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High detail stationary optimization models for gas networks. (English) Zbl 1364.90066
Summary: Economic reasons and the regulation of gas markets create a growing need for mathematical optimization of natural gas networks. Real life planning tasks often lead to highly complex and extremely challenging optimization problems whose numerical treatment requires a breakdown into several simplified problems to be solved by carefully chosen hierarchies of models and algorithms. This paper presents stationary NLP type models of gas networks that are primarily designed to include detailed nonlinear physics in the final optimization steps for mid term planning problems after fixing discrete decisions with coarsely approximated physics.

90B10 Deterministic network models in operations research
90C06 Large-scale problems in mathematical programming
90C30 Nonlinear programming
90C90 Applications of mathematical programming
90C35 Programming involving graphs or networks
SNOPT; SIMONE; Ipopt; GasLib
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[1] Bales P (2005) Hierarchische Modellierung der Eulerschen Flussgleichungen in der Gasdynamik. Master’s thesis, Technische Universität Darmstadt
[2] Banda, MK; Herty, M, Multiscale modeling for gas flow in pipe networks, Math Met Appl Sci, 31, 915-936, (2008) · Zbl 1142.93304
[3] Banda, MK; Herty, M; Klar, A, Gas flow in pipeline networks, Netw Heterogen Media, 1, 41-56, (2006) · Zbl 1108.76063
[4] Borraz-Sánchez C, Ríos-Mercado RZ (2004) A procedure for finding initial feasible solutions on cyclic natural gas networks. In: Proceedings of the 2004 NSF Design, Service and Manufacturing Grantees and Research Conference, Dallas · Zbl 1142.93304
[5] Borraz-Sánchez C, Ríos-Mercado RZ (2005) A hybrid meta-heuristic approach for natural gas pipeline network optimization. In: Blesa M, Blum C, Roli A, Sampels M (eds.) Hybrid Metaheuristics, Lecture Notes in Computer Science, vol. 3636, pp. 54-65. Springer. doi:10.1007/11546245_6
[6] Boyd EA, Scott LR, Wu S (1997) Evaluating the quality of pipeline optimization algorithms. In: PSIG 29th Annual Meeting, Tucson, Arizona. Pipeline Simulation Interest Group. Paper 9709 · Zbl 1108.76063
[7] Brouwer, J; Gasser, I; Herty, M, Gas pipeline models revisited: model hierarchies, nonisothermal models, and simulations of networks, Multiscale Model Simul, 9, 601-623, (2011) · Zbl 1254.76124
[8] Burgschweiger J, Gnädig B, Steinbach MC (2008) Optimization models for operative planning in drinking water networks. Optim Eng 10(1):43-73 doi:10.1007/s11081-008-9040-8. Published in print 2009 · Zbl 1273.76072
[9] Burgschweiger, J; Gnädig, B; Steinbach, MC, Nonlinear programming techniques for operative planning in large drinking water networks, Open Appl Math J, 3, 14-28, (2009) · Zbl 1322.90013
[10] Carter RG (1996) Compressor station optimization: Computational accuracy and speed. In: 28th Annual Meeting. Pipeline Simulation Interest Group. Paper 9605
[11] Carter RG (1998) Pipeline optimization: Dynamic Programming after 30 years. In: 30th Annual Meeting. Pipeline Simulation Interest Group Paper 9803
[12] Carter RG, Schroeder DW, Harbick TD (1994) Some causes and effects of discontinuities in modeling and optimizing gas transmission networks. Tech. rep., Stoner Associates, Carlisle
[13] Cerbe G (2008) Grundlagen der Gastechnik. Hanser, Munich
[14] Chodanowitsch, IJ; Odischarija, GE, Analiž žavisimosti dlja koeffizienta gidravličeskogo soprotivlenija (analysis of the relations of friction coefficients), gazovaya promyšlennost, 11, 38-42, (1964)
[15] Cobos-Zaleta D, Ríos-Mercado RZ (2002) A MINLP model for a problem of minimizing fuel consumption on natural gas pipeline networks. In: Proceedings of the XI Latin-Ibero-American Conference on Operations Research, pp. 1-9. Paper A48-01 · Zbl 1086.90010
[16] Colebrook, CF, Turbulent flow in pipes with particular reference to the transition region between smooth and rough pipe laws, J Inst Civil Eng, 11, 133-156, (1939)
