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Deciding Feasibility of a Booking in the European Gas Market on a Cycle is in P

Martine Labbé(martine.labbe***at***ulb.ac.be)
Fränk Plein(frank.plein***at***ulb.ac.be)
Martin Schmidt(martin.schmidt***at***uni-trier.de)
Johannes Thürauf(johannes.thuerauf***at***fau.de)

Abstract: We show that the feasibility of a booking in the European entry-exit gas market can be decided in polynomial time on single-cycle networks. The feasibility of a booking can be characterized by solving polynomially many nonlinear potential-based flow models for computing so-called potential-difference maximizing load flow scenarios. We thus analyze the structure of these models and exploit both the cyclic graph structure as well as specific properties of potential-based flows. This enables us to solve the decision variant of the nonlinear potential-difference maximization by reducing it to a system of polynomials of constant dimension that is independent of the cycle's size. This system of fixed dimension can be handled with tools from real algebraic geometry to derive a polynomial-time algorithm. The characterization in terms of potential-difference maximizing load flow scenarios then leads to a polynomial-time algorithm for deciding the feasibility of a booking. Our theoretical results extend the existing knowledge about the complexity of deciding the feasibility of bookings from trees to single-cycle networks.

Keywords: Gas networks, European entry-exit market, Bookings, Potential-based flows, Computational complexity, Cycle

Category 1: Network Optimization

Category 2: Applications -- OR and Management Sciences

Citation:

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Entry Submitted: 11/12/2019
Entry Accepted: 11/12/2019
Entry Last Modified: 11/12/2019

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