability of our theoretical results by computing globally optimal arc sizes for a realistic hydrogen transport network of Eastern Germany.}, language = {en} } @article{ScheweSchmidt2018, author = {Schewe, Lars and Schmidt, Martin}, title = {The Impact of Potential-Based Physics ModelsĀ on Pricing in Energy Networks}, series = {Central European Journal of Operations Research}, journal = {Central European Journal of Operations Research}, number = {28(3)}, pages = {1003 -- 1029}, year = {2018}, abstract = {Pricing of access to energy networks is an important issue in liberalized energy sectors because of the natural monopoly character of the underlying transport infrastructures. We introduce a general pricing framework for potential-based energy flows in arbitrarily structured transport networks. In different specifications of our general pricing model we discuss first- and second-best pricing results and compare different pricing outcomes of potential-free and potential-based energy flow models. Our results show that considering nonlinear laws of physics leads to significantly different pricing results on networks and that these differences can only be seen in sufficiently complex, e.g., cyclic, networks as they can be found in real-world situations.}, language = {en} }