[17] Domschke, P; Geißler, B; Kolb, O; Lang, J; Martin, A; Morsi, A, Combination of nonlinear and linear optimization of transient gas networks, INFORMS J Comput, 23, 605-617, (2011) · Zbl 1243.90030
[18] Ehrhardt, K; Steinbach, MC, KKT systems in operative planning for gas distribution networks, Proc Appl Math Mech, 4, 606-607, (2004) · Zbl 1354.90023
[19] Ehrhardt, K; Steinbach, MC; Bock, HG (ed.); Kostina, E (ed.); Phu, HX (ed.); Rannacher, R (ed.), Nonlinear optimization in gas networks, 139-148, (2005), Berlin
[20] Feistauer M (1993) Mathematical Methods in Fluid Dynamics. Pitman Monographs and Surveys in Pure and Applied Mathematics Series, vol. 67. Longman Scientific & Technical, Harlow · Zbl 0819.76001
[21] Finnemore EJ, Franzini JE (2002) Fluid mechanics with engineering applications, 10th edn. McGraw-Hill, New York
[22] Fügenschuh A, Geißler B, Gollmer R, Hayn C, Henrion R, Hiller B, Humpola J, Koch T, Lehmann T, Martin A, Mirkov R, Morsi A, Rövekamp J, Schewe L, Schmidt M, Schultz R, Schwarz R, Schweiger J, Stangl C, Steinbach MC, Willert B (2013) Mathematical optimization for challenging network planning problems in unbundled liberalized gas markets. Energy Syst. pp. 1-25. doi:10.1007/s12667-013-0099-8
[23] GasLib: a library of gas network instances. http://gaslib.zib.de
[24] Geißler B (2011) Towards globally optimal solutions for MINLPs by discretization techniques with applications in gas network optimization. Ph. D. dissertation, University of Erlangen-Nuremberg, Germany
[25] Gill, PE; Murray, W; Saunders, MS, SNOPT: an SQP algorithm for large-scale constrained optimization, SIAM J. Optim., 12, 979-1006, (2002) · Zbl 1027.90111
[26] Gugat, M, Boundary controllability between sub- and supercritical flow, SIAM J. Control Optim., 42, 1056-1070, (2003) · Zbl 1047.35087
[27] Gugat, M; Leugering, G, Global boundary controllability of the de st, Venant equations between steady states. Annales de l’Institut Henri Poincare (C) Non Linear Analysis, 20, 1-11, (2003) · Zbl 1032.93030
[28] Gugat M, Leugering, G, Schittkowski K, Schmidt EJPG (2011) Modelling, stabilization, and control of flow in networks of open channels. In: Grötschel M, Krumke SO, Rambau J (eds.) Online optimization of large scale systems. Springer, Berlin, pp 251-270 · Zbl 0987.93056
[29] Hackländer P (2002) Integrierte Betriebsplanung von Gasversorgungssystemen. Ph. D. dissertation, Universität Wuppertal (2002)
[30] Hofer, P, Beurteilung von fehlern in rohrnetzberechnungen (error evaluation in calculation of pipelines), GWF Gas, 11, 113-119, (1973)
[31] Jeníček T (1993) Steady-state optimization of gas transport. In: Proceedings of 2nd international workshop SIMONE on innovative approaches to modeling and optimal control of large scale pipeline networks, pp. 26-38 · Zbl 1024.76009
[32] Jeníček T, Králik J, Štěrba J, Vostrý Z, Záworka J (1993) Study to analyze the possibilities and features of an optimization system (optimum control system) to support the dispatching activities of Ruhrgas. Vertrauliche Dokumentation, LIWACOM Informationstechnik GmbH Essen
[33] Katz DLV (1959) Handbook of natural gas engineering. McGraw-Hill series in chemical engineering, McGraw-Hill, New York
[34] Koch T, Bargmann D, Ebbers M, Fügenschuh A, Geißler B, Geißler N, Gollmer R, Gotzes U, Hayn C, Heitsch H, Henrion R, Hiller B, Humpola J, Joormann I, Kühl V, Lehmann T, Leövey H, Martin A, Mirkov R, Möller A, Morsi A, Oucherif D, Pelzer A, Pfetsch ME, Schewe L, Römisch W, Rövekamp J, Schmidt M, Schultz R, Schwarz R, Schweiger J, Spreckelsen K, Stangl C, Steinbach MC, Steinkamp A, Wegner-Specht I, Willert BM, Vigerske S (2014) Evaluating gas network capacities, In preparation
[35] Králik J (1993) Compressor stations in SIMONE. In: Proceedings of 2nd international workshop SIMONE on innovative approaches to modeling and optimal control of large scale pipeline networks, pp. 93-117 · Zbl 1126.90053
[36] Králik, J; Stiegler, P; Vostrý, Z; Závorka, J, A universal dynamic simulation model of gas pipeline networks, IEEE Trans Syst Man Cybern, 14, 597-606, (1984)
