Optimization of the Design and Partial-Load Operation of Power Plants Using Mixed-Integer Nonlinear Programming

  • Marc Jüdes
  • Stefan Vigerske
  • George Tsatsaronis
Part of the Energy Systems book series (ENERGY)

Summary

This paper focuses on the optimization of the design and operation of combined heat and power plants (cogeneration plants). Due to the complexity of such an optimization task, conventional optimization methods consider only one operation point that is usually the full-load case. However, the frequent changes in demand lead to operation in several partial-load conditions. To guarantee a technically feasible and economically sound operation, we present a mathematical programming formulation of a model that considers the partial-load operation already in the design phase of the plant. This leads to a nonconvex mixed-integer nonlinear program (MINLP) due to discrete decisions in the design phase and discrete variables and nonlinear equations describing the thermodynamic status and behavior of the plant. The model is solved using an extended Branch and Cut algorithm that is implemented in the solver LaGO. We describe conventional optimization approaches and show that without consideration of different operation points, a flexible operation of the plant may be impossible. Further, we address the problem associated with the uncertain cost functions for plant components.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    C. S. Adjiman, S. Dallwig, C. A. Floudas, and A. Neumaier. A global optimization method, αBB, for general twice-differentiable constrained NLPs — I. Theoretical advances. Computers and Chemical Engineering, 22:1137–1158, 1998.CrossRefGoogle Scholar
  2. 2.
    C. S. Adjiman and C. A. Floudas. Rigorous convex underestimators for general twice-differentiable problems. Journal of Global Optimization, 9:23–40, 1997.MathSciNetCrossRefGoogle Scholar
  3. 3.
    T. Ahadi-Oskui. Optimierung des Entwurfs komplexer Energieumwandlungsan-lagen. In Fortschritt-Berichte, number 543 in Series 6. VDI-Verlag, Düsseldorf, Germany, 2006.Google Scholar
  4. 4.
    T. Ahadi-Oskui, H. Alperin, I. Nowak, F. Cziesla, and G. Tsatsaronis. A Relaxation-Based Heuristic for the Design of Cost-Effective Energy Conversion Systems. Energy, 31:1346–1357, 2006.CrossRefGoogle Scholar
  5. 5.
    T. Ahadi-Oskui, S. Vigerske, I. Nowak, and G. Tsatsaronis. Optimizing the design of complex energy conversion systems by branch and cut. Preprint 07-11, Department of Mathematics, Humboldt-University Berlin. available at http://www.math.hu-berlin.de/publ/pre/2007/P-07-11.pdf and submitted, 2007.
  6. 6.
    ARKI Consulting and Development A/S and GAMS Inc. SBB. http://www.gams.com/solvers/solvers.htm#SBB, 2002.
  7. 7.
    J. Axmann, R. Dobrowolski, and R. Leithner. Evolutionäre Algorithmen zur Optimierung von Kraftwerkskonzepten und Anlagenbauteilen. In Fortschritt-Berichte, number 438 in Reihe 6, pages 251–265. VDI-Verlag, Düsseldorf, Germany, 1997.Google Scholar
  8. 8.
    A. Bejan, G. Tsatsaronis, and M. Moran. Thermal Design and Optimization. Wiley, New York, USA, 1996.MATHGoogle Scholar
  9. 9.
    M.S. Boddy and D.P. Johnson. A new method for the global solution of large systems of continuous constraints. In Ch. Bliek, Ch. Jermann, and A. Neumaier, editors, Global Optimization and Constraint Satisfaction, volume 2861 of Lecture Notes in Computer Science, pages 143–156. Springer, Berlin, 2003.Google Scholar
  10. 10.
    C. G. E. Boender and H. E. Romeijn. Stochastic methods. In R. Horst and P. Pardalos, editors, Handbook of Global Optimization, pages 829–869. Kluwer, Dordrecht, 1995.CrossRefGoogle Scholar
  11. 11.
    P. Bonami, L.T. Biegler, A.R. Conn, G. Cornuéjols, I.E. Grossmann, C.D. Laird, J. Lee, A. Lodi, F. Margot, N. Sawaya, and A. Wächter. An algorithmic framework for convex mixed integer nonlinear programs. Discrete Optimization, 5:186–204, 2008.MathSciNetCrossRefMATHGoogle Scholar
  12. 12.
    C. Bouvy. Kombinierte Struktur- und Einsatzoptimierung von Energiever-sorgungssystemen mit einer Evolutionsstrategie. Shaker Verlag, Aachen, 2007.Google Scholar
  13. 13.
    C. Bouvy and S. Herbergs. Mehrkriterielle Optimierung dezentraler Energiev-ersorgungssysteme mit evolutionären Algorithmen. In Optimierung in der En-ergiewirtschaft, number 1908 in Fortschitt-Berichte, pages 265–277. VDI-Verlag, Düsseldorf, Germany, 2005.Google Scholar
  14. 14.
