@misc{LenzSerrano, author = {Lenz, Ralf and Serrano, Felipe}, title = {Tight Convex Relaxations for the Expansion Planning Problem}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-81459}, abstract = {Secure energy transport is considered as highly relevant for the basic infrastructure of nowadays society and economy. To satisfy increasing demands and to handle more diverse transport situations, operators of energy networks regularly expand the capacity of their network by building new network elements, known as the expansion planning problem. A key constraint function in expansion planning problems is a nonlinear and nonconvex potential loss function. In order to improve the algorithmic performance of state-of-the-art MINLP solvers, this paper presents an algebraic description for the convex envelope of this function. Through a thorough computational study, we show that this tighter relaxation tremendously improve the performance of the MINLP solver SCIP on a large test set of practically relevant instances for the expansion planning problem. In particular, the results show that our achievements lead to an improvement of the solver performance for a development version by up to 58\%.}, language = {en} } @misc{LenzSchwarz, author = {Lenz, Ralf and Schwarz, Robert}, title = {Optimal Looping of Pipelines in Gas Networks}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-61564}, abstract = {In this paper, we compare several approaches for the problem of gas network expansions using loops, that is, to build new pipelines in parallel to existing ones. We present different model formulations for the problem of continuous loop expansions as well as discrete loop expansions. We then analyze problem properties, such as the structure and convexity of the underlying feasible regions. The paper concludes with a computational study comparing the continuous and the discrete formulations.}, language = {en} } @misc{LenzBecker, author = {Lenz, Ralf and Becker, Kai-Helge}, title = {Optimization of Capacity Expansion in Potential-driven Networks including Multiple Looping - A comparison of modelling approaches}, issn = {1438-0064}, doi = {10.1007/s00291-021-00648-7}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-69726}, abstract = {In commodity transport networks such as natural gas, hydrogen and water networks, flows arise from nonlinear potential differences between the nodes, which can be represented by so-called "potential-driven" network models. When operators of these networks face increasing demand or the need to handle more diverse transport situations, they regularly seek to expand the capacity of their network by building new pipelines parallel to existing ones ("looping"). The paper introduces a new mixed-integer non-linear programming (MINLP) model and a new non-linear programming (NLP) model and compares these with existing models for the looping problem and related problems in the literature, both theoretically and experimentally. On this basis, we give recommendations about the circumstances under which a certain model should be used. In particular, it turns out that one of our novel models outperforms the existing models. Moreover, the paper is the first to include the practically relevant option that a particular pipeline may be looped several times.}, language = {en} } @misc{Lenz, author = {Lenz, Ralf}, title = {Pipe Merging for Transient Gas Network Problems}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-82116}, abstract = {In practice, transient gas transport problems frequently have to be solved for large-scale gas networks. Gas network optimization problems typically belong to the class of Mixed-Integer Nonlinear Programming Problems (MINLP). However current state-of-the-art MINLP solvers are not yet mature enough to solve large-scale real-world instances. Therefore, an established approach in practice is to solve the problems with respect to a coarser representation of the network and thereby reducing the size of the underlying model. Two well-known aggregation methods that effectively reduce the network size are parallel and serial pipe merges. However, these methods have only been studied in stationary gas transport problems so far. This paper closes this gap and presents parallel and serial pipe merging methods in the context of transient gas transport. To this end, we introduce the concept of equivalent and heuristic subnetwork replacements. For the heuristic methods, we conduct a huge empirical evaluation based on real-world data taken from one of the largest gas networks in Europe. It turns out that both, parallel and serial pipe merging can be considered as appropriate aggregation methods for real-world transient gas flow problems.}, language = {en} } @misc{HoppmannHenningsLenzetal., author = {Hoppmann, Kai and Hennings, Felix and Lenz, Ralf and Gotzes, Uwe and Heinecke, Nina and Spreckelsen, Klaus and Koch, Thorsten}, title = {Optimal Operation of Transient Gas Transport Networks}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-73639}, language = {en} }