Decomposable robust two‐stage optimization: An application to gas network operations under uncertainty

Aßmann, Denis; Liers, Frauke; Stingl, Michael

doi:10.1002/net.21871

Cited by 22 publications

(16 citation statements)

References 42 publications

(103 reference statements)

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“…Under Condition 1, the nodal injections are fixed a priori and the GF task aims at finding the associated (ψ, φ). Albeit Definition 1 considered the GF task with multiple fixedpressure nodes, the setup of a single fixed-pressure node is commonly met; see [10], [8], [11], [25]. Regarding Condition 2, although it may seem restrictive at the outset, it is satisfied by several practical gas networks [26].…”

Section: B Exactness Of the Relaxationmentioning

confidence: 99%

Natural Gas Flow Solvers Using Convex Relaxation

Singh

Kekatos

2020

IEEE Trans. Control Netw. Syst.

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In addition to their lower emissions and fast ramping capabilities, gas-fired electric power generation is increasing due to newly discovered supplies and declining prices. The vast infrastructure development, gas flow dynamics, and complex interdependence of gas with electric power networks call for advanced computational tools. Solving the equations relating gas injections to pressures and pipeline flows lies at the heart of natural gas network (NGN) operation, yet existing solvers require careful initialization and uniqueness has been an open question. In this context, this work considers the nonlinear steady-state version of the gas flow (GF) problem. It first establishes that the solution to the GF problem is unique under arbitrary gas network topologies, compressor types, and sets of specifications. For GF setups where pressure is specified on a single (reference) node and compressors do no appear in cycles, the GF task is posed as an convex minimization. To handle more general setups, a GF solver relying on a mixed-integer quadraticallyconstrained quadratic program (MI-QCQP) is also devised. This solver can be used for any GF setup and any network. It introduces binary variables to capture flow directions; relaxes the pressure drop equations to quadratic inequality constraints; and uses a carefully selected objective to promote the exactness of this relaxation. The relaxation is provably exact in networks with non-overlapping cycles and a single fixed-pressure node. The solver handles efficiently the involved bilinear terms through McCormick linearization. Numerical tests validate our claims, demonstrate that the MI-QCQP solver scales well, and that the relaxation is exact even when the sufficient conditions are violated, such as in networks with overlapping cycles and multiple fixed-pressure nodes.

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Section: B Exactness Of the Relaxationmentioning

confidence: 99%

Natural Gas Flow Solvers Using Convex Relaxation

Singh

Kekatos

2020

IEEE Trans. Control Netw. Syst.

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“…A graphical representation is given in Figure 3. We set the pressure bounds to [2,2] for node s 1 and to [1,2] for the remaining nodes. Furthermore, the lower and upper bounds for the compression ratio are given by [ε − , ε + ] = [2,3] and the pressure drop coefficient Λ a equals 0.5 for every arc a ∈ A \ A cs .…”

Section: A Mixed-integer Nonlinear Flow Model For Active Networkmentioning

confidence: 99%

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

2019

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In this work, we analyze the structural properties of the set of feasible bookings in the European entry-exit gas market system. We present formal definitions of feasible bookings and then analyze properties that are important if one wants to optimize over them. Thus, we study whether the sets of feasible nominations and bookings are bounded, convex, connected, conic, and star-shaped. The results depend on the specific model of gas flow in a network. Here, we discuss a simple linear flow model with arc capacities as well as nonlinear and mixed-integer nonlinear models of passive and active networks, respectively. It turns out that the set of feasible bookings has some unintuitive properties. For instance, we show that the set is nonconvex even though only a simple linear flow model is used.

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“…, k). (1) Here x ∈ R n is a decision vector, z ∈ R m is an uncertain parameter, g 0 : R n → R is the objective function and g : R n × R m → R k is the constraint mapping. The decision support schemes with non-deterministic parameters have to take into account the nature and source of uncertainty while balancing the objective and the constraints of the problem.…”

Section: Joint Probabilistic/robust Constraintsmentioning

confidence: 99%

Joint Model of Probabilistic-Robust (Probust) Constraints Applied to Gas Network Optimization

et al. 2020

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Optimization problems under uncertain conditions abound in many real-life applications. While solution approaches for probabilistic constraints are often developed in case the uncertainties can be assumed to follow a certain probability distribution, robust approaches are usually applied in case solutions are sought that are feasible for all realizations of uncertainties within some predefined uncertainty set. As many applications contain different types of uncertainties that require robust as well as probabilistic treatments, we deal with a class of joint probabilistic/robust constraints. Focusing on complex uncertain gas network optimization problems, we show the relevance of this class of problems for the task of maximizing free booked capacities in an algebraic model for a stationary gas network. We furthermore present approaches for finding their solution. Finally, we study the problem of controlling a transient system that is governed by the wave equation. The task consists in determining controls such that a certain robustness measure remains below some given upper bound with high probability.

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Decomposable robust two‐stage optimization: An application to gas network operations under uncertainty

Cited by 22 publications

References 42 publications

Natural Gas Flow Solvers Using Convex Relaxation

Natural Gas Flow Solvers Using Convex Relaxation

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

Joint Model of Probabilistic-Robust (Probust) Constraints Applied to Gas Network Optimization

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