    J. Bruno, F. Fernandez, F. Castells, and I. Grossmann. A Rigorous MINLP Model for the Optimal Synthesis and Operation of Utility Plants. Transactions of the Institution of Chemical Engineers, 76:246–258, 1998.CrossRefGoogle Scholar
  15. 15.
    M. R. Bussieck, A. S. Drud, and A. Meeraus. MINLPLib — A Collection of Test Models for Mixed-Integer Nonlinear Programming. INFORMS Journal on Computing, 15(1):114–119, 2003.MathSciNetCrossRefMATHGoogle Scholar
  16. 16.
    F. Cziesla. Produktkostenminimierung beim Entwurf komplexer Energieum-wandlungsanlagen mit Hilfe von wissensbasierten Methoden. In Fortschritt-Berichte, number 438 in Reihe 6. VDI-Verlag, Düsseldorf, 2000.Google Scholar
  17. 17.
    DEWI, E.ON Netz, EWI, RWE Transportnetz Strom, and VE Transmission. Energiewirtschaftliche Planung für die Netzintegration von Windenergie in Deutschland an Land und Offshore bis zum Jahr 2020. http://www.eon-netz.com/Ressources/downloads/dena_haupt_studie.pdf, February 2005. Studie im Auftrag der Deutschen Energie-Agentur GmbH (dena).
  18. 18.
    M. A. Duran and I. E. Grossmann. An outer-approximation algorithm for a class of mixed-integer nonlinear programs. Mathematical Programming, 36:307–339, 1986.MathSciNetCrossRefMATHGoogle Scholar
  19. 19.
    A. Epe, C. Küchler, W. Römisch, S. Vigerske, H.-J. Wagner, C. Weber, and O. Woll. Stochastic programming with recombining scenario trees — optimization of dispersed energy supply. Chapter 15 in this book.Google Scholar
  20. 20.
    M. Fenski. Prozessanalyse mittels selbstorganisierender neuronaler Karten am Beispiel eines kombinierten Gas- und Dampfturbinenwerks mit Fernwärme-auskopplung. Diplomarbeit, Technische Universität Berlin, 2006.Google Scholar
  21. 21.
    R. Fletcher and S. Leyffer. Solving Mixed Integer Nonlinear Programs by Outer Approximation. Mathematical Programming, 66(3(A)):327–349, 1994.MathSciNetCrossRefMATHGoogle Scholar
  22. 22.
    C. A. Floudas, I. G. Akrotirianakis, C. Caratzoulas, C. A. Meyer, and J. Kallrath. Global optimization in the 21st century: Advances and challenges. Computers and Chemical Engineering, 29(6):1185–1202, 2005.CrossRefGoogle Scholar
  23. 23.
    C.A Frangopoulos. Optimal Synthesis and Operation of Thermal Systems by the Thermoeconomic Functional Approach. Transactions of the ASME, Journal of Engineering for Gas Turbines and Power, 114:707–714, 1992.CrossRefGoogle Scholar
  24. 24.
    GAMS Development Corp. GAMS — The Solver Manuals. GAMS, Washington DC, 2007.Google Scholar
  25. 25.
    Gas Turbine World 2006 Handbook. Pequot, Fairfield, 2006.Google Scholar
  26. 26.
    M. Gebhardt, H. Kohl, and T. Steinrötter. Preisatlas, Ableitung von Kosten-funktionen für Komponenten der rationellen Energienutzung. http://www.iuta.de/thermodynamik/Preisatlas_Download.htm, June 2002.
  27. 27.
    R. Horst and P. Pardalos. Handbook of Global Optimization. Kluwer, Dordrecht, 1995.CrossRefMATHGoogle Scholar
  28. 28.
    K. Hüttenhofer and A. Lezuo. Cogeneration Power Plant Concepts Using Advanced Gas Turbines. VGB PowerTech, 81(6):50–56, 2001.Google Scholar
  29. 29.
    M. Jüdes, F. Cziesla, W. Ahrens, J. Petri, and G. Tsatsaronis. Neuronale Netze als Hilfsmittel zur Betriebsbewertung am Beispiel einer industriellen Kraft-Wärme-Kopplungsanlage. In Optimierung in der Energieversorgung, number 1792 in VDI-Berichte, pages 201–213. VDI-Verlag, 2003.Google Scholar
  30. 30.
    M. Jüdes and G. Tsatsaronis. Cost Effective Design Optimization and Maintenance Strategies with Consideration of the Partial Load Behavior of Power Plants. In A. Mirandola, Ö. Arnas, and A. Lazzaretto, editors, Proceedings of ECOS 2007, Padova, Italy, volume I, pages 251–258, June, 25–28 2007.Google Scholar
  31. 31.
    M. Jüdes and G. Tsatsaronis. Design Optimization of Power Plants by Considering Multiple Partial Load Operation Points. In 2007 ASME International Mechanical Engineering Congress and Exposition, November 11–15, Seattle, Washington USA, IMECE2007. ASME, 2007.Google Scholar
  32. 32.
