Optimization of capacity expansion in potential-driven networks including multiple looping: a comparison of modelling approaches

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 nonlinear programming model and a new nonlinear programming 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 to practitioners 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 with respect to computational time, the number of solutions found, the number of instances solved and cost savings. Moreover, the paper extends the models for optimizing over multiple demand scenarios and is the first to include the practically relevant option that a particular pipeline may be looped several times.