[37] Králik, J; Stiegler, P; Vostrý, Z; Záworka, J, Modeling the dynamics of flow in gas pipelines, IEEE Trans Syst Man Cybern, 14, 586-596, (1984)
[38] Králik J, Stiegler P, Vostrý Z, Záworka J (1988) Dynamic modeling of large-scale networks with application to gas distribution, Studies in Automation and Control, vol. 6. Elsevier Sci. Publ., New York
[39] Kunz O, Klimeck R, Wagner W, Jaeschke M (2007) The GERG-2004 wide-range equation of state for natural gases and other mixtures. No. 557 in Fortschritt-Berichte VDI, Reihe 6. VDI Verlag, Düsseldorf (2007). GERG Technical Monograph 15
[40] Leugering, G; Schmidt, EJPG, On the modelling and stabilization of flows in networks of open canals, SIAM J Control Optim, 41, 164-180, (2002) · Zbl 1024.76009
[41] LIWACOM Informations GmbH and SIMONE Research Group s.r.o.: Gleichungen und Methoden Benutzerhandbuch (2004) · Zbl 1032.93030
[42] Lurie MV (2008) Modeling of oil product and gas pipeline transportation. Wiley-VCH, Heidelberg
[43] Martin, A., Geißler B, Hayn C, Hiller B, Humpola J, Koch T, Lehmann T, Morsi A, Pfetsch M, Schewe L, Schmidt M, Schultz R, Schwarz R, Schweiger J, Steinbach MC, Willert BM (2011) Optimierung Technischer Kapazitäten in Gasnetzen. In: Optimierung in der Energiewirtschaft, VDI-Berichte, 2157:105-114
[44] Martin, A; Mahlke, D; Moritz, S, A simulated annealing algorithm for transient optimization in gas networks, Math Methods Oper Res, 66, 99-115, (2007) · Zbl 1126.90053
[45] Martin, A; Möller, M; Bock, HG (ed.); Kostina, E (ed.); Phu, HX (ed.); Rannacher, R (ed.), Cutting planes for the optimization of gas networks, (2005)
[46] Martin, A; Möller, M; Moritz, S, Mixed integer models for the stationary case of gas network optimization, Math Program, 105, 563-582, (2006) · Zbl 1085.90035
[47] Mischner, J, Notices about hydraulic calculations of gas pipelines, J-GWFGas, 4, 158-273, (2012)
[48] Möller M (2004) Mixed integer models for the optimisation of gas networks in the stationary case. Ph. D. dissertation. Technische Universität Darmstadt
[49] Moritz S (2007) A mixed integer approach for the transient case of gas network optimization. Ph. D. dissertation. Technische Universität Darmstadt · Zbl 1149.90380
[50] de Nevers N (1970) Fluid mechanics. Addison-Wesley series in chemical engineering. Addison-Wesley Pub. Co. URL http://books.google.co.in/books?id=ERBRAAAAMAAJ
[51] Nikuradse J (1933) Strömungsgesetze in rauhen Rohren. Forschungsheft auf dem Gebiete des Ingenieurwesens. VDI-Verlag, Düsseldorf · JFM 59.1462.02
[52] Nikuradse J (1950) Laws of flow in rough pipes, Technical Memorandum. vol. 1292. National Advisory Committee for Aeronautics, Washington · Zbl 1243.90030
[53] Odom FM, Muster GL (2009) Tutorial on modeling of gas turbine driven centrifugal compressors. Tech. Rep. 09A4, Pipeline Simulation Interest Group
[54] Osiadacz, A, Nonlinear programming applied to the optimum control of a gas compressor station, Int J Numer Methods Eng, 15, 1287-1301, (1980) · Zbl 0466.76064
[55] Oucherif D (2009) Approximation der stationären Impulsgleichung realer Gase in Pipelines. Diploma thesis, Leibniz Universität Hannover · Zbl 1254.76124
[56] Papay I (1968) OGIL Musz. Tud. Kozl
[57] Pfetsch ME, Fügenschuh A, Geißler B, Geißler N, Gollmer R, Hiller B, Humpola J, Koch T, Lehmann T, Martin A, Morsi A, Rövekamp J, Schewe L, Schmidt M, Schultz R, Schwarz R, Schweiger J, Stangl C, Steinbach MC, Vigerske S, Willert BM (2012) Validation of nominations in gas network optimization: Models, methods, and solutions. ZIB Report 12-41, Zuse Institute Berlin, Takustr.7, 14195 Berlin. Submitted · Zbl 1325.90019
[58] Pratt, KF; Wilson, JG, Optimization of the operation of gas transmission systems, Trans Inst Meas Control, 6, 261-269, (1984)
[59] Redlich O, Kwong JNS (1949) On the Thermodynamics of Solutions. V. An equation of state. Fugacities of Gaseous Solutions. Chem Rev 44(1):233-244 . doi:10.1021/cr60137a013. PMID: 18125401 · Zbl 1119.93045
[60] Ríos-Mercado, RZ; Kim, S; Boyd, AE, Efficient operation of natural gas transmission systems: a network-based heuristic for cyclic structures, Comput Oper Res, 33, 2323-2351, (2006) · Zbl 1086.90010
