×

Deterministic global optimization of steam cycles using the IAPWS-IF97 model. (English) Zbl 1457.90112

Summary: The IAPWS-IF97 [ W. Wagner et al., “The IAPWS industrial formulation 1997 for the thermodynamic properties of water and steam”, J. Eng. Gas. Turbines and Power 122, No. 1, 150–182 (2000; doi:10.1115/1.483186)] is the state-of-the-art model for the thermodynamic properties of water and steam for industrial applications and is routinely used for simulations of steam power cycles and utility systems. Its use in optimization-based design, however, has been limited because of its complexity. In particular, deterministic global optimization of problems with the IAPWS-IF97 is challenging because general-purpose methods lead to rather weak convex and concave relaxations, thus resulting in slow convergence. Furthermore, the original domains of many functions from the IAPWS-IF97 are nonconvex, while common global solvers construct relaxations over rectangular domains. Outside the original domains, however, many of the functions take very large values that lead to even weaker relaxations. Therefore, we develop tighter relaxations of relevant functions from the IAPWS-IF97 on the basis of an analysis of their monotonicity and convexity properties. We modify the functions outside their original domains to enable tighter relaxations, while we keep them unchanged on their original domains where they have physical meaning. We discuss the benefit of the relaxations for three case studies on the design of bottoming cycles of combined cycle power plants using our open-source deterministic global solver MAiNGO. The derived relaxations result in drastic reductions in computational time compared with McCormick relaxations and can make design problems tractable for global optimization.

MSC:

90C26 Nonconvex programming, global optimization
90C90 Applications of mathematical programming
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Åberg M, Windahl J, Runvik H, Magnusson F (2017) Optimization-friendly thermodynamic properties of water and steam. In: Proceedings of the 12th international modelica conference, Prague, Czech Republic, May 15-17, 2017. Linköping University Electronic Press, Linköpings Universitet, pp 449-458
[2] Adjiman, CS; Dallwig, S.; Floudas, CA; Neumaier, A., A global optimization method, \( \alpha\) BB, for general twice-differentiable constrained NLPs- I. Theoretical advances, Comput Chem Eng, 22, 1137-1158 (1998)
[3] Ahadi-Oskui, T.; Alperin, H.; Nowak, I.; Cziesla, F.; Tsatsaronis, G., A relaxation-based heuristic for the design of cost-effective energy conversion systems, Energy, 31, 1346-1357 (2006)
[4] Ahadi-Oskui, T.; Vigerske, S.; Nowak, I.; Tsatsaronis, G., Optimizing the design of complex energy conversion systems by branch and cut, Comput Chem Eng, 34, 1226-1236 (2010)
[5] Androulakis, IP; Maranas, CD; Floudas, CA, \( \alpha\) BB: a global optimization method for general constrained nonconvex problems, J Glob Optim, 7, 337-363 (1995) · Zbl 0846.90087
[6] Bendtsen C, Stauning O (2012) FADBAD++, a flexible C++ package for automatic differentiation. Version 2.1. http://www.fadbad.com. Accessed 18 Oct 2016
[7] Bongartz, D.; Mitsos, A., Deterministic global optimization of process flowsheets in a reduced space using McCormick relaxations, J Glob Optim, 69, 761-796 (2017) · Zbl 1386.90112
[8] Bongartz D, Najman J, Sass S, Mitsos A (2018) MAiNGO-McCormick-based Algorithm for mixed-integer Nonlinear Global Optimization. Process Systems Engineering (AVT.SVT), RWTH Aachen University. http://permalink.avt.rwth-aachen.de/?id=729717. Accessed 25 Oct 2019
[9] Bruno, J.; Fernandez, F.; Castells, F.; Grossmann, I., A rigorous MINLP model for the optimal synthesis and operation of utility plants, Chem Eng Res Des, 76, 246-258 (1998)
