Chapter 5: Mathematical optimization for evaluating gas network capacities

Abstract

This chapter describes the way we use mathematical optimization to dealwith the planning problems outlined in the preceding chapter. Ourmain tool is a hierarchy of different optimization models. We present different approaches that are detailed in the following chapters and discuss the corresponding modeling decisions that have to be taken. As discussed in Chapter 4, simulation is state of the art in gas transportation planning. In order to extend the application of simulation to a fully automatic planning process, one needs to incorporate (discrete) decisions that network operators are allowed to take for active elements. Moreover, these decisions should be optimal in some sense. Consequently, we arrive at optimization models and methods for gas transportation. As we are interested in midto long-term planning, we are considering stationary gas flows. The main goal is to get (stationary) optimization tools that are able to match the quality of stationary solutions obtained by simulation tools. One classical way of achieving this goal is to set up one optimization model that tries to capture all relevant aspects of the problem. However, the (global) solution of such a master model for real-life networks is way beyond the capabilities of today’s optimization methods, and it will probably not be possible to compute such a solution within any realistic time. Consequently, one needs to simplify and approximate certain aspects. This leads to the notorious problem of finding a good compromise between a relatively accurate modeling of the physics of the problem (as in the case of most nonlinear models) and the incorporation of the combinatorics of the problem (as in the case of many “discrete” models). Good solution methods have been developed for each of the resulting models. Our approach is to develop a hierarchy of models that capture different aspects of the problem. The primary principle of organization is along faithfulness to the underlying physics. However, it will turn out that not all models allow a strict hierarchy in the sense that solutions from a finer model can always be “coarsened” to a solution in the coarser model. Additionally, the different network elements all need their own models. So the building blocks of our hierarchy are different models for each component. These blocks will be outlined in the following sections. The following chapters will then show how the different components can be integrated into coherentmathematical programmingmodels. These chapters are organized by