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Natural Gas Flow Solvers using Convex Relaxation [article]

Manish Kumar Singh, Vassilis Kekatos
2020 arXiv   pre-print
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  ...  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  ...  It has been recently shown that exact relaxation of network flow optimization problems may be guaranteed using a convex penalty [27] .  ... 
arXiv:1906.01711v2 fatcat:sa5m3vkx4rdhxfcme7tjeawju4

Natural Gas Short-Term Operation Problem with Dynamics: A Rank Minimization Approach

Reza Bayani, Saeed D. Manshadi
2022 IEEE Transactions on Smart Grid  
This work presents a convex relaxation scheme for the original non-linear and non-convex natural gas flow equations with dynamics, utilizing a rank minimization approach to ensure the tightness.  ...  The results demonstrate how changes in the natural gas demand are met by adjustment in the pressure within pipelines rather than the output of natural gas suppliers.  ...  The non-convex model is solved by IPOPT [39] , while the MOSEK [40] solver is used to solve the proposed formulation.  ... 
doi:10.1109/tsg.2022.3158232 fatcat:cukkkaqs5rcu3fmc56bfyzkdvm

Natural Gas Flow Equations: Uniqueness and an MI-SOCP Solver [article]

Manish K. Singh, Vassilis Kekatos
2018 arXiv   pre-print
To find this solution, we put forth a mixed-integer second-order cone program (MI-SOCP)-based solver relying on a relaxation of the gas flow equations.  ...  Unlike existing alternatives, the devised solver does not need proper initialization or knowing the gas flow directions beforehand, and can handle gas networks with compressors.  ...  GAS FLOW PROBLEM Consider a natural gas network (GN) modeled by a directed graph G = (N , P).  ... 
arXiv:1809.09025v1 fatcat:mgpolpnqcnbuvgvcisb2bdzudm

A Data-Driven Warm Start Approach for Convex Relaxation in Optimal Gas Flow [article]

Haizhou Liu, Lun Yang, Xinwei Shen, Qinglai Guo, Hongbin Sun, Mohammad Shahidehpour
2020 arXiv   pre-print
In this letter, we propose a data-driven warm start approach, empowered by artificial neural networks, to boost the efficiency of convex relaxations in optimal gas flow.  ...  Case studies show that this approach significantly decreases the number of iterations for the convex-concave procedure algorithm, and optimality and feasibility of the solution can still be guaranteed.  ...  Inspired by its distinct properties, we propose a data-driven convex relaxation approach for the optimal gas flow problem.  ... 
arXiv:2012.10125v1 fatcat:tlyne6qvnnachlyewqxmocdzdi

Maximum Throughput Problem in Dissipative Flow Networks with Application to Natural Gas Systems [article]

Sidhant Misra, Marc Vuffray, Michael Chertkov
2015 arXiv   pre-print
Finally, we illustrate application of these general results to balanced, i.e. steady, natural gas networks also validating the theory results through simulations on a test case.  ...  When the dissipation function follows a power law with exponent greater than one, we suggest a mixed integer convex relaxation of the maximum throughput problem.  ...  The authors also acknowledge partial support of the Advanced Grid Modeling Program in the US Department of Energy Office of Electricity.  ... 
arXiv:1504.02370v1 fatcat:4tm4jtgdnna6dnz4zh5ab5hwii

Convex Relaxations for Gas Expansion Planning

Conrado Borraz-Sánchez, Russell Bent, Scott Backhaus, Hassan Hijazi, Pascal Van Hentenryck
2016 INFORMS journal on computing  
Given the non-convex nature of the problem, a convex mixed-integer second-order cone relaxation is introduced.  ...  .: Convex Relaxations for Gas Expansion Planning Borraz-Sánchez et al.: Convex Relaxations for Gas Expansion Planning Article submitted to INFORMS Journal on Computing; manuscript no.  ...  Through the use of variational inequality theory, the author shows convexity of the nonlinear gas flow system under the assumption that the gas net inlet (pressure) is fixed at all supply and demand nodes  ... 
doi:10.1287/ijoc.2016.0697 fatcat:w3xlrhqapraedoo7f2b3zawe2m

Page 386 of SPE Production & Operations Vol. 22, Issue 4 [page]

2007 SPE Production & Operations  
For naturally flowing wells, a global optimum can be proved to be found for the resulting opti mization problem because of the convexity of the problem.  ...  By using a hybrid solver consisting of a genetic > 4— A good well with lift on ©— A well needs lift to flow Oil production rate Gas lift rate Fig. 5—A gas lift performance curve relates the lift-gas rate  ... 