[10] Chachuat B, Houska B, Paulen R, Perić N, Rajyaguru J, Villanueva M (2015) Set-theoretic approaches in analysis, estimation and control of nonlinear systems. IFAC-PapersOnLine 48:981-995. https://omega-icl.github.io/mcpp/. Accessed 25 Oct 2019
[11] Falk, JE; Soland, RM, An algorithm for separable nonconvex programming problems, Manag Sci, 15, 550-569 (1969) · Zbl 0172.43802
[12] Forrest JJ, Vigerske S, Ralphs T, Hafer L, Fasano JP, Santos HG, Saltzman M, Gassmann H, Kristjansson B, King A (2019) COIN-OR linear programming solver. https://github.com/coin-or/Clp. Accessed 25 Oct 2019
[13] Gleixner, AM; Berthold, T.; Müller, B.; Weltge, S., Three enhancements for optimization-based bound tightening, J Glob Optim, 67, 731-757 (2017) · Zbl 1369.90106
[14] Hasan, FMM, An edge-concave underestimator for the global optimization of twice-differentiable nonconvex problems, J Glob Optim, 71, 735-752 (2018) · Zbl 1422.90038
[15] International Energy Agency (2019) Electricity information: overview. https://webstore.iea.org/electricity-information-2019. Accessed 6 Oct 2019
[16] Khan, KA; Barton, PI, A vector forward mode of automatic differentiation for generalized derivative evaluation, Optim Method Softw, 30, 1185-1212 (2015) · Zbl 1329.49023
[17] Koch, C.; Cziesla, F.; Tsatsaronis, G., Optimization of combined cycle power plants using evolutionary algorithms, Chem Eng Process, 46, 1151-1159 (2007)
[18] Lerch M, Tischler G, Wolff von Gudenberg J, Hofschuster W, Krämer W (2011) FILIB++ Interval Library (V 3.0.2). http://www2.math.uni-wuppertal.de/wrswt/software/filib.html. Accessed 25 Oct 2019 · Zbl 1365.65140
[19] Locatelli, M.; Schoen, F., Global optimization: theory, algorithms, and applications (2013), Philadelphia: MOS-SIAM, Philadelphia · Zbl 1286.90003
[20] Luo, X.; Zhang, B.; Chen, Y.; Mo, S., Modeling and optimization of a utility system containing multiple extractions steam turbines, Energy, 36, 3501-3512 (2011)
[21] Manassaldi, JI; Mussati, SF; Scenna, NJ, Optimal synthesis and design of heat recovery steam generation (HRSG) via mathematical programming, Energy, 36, 475-485 (2011)
[22] Manassaldi, JI; Arias, AM; Scenna, NJ; Mussati, MC; Mussati, SF, A discrete and continuous mathematical model for the optimal synthesis and design of dual pressure heat recovery steam generators coupled to two steam turbines, Energy, 103, 807-823 (2016)
[23] McCormick, G., Computability of global solutions to factorable nonconvex programs: Part I—Convex underestimating problems, Math Prog, 10, 147-175 (1976) · Zbl 0349.90100
[24] Meyer, CA; Floudas, CA, Convex envelopes for edge-concave functions, Math Prog, 103, 207-224 (2005) · Zbl 1099.90045
[25] Mistry, M.; Misener, R., Optimising heat exchanger network synthesis using convexity properties of the logarithmic mean temperature difference, Comput Chem Eng, 94, 1-17 (2016)
[26] Nadir, M.; Ghenaiet, A., Thermodynamic optimization of several (heat recovery steam generator) HRSG configurations for a range of exhaust gas temperatures, Energy, 86, 685-695 (2015)
[27] Najman J, Mitsos A (2016) Convergence order of McCormick relaxations of LMTD function in heat exchanger networks. In: Kravanja Z, Bogataj M (eds) Proceedings of the 26th European symposium on computer aided process engineering—ESCAPE 26, pp 1605-1610
[28] Najman, J.; Mitsos, A., On tightness and anchoring of McCormick and other relaxations, J Glob Optim, 74, 677-703 (2019) · Zbl 1425.49014
[29] Najman, J.; Bongartz, D.; Mitsos, A., Convex relaxations of componentwise convex functions, Comput Chem Eng, 130, 106527 (2019)
[30] Najman, J.; Bongartz, D.; Mitsos, A., Relaxations of thermodynamic property and costing models in process engineering, Comput Chem Eng, 130, 106571 (2019)
[31] Nowak, I.; Vigerske, S., LaGO: a (heuristic) branch and cut algorithm for nonconvex MINLPs, Cent Eur J Oper Res, 16, 127-138 (2008) · Zbl 1152.90665
