TY - INPR A1 - Strubberg, Lea A1 - Lutz, Annette A1 - Börner, Pascal A1 - Pfetsch, Marc A1 - Skutella, Martin A1 - Klimm, Max T1 - Valid Cuts for the Design of Potential-based Flow Networks N2 - The construction of a cost minimal network for flows obeying physical laws is an important problem for the design of electricity, water, hydrogen, and natural gas infrastructures. We formulate this problem as a mixed-integer non-linear program. Its non-convexity, due to the poten- tial flow, together with the binary variables, indicating the decision to build a connection, make these problems challenging to solve. We develop a novel class of valid inequalities on the fractional relaxations of the bi- nary variables. Further, we show that this class of inequalities can be sep- arated in polynomial for solutions to a fractional relaxation. This makes it possible to incorporate these inequalities into a branch-and-bound al- gorithm. The advantage of these inequalities is lastly demonstrated in a computational study on the design of real-world gas transport networks. KW - potential based flows KW - topology optimization KW - MINLP Y1 - 2025 ER - TY - CHAP A1 - Pfetsch, Marc A1 - Schmidt, Martin A1 - Skutella, Martin A1 - Thürauf, Johannes T1 - Potential-Based Flows - An Overview T2 - Mathematical Modelling, Simulation and Optimization using the Example of Gas Networks N2 - Potential-based flows provide an algebraic way to model static physical flows in networks, for example, in gas, water, and lossless DC power networks. The flow on an arc in the network depends on the difference of the potentials at its end-nodes, possibly in a nonlinear way. Potential-based flows have several nice properties like uniqueness and acyclicity. The goal of this paper is to provide an overview of the current knowledge on these models with a focus on optimization problems on such networks. We cover basic properties, computational complexity, monotonicity, uncertain parameters, and the corresponding behavior of the network as well as topology optimization. Y1 - 2026 PB - Springer-Nature ER - TY - INPR A1 - Börner, Pascal A1 - Giesselmann, Jan A1 - Kumar, Varun M. A1 - Pfetsch, Marc E. A1 - Thiele, Michael A1 - Tscherpel, Tabea T1 - Gas Mixtures on Networks: Modeling, Simulation and Optimization N2 - This chapter addresses mathematical models for isothermal mixtures of hydrogen and natural gas, motivated by the need for reliable simulation tools in future low-carbon energy systems. We analyze several classes of mixture models and investigate their convergence properties in the regime of strong interaction between constituents, covering stationary and instationary single-pipe settings as well as network flows. Since mixture models critically depend on the choice of pressure law, we compare the industry-standard GERG equation of state with simplified alternatives that preserve convex energies and reduce computational costs. For network applications, we discuss consistent coupling conditions across model classes, explore optimization of steady flows using the algebraic Weymouth formulation, and provide numerical evidence for its applicability in relevant operating regimes. The study reveals when simplified models are justified and outlines key open challenges for the modeling of gas mixtures. Y1 - ER - TY - JFULL A1 - Börner, Pascal A1 - Pfetsch, Marc E. A1 - Ulbrich, Stefan T1 - Mixing of Gases in Stationary Networks: Properties and Optimization N2 - This paper deals with the mixing of gases in stationary networks. We first derive a model and pressure law for mixing, for which there is empirical evidence for its accuracy. The model is based on the change of the speed of sound in gas mixtures. We then consider stationary gas networks. The existence result for solutions of single gas flow on networks is extended to mixtures. Further, we establish an easy to check criterion for uniqueness of solutions on the network. This results in a uniqueness proof of solutions on all networks with a mixture of natural gas and low hydrogen percentages. We then develop a solution algorithm that alternates between the solution of a single gas problem and update of the mixture ratios. In a computational study, different model variants and their impact on performance are compared. Moreover, the increased complexity of solving stationary gas transport problems with mixing is evaluated. KW - gas network optimization KW - gas mixing KW - MINLP KW - global optimization Y1 - ER -