[61] Ríos-Mercado, RZ; Wu, S; Scott, LR; Boyd, AE, A reduction technique for natural gas transmission network optimization problems, Ann Oper Res, 117, 217-234, (2002) · Zbl 1028.90501
[62] Saleh, J (eds) (2002) Fluid Flow Handbook. McGraw-Hill Handbooks, New York
[63] Schmidt M, Steinbach MC, Willert BM (2013) A primal heuristic for nonsmooth mixed integer nonlinear optimization. In: Jünger M, Reinelt G (eds.) Facets of Combinatorial Optimization, pp. 295-320. Springer, Berlin, Heidelberg (2013). doi:10.1007/978-3-642-38189-8_13 · Zbl 1317.90212
[64] Schmidt M, Steinbach MC, Willert BM (2014) High detail stationary optimization models for gas networks—Part 2: Validation and results, In preparation
[65] Sekirnjak E (1998) Mixed integer optimization for gas transmission and distribution systems. Presentation manuscript, INFORMS-Meeting, Seattle · Zbl 1232.90355
[66] Sekirnjak E (1999) Transiente Technische Optimierung (TTO-Prototyp). Vertrauliche Dokumentation, PSI AG, Berlin
[67] SIMONE software: http://www.liwacom.de · Zbl 0843.00011
[68] Starling KE, Savidge JL (1992) Compressibility factors of natural gas and other related hydrocarbon gases. Transmission Measurement Committee report. American Gas Association, New York
[69] Steinbach, MC, On PDE solution in transient optimization of gas networks, J Comput Appl Math, 203, 345-361, (2007) · Zbl 1119.93045
[70] van der Hoeven T (2004) Math in gas and the art of linearization. Ph.D. thesis, Rijksuniversiteit Groningen · Zbl 1064.65158
[71] Villalobos-Morales Y, Cobos-Zaleta D, Flores-Villarreal HJ, Borraz-Sánchez C, Ríos-Mercado RZ (2003) On NLP and MINLP formulations and preprocessing for fuel cost minimization of natural gas transmission networks. In: Proceedings of the 2003 NSF Design, Service and Manufacturing Grantees and Research Conference. Birmingham
[72] Vostrý, Z (1993) Transient optimization of gas transport and distribution. In: Proceedings of 2nd international workshop SIMONE on innovative approaches to modeling and optimal control of large scale pipeline networks, pp 53-62
[73] Wächter, A; Biegler, LT, On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming, Math Program, 106, 25-57, (2006) · Zbl 1134.90542
[74] Weimann A (1978) Modellierung und Simulation der Dynamik von Gasnetzen im Hinblick auf Gasnetzführung und Gasnetzüberwachung. Ph. D. dissertation, Technische Universität München
[75] Weymouth TR (1912) Problems in natural gas engineering. Transactions of the American Society of Mechanical Engineers 34:185-231 URL http://archive.org/details/transactionsofa34amer
[76] Wikipedia: Redlich-Kwong equation of state (2012). URL http://en.wikipedia.org/wiki/Redlich-Kwong_equation_of_state. Accessed 11 April 2012
[77] Wolf, D; Smeers, Y, The gas transmission problem solved by an extension of the simplex algorithm, Manag Sci, 46, 1454-1465, (2000) · Zbl 1232.90355
[78] Wong, PJ; Larson, RE, Optimization of natural-gas pipeline systems via dynamic programming, IEEE Trans Autom Control, 13, 475-481, (1968)
[79] Wong, PJ; Larson, RE, Optimization of tree-structured natural-gas transmission networks, J Math Anal Appl, 24, 613-626, (1968)
[80] Wright S, Somani M, Ditzel C (1998) Compressor station optimization. In: 30th Annual Meeting. Pipeline Simulation Interest Group. Paper 9805
[81] Wu S (1998) Steady-state simulation and fuel cost minimization of gas pipeline networks. ProQuest LLC, Ann Arbor, MI (1998). URL http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqdiss&rft_dat=xri:pqdiss:9902937. Thesis (Ph.D.)-University of Houston · Zbl 1254.76124
[82] Wu, S; Ríos-Mercado, RZ; Boyd, AE; Scott, LR, Model relaxations for the fuel cost minimization of steady-state gas pipeline networks, Math Comput Model, 31, 197-220, (2000)
[83] Záworka J (1993) Project SIMONE—Achievements and running development. In: Proceedings of 2nd international workshop SIMONE on innovative approaches to modeling and optimal control of large scale pipeline networks, pp. 1-24
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