Untitled

Ríos‐Mercado, Roger Z.; Wu, Suming; Scott, L. Ridgway; Boyd, Emily

doi:10.1023/a:1021529709006

Cited by 67 publications

(11 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…A key property of potential-based flow networks without controllable elements is the uniqueness of flows for given supplies and withdrawals. This result has been established in early works for fluid flow networks in [30] and more generally for potential-based flows in [35,36]. It marks the key difference compared to classical linear flow models.…”

Section: Introductionsupporting

confidence: 54%

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

Plein

Schmidt

2019

Optim Eng

View full text Add to dashboard Cite

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 Bookings are special capacity right contracts that guarantee that a specified amount of gas can be supplied or withdrawn at certain entry or exit nodes of the network.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.

show abstract

Section: Introductionsupporting

confidence: 54%

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

Plein

Schmidt

2019

Optim Eng

View full text Add to dashboard Cite

show abstract

“…Assumption 1 eliminates this possibility and allows us to show the uniqueness of the flows corresponding to any given nomination. To this end, we extend the results of Maugis (1977); Collins et al (1978); Ríos-Mercado et al (2002) for passive networks. Theorem 4.2 Suppose that Assumption 1 holds.…”

Section: Assumption 1 No Active Element Is Part Of An Undirected Cycle In Gmentioning

confidence: 75%

A bilevel optimization approach to decide the feasibility of bookings in the European gas market

2021

View full text Add to dashboard Cite

The European gas market is organized as a so-called entry-exit system with the main goal to decouple transport and trading. To this end, gas traders and the transmission system operator (TSO) sign so-called booking contracts that grant capacity rights to traders to inject or withdraw gas at certain nodes up to this capacity. On a day-ahead basis, traders then nominate the actual amount of gas within the previously booked capacities. By signing a booking contract, the TSO guarantees that all nominations within the booking bounds can be transported through the network. This results in a highly challenging mathematical problem. Using potential-based flows to model stationary gas physics, feasible bookings on passive networks, i.e., networks without controllable elements, have been characterized in the recent literature. In this paper, we consider networks with linearly modeled active elements such as compressors or control valves. Since these active elements allow the TSO to control the gas flow, the single-level approaches for passive networks from the literature are no longer applicable. We thus present a bilevel model to decide the feasibility of bookings in networks with active elements. While this model is well-defined for general active networks, we focus on the class of networks for which active elements do not lie on cycles. This assumption allows us to reformulate the original bilevel model such that the lower-level problem is linear for every given upper-level decision. Consequently, we derive several single-level reformulations for this case. Besides the classic Karush–Kuhn–Tucker reformulation, we obtain three problem-specific optimal-value-function reformulations. The latter also lead to novel characterizations of feasible bookings in networks with active elements that do not lie on cycles. We compare the performance of our methods by a case study based on data from the .

show abstract

“…▪ A potential-based b-flow is said to be feasible if, in addition to (6), it obeys the flow bounds (3e) and potential bounds (3f). [13] and Ríos-Mercado et al [34]). Let G be a passive connected potential network and let b ∈ R V be a vector of node balances with ∑ v∈V b v = 0.…”

Section: Observation 31 Consider a Homogeneous Passive Network Of Omentioning

confidence: 95%

“…One can prove this theorem in different ways: The approach of [34] shows that the corresponding solution operators are monotone, which implies that a reduced system of equations has a unique solution.…”

Section: Observation 31 Consider a Homogeneous Passive Network Of Omentioning

confidence: 99%

Algorithmic results for potential‐based flows: Easy and hard cases

et al. 2018

View full text Add to dashboard Cite

Potential‐based flows are an extension of classical network flows in which the flow on an arc is determined by the difference of the potentials of its incident nodes. Such flows are unique and arise, for example, in energy networks. Two important algorithmic problems are to determine whether there exists a feasible flow and to maximize the flow between two designated nodes. We show that these problems can be solved for the single source and sink case by reducing the network to a single arc. However, if we additionally consider switches that allow to force the flow to 0 and decouple the potentials, these problems are NP‐hard. Nevertheless, for particular series‐parallel networks, one can use algorithms for the subset sum problem. Moreover, applying network presolving based on generalized series‐parallel structures allows to significantly reduce the size of realistic energy networks.

show abstract

Untitled

Cited by 67 publications

References 7 publications

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

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

A bilevel optimization approach to decide the feasibility of bookings in the European gas market

Algorithmic results for potential‐based flows: Easy and hard cases

Contact Info

Product

Resources

About