[32] Podolski WF, Schmalzer DK, Conrad V, Lowenhaupt DE, Winschel RA, Klunder EB, McIlvried III HG, Ramezan M, Stiegel GJ, Srivastava RD, Winslow J, Loftus PJ, Benson CE, Wheeldon JM, Krumpelt M, Smith FL (2008) Energy resources, conversion, and utilization. In: Green DW, Perry RH (eds) Perry’s chemical engineers’ handbook. McGraw-Hill, New York, pp 24-1 - 24-57
[33] Rockafellar, RT, Convex analysis (1970), Princeton: Princeton University Press, Princeton
[34] Ryoo, HS; Sahinidis, NV, Global optimization of nonconvex NLPs and MINLPs with applications in process design, Comput Chem Eng, 19, 551-566 (1995)
[35] Savola, T.; Tveit, TM; Fogelholm, CJ, A MINLP model including the pressure levels and multiperiods for CHP process optimisation, Appl Therm Eng, 27, 1857-1867 (2007)
[36] Schweidtmann, AM; Huster, WR; Lüthje, JT; Mitsos, A., Deterministic global process optimization: accurate (single-species) properties via artificial neural networks, Comput Chem Eng, 121, 67-74 (2019)
[37] Smith, EM; Pantelides, CC, Global optimisation of nonconvex MINLPs, Comput Chem Eng, 21, S791-S796 (1997)
[38] Tardella, F.; Floudas, CA; Pardalos, P., On the existence of polyhedral convex envelopes, Frontiers in global optimization, 563-573 (2004), Dordrecht: Kluwer Academic Publishers, Dordrecht · Zbl 1176.90473
[39] Tawarmalani, M.; Sahinidis, NV, Convexifixation and global optimization in continuous and mixed-integer nonlinear programming (2002), Dordrecht: Kluwer Academic Publishers, Dordrecht
[40] The International Association for the Properties of Water and Steam (2007a) IAPWS R7-97(2012)—Revised release on the IAPWS industrial formulation 1997 for the thermodynamic properties of water and steam. http://iapws.org/relguide/IF97-Rev.html. Accessed 29 Aug 2019
[41] The International Association for the Properties of Water and Steam (2007b) IAPWS R7-97(2012)—Revised supplementary release on backward equations for the functions T(p,h), v(p,h) and T(p,s), v(p,s) for Region 3 of the IAPWS Industrial Formulation 1997 for the thermodynamic properties of water and steam. http://iapws.org/relguide/IF97-Rev.html. Accessed 26 Sept 2019
[42] Tică, A.; Guéguen, H.; Dumur, D.; Faille, D.; Davelaar, F., Design of a combined cycle power plant model for optimization, Appl Energy, 98, 256-265 (2012)
[43] Tsoukalas, A.; Mitsos, A., Multivariate McCormick relaxations, J Glob Optim, 59, 633-662 (2014) · Zbl 1312.90068
[44] Wächter, A.; Biegler, LT, On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming, Math Prog, 106, 25-57 (2006) · Zbl 1134.90542
[45] Wagner, W.; Pruss, A., The IAPWS formulation 1995 for the thermodynamic properties of ordinary water substance for general and scientific use, J Phys Chem Ref Data, 31, 387-535 (2002)
[46] Wagner, W.; Cooper, JR; Dittmann, A.; Kijima, J.; Kretzschmar, HJ; Kruse, A.; Mareš, R.; Oguchi, K.; Sato, H.; Stocker, I.; Sifner, O.; Takaishi, Y.; Tanishita, I.; Trübenbach, J.; Willkommen, T., The IAPWS industrial formulation 1997 for the thermodynamic properties of water and steam, J Eng Gas Turbines Power, 122, 150-182 (2000)
[47] Wang, L.; Yang, Y.; Dong, C.; Morosuk, T.; Tsatsaronis, G., Systematic optimization of the design of steam cycles using MINLP and differential evolution, J Energy Resour Technol, 136, 031601 (2014)
[48] Wang, L.; Voll, P.; Lampe, M.; Yang, Y.; Bardow, A., Superstructure-free synthesis and optimization of thermal power plants, Energy, 91, 700-711 (2015)
[49] Wang, L.; Lampe, M.; Voll, P.; Yang, Y.; Bardow, A., Multi-objective superstructure-free synthesis and optimization of thermal power plants, Energy, 116, 1104-1116 (2016)
[50] Wang, L.; Yang, Z.; Sharma, S.; Mian, A.; Lin, TE; Tsatsaronis, G.; Maréchal, F.; Yang, Y., A review of evaluation, optimization and synthesis of energy systems: methodology and application to thermal power plants, Energies, 12, 73 (2019)
[51] Zebian, H.; Gazzino, M.; Mitsos, A., Multi-variable optimization of pressurized oxy-coal combustion, Energy, 38, 37-57 (2012)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.