    O. Knacke, O. Kubaschewski, and K. Hesselmann. Thermochemical Properties of Inorganic Substances. Springer, Berlin, Germany, 1991.Google Scholar
  33. 33.
    T. Kohonen. Self-Organizing Maps. Springer Verlag, Heidelberg, 2001.CrossRefMATHGoogle Scholar
  34. 34.
    M. Krämer. Modellanalyse zur Optimierung der Stromerzeugung bei hoher Einspeisung von Windenergie. In Fortschritt-Berichte, number 492 in Reihe 6. VDI-Verlag, Düsseldorf, Germany, 2003.Google Scholar
  35. 35.
    H. Marchand and L.A. Wolsey. Aggregation and mixed integer rounding to solve MIPs. Operations Research, 49(3):363–371, 2001.MathSciNetCrossRefMATHGoogle Scholar
  36. 36.
    J.R. Muñoz and M.R. von Spakovsky. A Decomposition Approach for the Large Scale Synthesis/Design Optimization of Highly Coupled, Highly Dynamic Energy Systems. International Journal of Applied Thermodynamics, 4(1):19–33, 2001.Google Scholar
  37. 37.
    J.R. Muñoz and M.R. von Spakovsky. The Application of Decomposition to the Large Scale Synthesis/Design Optimization of Aircraft Energy Systems. International Journal of Applied Thermodynamics, 4(2):61–74, 2001.Google Scholar
  38. 38.
    G. L. Nemhauser and L. A. Wolsey. Integer and Combinatorial Optimization. Wiley, New York, 1988.MATHGoogle Scholar
  39. 39.
    A. Neumaier. Interval Methods for Systems of Equations. Cambridge University Press, Cambridge, 1990.MATHGoogle Scholar
  40. 40.
    A. Neumaier. Complete search in continuous global optimization and constraint satisfaction. In Acta Numerica, volume 13, chapter 4, pages 271–370. Cambridge University Press, Cambridge, 2004.Google Scholar
  41. 41.
    A. Neumaier and S. Vigerske. personal communication, October 2006.Google Scholar
  42. 42.
    I. Nowak. Relaxation and Decomposition Methods for Mixed Integer Nonlinear Programming. Birkhäuser Verlag, Basel, Schweiz, 2005.MATHGoogle Scholar
  43. 43.
    I. Nowak, H. Alperin, and S. Vigerske. LaGO — an object oriented library for solving MINLPs. In Ch. Bliek, Ch. Jermann, and A. Neumaier, editors, Global Optimization and Constraint Satisfaction, volume 2861 of Lecture Notes in Computer Science, pages 31–43. Springer, Berlin, 2003.Google Scholar
  44. 44.
    I. Nowak and S. Vigerske. LaGO — Lagrangian Global Optimizer. https://projects.coin-or.org/LaGO.
  45. 45.
    I. Nowak and S. Vigerske. LaGO: a (heuristic) branch and cut algorithm for nonconvex MINLPs. Central European Journal of Operations Research, 16(2):127–138, 2008.MathSciNetCrossRefMATHGoogle Scholar
  46. 46.
    K. Papalexandri, E. Pistikopoulos, and B. Kalitventzeff. Modelling and Optimization Aspects in Energy Management and Plant Operation with Variable Energy Demands-Application to Industrial Problems. Computers and Chemical Engineering, 22(9):1319–1333, 1998.CrossRefGoogle Scholar
  47. 47.
    D. Paulus. Single-Component Optimal Heat Exchanger Effectiveness using Specific Exergy Costs and Revenues. In S. Kjelstrup, J. E. Hustad, T. Gundersen, A. Røsjorde, and G. Tsatsaronis, editors, Proceedings of ECOS 2005, Trond-heim, Norway, volume III, pages 1407–1414, June, 20–22 2005.Google Scholar
  48. 48.
    R. Peltier. TOP PLANTS: Tenaska Virginia Generating Station, Scottsville, Virginia. POWER magazine, 151(9):50–53, 2007.Google Scholar
  49. 49.
    R. Romero, A. Zobaa, E. Asada, and W. Freitas. Mathematical optimisation techniques applied to power systems operation and planning. International Journal of energy technology and policy, 5(4):393–403, 2007.CrossRefGoogle Scholar
  50. 50.
    T. Savola. Simulation and Optimisation of Power Production in Biomass-Fuelled Small-Scale CHP plants. Licentiate's thesis, Helsinki University of Technology, March 2005.Google Scholar
  51. 51.
    SOFBID. EBSILONProfessional. http://www.sofbid.com.
  52. 52.
    M. Tawarmalani and N. V. Sahinidis. Global optimization of mixed-integer nonlinear programs: A theoretical and computational study. Mathematical Programming, 99:563–591, 2004.MathSciNetCrossRefMATHGoogle Scholar
  53. 53.
    M. Tawarmalani and N.V. Sahinidis. Convexification and Global Optimization in Continuous and Mixed-Integer Nonlinear Programming: Theory, Algorithms, Software, and Applications. Kluwer, