Challenges in Optimal Control Problems for Gas and Fluid Flow in Networks of Pipes and Canals: From Modeling to Industrial Applications

Hante, Falk M.; Leugering, Günter; Martín, Alexander; Schewe, Lars; Schmidt, Martin

doi:10.1007/978-981-10-3758-0_5

Cited by 56 publications

(51 citation statements)

References 67 publications

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“…If a given value of u + ∈ F is fixed in (18), we obtain an optimal boundary control problem with a time-dependent control u − (t) at x = L and constant boundary control at x = 0. The turnpike results from Section 0.2.2 can be adapted to this situation.…”

Section: Optimal Boundary Control Problems With An Integer Control Comentioning

confidence: 99%

On the Turnpike Phenomenon for Optimal Boundary Control Problems with Hyperbolic Systems

Gugat¹,

Hante²

2019

SIAM J. Control Optim.

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We study problems of optimal boundary control with systems governed by linear hyperbolic partial differential equations. The objective function is quadratic and given by an integral over the finite time interval (0, T ) that depends on the boundary traces of the solution. If the time horizon T is sufficiently large, the solution of the dynamic optimal boundary control problem can be approximated by the solution of a steady state optimization problem. We show that for T → ∞ the approximation error converges to zero in the sense of the norm in L 2 (0, 1) with the rate 1/T , if the time interval (0, T ) is transformed to the fixed interval (0, 1). Moreover, we show that also for optimal boundary control problems with integer constraints for the controls the turnpike phenomenon occurs. In this case the steady state optimization problem also has the integer constraints. If T is sufficiently large, the integer part of each solution of the dynamic optimal boundary control problem with integer constraints is equal to the integer part of a solution of the static problem. A numerical verification is given for a control problem in gas pipeline operations.

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Section: Optimal Boundary Control Problems With An Integer Control Comentioning

confidence: 99%

On the Turnpike Phenomenon for Optimal Boundary Control Problems with Hyperbolic Systems

Gugat¹,

Hante²

2019

SIAM J. Control Optim.

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“…We consider three examples for which steady-state physical flows can be approximated using a potential-based flow model. (i) Gas transport networks: The physical nature of gas flow is governed by partial differential equations; see e.g., [20]. If one models stationary gas flows, these relations can be approximated by an algebraic equation coupling the mass flow on the arc and the difference of squared pressures at its incident nodes; see, e.g., Chapter [10] in the book [26].…”

Section: Main Definitions and Notationmentioning

confidence: 99%

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

Plein

Schmidt

2019

Optim Eng

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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.

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“…These examples are given by gas, water, and power networks, which illustrate the broad applicability of our model and results. In all of these cases, the models are an approximation of a description of the relevant physics, typically given by partial differential equations; see, for example, Hante et al .Example (Gas Transport Networks). In stationary models of gas transport networks, lines correspond to gas pipes and switches model valves.…”

Section: Basic Modelmentioning

confidence: 99%

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

et al. 2018

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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.

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Challenges in Optimal Control Problems for Gas and Fluid Flow in Networks of Pipes and Canals: From Modeling to Industrial Applications

Cited by 56 publications

References 67 publications

On the Turnpike Phenomenon for Optimal Boundary Control Problems with Hyperbolic Systems

On the Turnpike Phenomenon for Optimal Boundary Control Problems with Hyperbolic Systems

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

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

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