Computational optimization of gas compressor stations: MINLP models versus continuous reformulations

Rose, Daniel; Schmidt, Martin; Steinbach, Marc C.; Willert, Bernhard M.

doi:10.1007/s00186-016-0533-5

Cited by 53 publications

(33 citation statements)

References 39 publications

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“…For biquadratic functions f A (x, y), we have f A (x, y) = x Ay with A ∈ R 3×3 , x = (1, x, x 2 ) , and y = (1, y, y 2 ) . More details about the technical and physical background as well as on the mathematical modeling can be found in [4] or [22].…”

Section: The Cs Filementioning

confidence: 99%

GasLib—A Library of Gas Network Instances

Schmidt

Aßmann

Burlacu

et al. 2017

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102

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Abstract:The development of mathematical simulation and optimization models and algorithms for solving gas transport problems is an active field of research. In order to test and compare these models and algorithms, gas network instances together with demand data are needed. The goal of GasLib is to provide a set of publicly available gas network instances that can be used by researchers in the field of gas transport. The advantages are that researchers save time by using these instances and that different models and algorithms can be compared on the same specified test sets. The library instances are encoded in an XML (extensible markup language) format. In this paper, we explain this format and present the instances that are available in the library.Data Set: http://gaslib.zib.de Data Set License: CC BY 3.0 Keywords: gas transport; networks; problem instances; mixed-integer nonlinear optimization; GasLib MSC: 90-08; 90C90; 90B10 SummaryThe mathematical simulation and optimization of gas transport through pipeline systems is an important field of research with a large practical impact. Over the last decades, many different mathematical models on different levels of accuracy for different components of gas networks have been developed. On the basis of these models, several simulation and optimization algorithms have been proposed. We refer to [1][2][3] and the references therein for more information. With GasLib, we provide a set of network instances that can be used to test and compare such models and the algorithms for solving them.

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Section: The Cs Filementioning

confidence: 99%

GasLib—A Library of Gas Network Instances

Schmidt

Aßmann

Burlacu

et al. 2017

Data

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102

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“…Model (6) allows for setting up a reasonable objective function for our NLPs and is thus appropriate in this work. For more details, see [31,34,35] or [14].…”

Section: Compressorsmentioning

confidence: 99%

Model and Discretization Error Adaptivity Within Stationary Gas Transport Optimization

2018

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The minimization of operation costs for natural gas transport networks is studied. Based on a recently developed model hierarchy ranging from detailed models of instationary partial differential equations with temperature dependence to highly simplified algebraic equations, modeling and discretization error estimates are presented to control the overall error in an optimization method for stationary and isothermal gas flows. The error control is realized by switching to more detailed models or finer discretizations if necessary to guarantee that a prescribed model and discretization error tolerance is satisfied in the end. We prove convergence of the adaptively controlled optimization method and illustrate the new approach with numerical examples.

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“…For the compressor model we consider the characteristic diagram model for turbo-compressors describing the relation between the adiabatic enthalpy and the volumetric flow rate [4,7].…”

Section: Compressor Modelingmentioning

confidence: 99%

“…Their behavior is usually described by characteristic diagrams reflecting the connection of the volumetric flow and the enthalpy change or shaft torque. Such models are commonly used for an optimal control of compressors and compressor stations [4,7] using stationary models for the gas flow through the pipes. For transient simulations of gas networks, simplified compressor models have been studied in [1][2][3].…”

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Transient Modeling and Simulation of Gas Pipe Networks with Characteristic Diagram Models for Compressors

Huck

Tischendorf

2017

Proc Appl Math and Mech

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One challenge for the simulation and optimization of real gas pipe networks is the treatment of compressors. Their behavior is usually described by characteristic diagrams reflecting the connection of the volumetric flow and the enthalpy change or shaft torque. Such models are commonly used for an optimal control of compressors and compressor stations [4,7] using stationary models for the gas flow through the pipes. For transient simulations of gas networks, simplified compressor models have been studied in [1][2][3]. Here, we present a transient simulation of gas pipe networks with characteristic diagram models of compressors using a stable network formulation as (partial) differential-algebraic system. Let G = (V, E) a directed graph with vertices V = V + ∪ V − and edges E = E P ∪ E C where V − and V + are the nodes where gas can enter and exit the network respectively and E P and E C being the set of pipes and compressors respectively. In addition we define the sets δ − (u) and δ + (u) as the set of edges that are directed towards and away from node u ∈ V respectively.Theorem 1.1 Let G = (V, E) be a connected, directed graph that describes a gas network with pipes and compressors and letThen it holds, that the pipes can be directed in a way that Pipe ModelingWe model pipes by a simplification of the isothermal Euler equations [2] ∂ t p e + c 2 a e ∂ x q e = 0, ∂ t q e + a e ∂ x p e = − λ e c 2 2D e a e q e |q e | p e − ga e h e c 2 p e , e ∈ E P (1) on [0, T ] × [0, e ] where p and q are the pressure and mass flow along pipe e, a e is the cross-sectional area, D e the diameter, λ e the friction factor, g the gravitational acceleration, h e the elevation of the pipe, c is the speed of sound, e the length of the pipe. Also we identify the point x = 0 with the position at the node u and x = e with node v for e = (u, v). Such a modeling is known to describe the gas flow through a pipe sufficiently well if the velocity of the gas is much less than the speed of sound which is usually the case for real gas transport networks. Compressor ModelingFor the compressor model we consider the characteristic diagram model for turbo-compressors describing the relation between the adiabatic enthalpy and the volumetric flow rate [4,7].Here H e is the adiabatic enthalpy, Q the volumetric flow rate, q e the massflow and n e the speed. Ψ e (Q, n) =Q T e A ene with A e ∈ R 3×3Q e = (1, Q e , Q 2 e ) andn e = (1, n e , n 2 e ) . The fourth equation of (2) determines the control of the compressor. We model the entry-nodes as a boundary condition for the pressure, leading to p e (t, 0) = p Γ u (t) for e ∈ δ + (u), u ∈ V + . For the nodes u ∈ V − we model the coupling by balance equations for the massflows e P ∈δ − (u) q e P (t, e P ) − e P ∈δ + (u) q e P (t, 0) + e C ∈δ − (u) q e C (t) − e C ∈δ + (u) q e C (t) = q Γ u (t)

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Computational optimization of gas compressor stations: MINLP models versus continuous reformulations

Cited by 53 publications

References 39 publications

GasLib—A Library of Gas Network Instances

GasLib—A Library of Gas Network Instances

Model and Discretization Error Adaptivity Within Stationary Gas Transport Optimization

Transient Modeling and Simulation of Gas Pipe Networks with Characteristic Diagram Models for Compressors

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