Convex Relaxations of Maximal Load Delivery for Multi-contingency Analysis of Joint Electric Power and Natural Gas Transmission Networks [article]

Byron Tasseff, Carleton Coffrin, Russell Bent
2021 arXiv   pre-print
To increase its tractability, we present a mixed-integer convex relaxation of the MLD problem.  ...  Recent increases in gas-fired power generation have engendered increased interdependencies between natural gas and power transmission systems.  ...  Here, for brevity, we omit the derivation of the full mixedinteger convex relaxation used throughout the remainder of this study.  ... 
arXiv:2108.12361v1 fatcat:6sp4uskbojhsjfllbtidgyhy24

Distributed Optimal Gas-Power Flow Using Convex Optimization and ADMM [article]

Cheng Wang, Wei Wei, Jianhui Wang, Linquan Bai, Yile Liang
2016 arXiv   pre-print
At the power distribution system side, convex relaxation is performed on the non-convex branch flow equations, and the optimal power flow (OPF) subproblem gives rise to a second order cone program.  ...  At the gas distribution system side, the non-convex Weymouth gas flow equations is convexified as quadratic constraints.  ...  [8] and [10] use coarse approximations to make the PDEs trackable. [11] directly use the PDEs to depict gas flow dynamics and solve OGPF using a nonlinear solver.  ... 
arXiv:1610.04681v1 fatcat:u4hk2pjndjanbox5fcwndniimm

Applying Convex Optimal Power Flow to Combined Economic and Emission Dispatch

Zhao Yuan, Mohammad Reza Hesamzadeh
2016 Journal of Geoscience and Environment Protection  
The advantage of using convex power flow model is that global optimal solutions can be obtained by using mature industrial strength nonlinear solvers such as MOSEK.  ...  In this paper, we use the convex optimal power flow model to formulate the combined economic and emission dispatch problem.  ...  Conclusion In this paper, we prove the feasibility of using convex optimal power flow model to solve the combined economic and emission dispatch problem.  ... 
doi:10.4236/gep.2016.47002 fatcat:gpfz6punwnevhloaejqtapmegm

Validation of nominations in gas network optimization: models, methods, and solutions

Marc E. Pfetsch, Armin Fügenschuh, Björn Geißler, Nina Geißler, Ralf Gollmer, Benjamin Hiller, Jesco Humpola, Thorsten Koch, Thomas Lehmann, Alexander Martin, Antonio Morsi, Jessica Rövekamp (+9 others)
2014 Optimization Methods and Software  
We describe a two-stage approach to solve the resulting complex and numerically difficult non-convex mixed-integer nonlinear feasibility problem.  ...  In this article we investigate methods to solve a fundamental task in gas transportation, namely the validation of nomination problem: Given a gas transmission network consisting of passive pipelines and  ...  We thank Klaus Spreckelsen from Open Grid Europe GmbH for his support and Timo Berthold and Stefan Heinz from the Matheon B20 project for their support on adapting the SCIP solver.  ... 
doi:10.1080/10556788.2014.888426 fatcat:sn5inwmscjc7dl4o4iwhiywgbq

Mathematical programming techniques in water network optimization

Claudia D'Ambrosio, Andrea Lodi, Sven Wiese, Cristiana Bragalli
2015 European Journal of Operational Research  
The basic underlying model in both cases is a nonlinear network flow model, and we give an overview on the more specific modeling aspects in each case.  ...  Acknowledgments We would like to thank Jesco Humpola for sharing insights on nonlinear network flows and Stefan Vigerske and Ambros Gleixner for giving technical advice regarding SCIP.  ...  The convex leaf problems are therefore solved by an NLP solver via different relaxation strategies.  ... 
doi:10.1016/j.ejor.2014.12.039 fatcat:bnz2xndmdrayjfyvomcp2dg7hi

Natural Gas Maximal Load Delivery for Multi-contingency Analysis [article]

Byron Tasseff, Carleton Coffrin, Russell Bent, Kaarthik Sundar, Anatoly Zlotnik
2020 arXiv   pre-print
To address this challenge, we present a mixed-integer convex relaxation of the MLD problem and use it to determine bounds on the transport capacity of a gas pipeline system.  ...  To demonstrate the effectiveness of the relaxation, the exact and relaxed formulations are compared across a large number of randomized damage scenarios on nine natural gas pipeline network models ranging  ...  Similar convex relaxations for gas pipeline flow have been explored subsequently (Wu et al., 2017; Chen et al., 2018) .  ... 
arXiv:2009.14726v2 fatcat:5udjoy57pzhctgeojk2h52nbpa

Decentralized Optimization of Electricity-Natural Gas Flow Considering Dynamic Characteristics of Networks

Weicong Wu, Tao Yu, Zhuohuan Li, Hanxin Zhu
2020 Applied Sciences  
of multipliers (ADMM) algorithm at each iteration of PCCP to develop a decentralized collaborative optimization of power flow and natural gas flow.  ...  For space-time related line packs, this paper studies the optimal multi-energy flow (OMEF) model of an integrated electricity-gas system, taking into account the dynamic characteristics of a natural gas  ...  For the natural gas system model considering the dynamic characteristics, the positive and negative natural gas flow are introduced into the model, and the PCCP method is used to convexize the flow equation  ... 
doi:10.3390/app10103348 fatcat:clwnd7t2lrfw5lg63es4az5q34

On the Flow Problem in Water Distribution Networks: Uniqueness and Solvers [article]

Manish K. Singh, Vassilis Kekatos
2020 arXiv   pre-print
For networks with non-overlapping cycles, a provably exact convex relaxation of the pressure drop equations yields a mixed-integer quadratically-constrained quadratic program (MI-QCQP) solver.  ...  To this end, this work revisits the physical laws governing water flow and provides a hierarchy of solvers of complementary value.  ...  We shall next address the natural question: Q1) Can one use one of the aforesaid OWF solvers to solve the WF task?  ... 
arXiv:1901.03676v2 fatcat:muhidcdhsbbp3pdsqx54hpwjyq
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