Summary
The operative planning problem in natural gas distribution networks is addressed. An optimization model focusing on the governing PDE and other nonlinear aspects is presented together with a suitable discretization for transient optimization in large networks by SQP methods. Computational results for a range of related dynamic test problems demonstrate the viability of the approach.
This work has been supported by the Federal Ministry of Education and Science (BMBF) under grant 03STM5B4.
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References
E. A. Boyd, L. R. Scott, and S. Wu, Evaluating the quality of pipeline optimization algorithms, in 29th Annual Meeting, Pipeline Simulation Interest Group, 1997. Paper 9709.
R. G. Carter, Pipeline optimization: Dynamic Programming after 30 years, in 30th Annual Meeting, Pipeline Simulation Interest Group, 1998. Paper 9803.
E. M. Gertz, P. E. Gill, and J. Muethering, Users guide for SnadiOpt: a package adding automatic differentiation to SNOPT, Technical Memorandum ANL/MCS-TM-245, Argonne National Labs, Jan. 2001.
P. E. Gill, W. Murray, and M. S. Saunders, SNOPT: An SQP algorithm for large-scale constrained optimization, SIAM J. Optim., 12 (2002), pp. 979–1006.
M. Gugat, G. Leugering, K. Schittkowski, and E. J. P. G. Schmidt, Modelling, stabilization, and control of flow in networks of open channels, in Online Optimization of Large Scale Systems, M. Grötschel, S. O. Krumke, and J. Rambau, eds., Springer, Berlin, 2001, pp. 251–270.
P. Hackländer, Integrierte Betriebsplanung von Gasversorgungssystemen, Verlag Mainz, Wissenschaftsverlag, Aachen, 2002.
T. Heidenreich, Linearisierung in transienten Optimierungsmodellen des Gastransports, Universität Duisburg, 2002.
J. Krälik, P. Stiegler, Z. Vostry, and J. Zavorka, A universal dynamic simulation model of gas pipeline networks, IEEE Trans. Syst., Man, Cybern., SMC-14 (1984), pp. 597–606.
A. Martin and M. Möller, Cutting planes for the optimization of gas networks, Preprint 2253, Fachbereich Mathematik, Technische Universität Darmstadt, 2002.
K. F. Pratt and J. G. Wilson, Optimization of the operation of gas transmission systems, Transactions of the Institute of Measurement and Control, 6 (1984), pp. 261–269.
D. Rist, Dynamik realer Gase, Springer, Berlin, 1996.
E. Sekirnjak, Mixed integer optimization for gas transmission and distribution systems. Vortragsmanuskript, INFORMS-Meeting, Seattle, Oct. 1998.
Z. Vostrý, 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, Prague, 1993, pp. 53–62.
J. F. Wilkinson, D. V. Holliday, E. H. Batey, and K. W. Hannah, Transient Flow in Natural Gas Transmission Systems, American Gas Association, 1964.
D. D. Wolf and Y. Smeers, The gas transmission problem solved by an extension of the simplex algorithm, Management Sci., 46 (2000), pp. 1454–1465.
P. J. Wong and R. E. Larson, Optimization of tree-structured natural-gas transmission networks, J. Math. Anal. Appl., 24 (1968), pp. 613–626.
S. Wright, M. Somani, and C. Ditzel, Compressor station optimization, in 30th Annual Meeting, Pipeline Simulation Interest Group, 1998. Paper 9805.
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Ehrhardt, K., Steinbach, M.C. (2005). Nonlinear Optimization in Gas Networks. In: Bock, H.G., Phu, H.X., Kostina, E., Rannacher, R. (eds) Modeling, Simulation and Optimization of Complex Processes. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-27170-8_11
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DOI: https://doi.org/10.1007/3-540-27170-8_11
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