Bookings in the European gas market: characterisation of feasibility and computational complexity results

Abstract

As a consequence of the liberalisation of the European gas market in the last decades, gas trading and transport have been decoupled. At the core of this decoupling are so-called bookings and nominations. Bookings are special capacity right contracts that guarantee that a specified amount of gas can be supplied or withdrawn at certain entry or exit nodes of the network. These supplies and withdrawals are nominated at the day-ahead. The special property of bookings then is that they need to be feasible, i.e., every nomination that complies with the given bookings can be transported. While checking the feasibility of a nomination can typically be done by solving a mixed-integer nonlinear feasibility problem, the verification of feasibility of a set of bookings is much harder. The reason is the robust nature of feasibility of bookingsnamely that for a set of bookings to be feasible, all compliant nominations, i.e., infinitely many, need to be checked for feasibility. In this paper, we consider the question of how to verify the feasibility of given bookings for a number of special cases. For our physics model we impose a steady-state potential-based flow model and disregard controllable network elements. For this case we derive a characterisation of feasible bookings, which is then used to show that the problem is in coNP for the general case but can be solved in polynomial time for linear potential-based flow models. Moreover, we present a dynamic programming approach for deciding the feasibility of a booking in tree-shaped networks even for nonlinear flow models. It turns out that the hardness of the problem mainly depends on the combination of the chosen physics model as well as the specific network structure under consideration. Thus, we give an overview over all settings for which the hardness of the problem is known and finally present a list of open problems.Date: June 5, 2019. 2010 Mathematics Subject Classification. 90B10, 90C30, 90C35, 90C39, 90C90.

Structural properties of feasible bookings in the European entry–exit gas market system

“…From a mathematical point of view, the feasibility of a booking can be seen as some special case of robust feasibility in the sense of robust optimization [6]. In this context, an efficient test for checking the feasibility of a booking in a passive tree-structured network is given in [45] and the feasibility of bookings as well as complexity results for checking this feasibility is studied in [36]. Other related problems like the computation of maximum possible bookings (the so-called technical capacity) are introduced in [40].…”

Announcement: Howard Rosenbrock Prize 2020

“…The prize recognizes outstanding research contributions that demonstrate Howard Rosenbrock's own dedication to bridging the gap between optimization and engineering. I am delighted to announce this year's winners of the 2020 Rosenbrock Prize are Martine Labbé, Fränk Plain, and Martin Schmidt for their paper, Bookings in the European gas market: characterization of feasibility and computational complexity results (Labbé et al 2020).…”

Deciding feasibility of a booking in the European gas market on a cycle is in P for the case of passive networks

“…Next, we introduce the notion of feasibility for nominations and bookings. We model stationary gas flows using an abstract physics model based on the Weymouth pressure drop equation and potential flows; see, e.g., [19] or [25]. It consists of arc flow variables and potentials on the nodes .…”

“…It is shown in Theorem 10 of [25] that a feasible booking b can be characterized by constraints on the maximum potential differences between all pairs of nodes. Therefore, the authors introduce, for every fixed pair of nodes ( w 1 , w 2 ) ∈ V 2 , the following problem where is the corresponding optimal value function (depending on the booking b ).…”

“…On the other hand, structural properties of the sets of feasible nominations and bookings such as nonconvexity and star‐shapedness are discussed in [32]. For networks consisting of pipes only, a characterization of feasible bookings is given in [25] by conditions on nominations with maximum potential difference in the network. Using a linear potential‐based flow model, these nominations can be computed efficiently using linear programming.…”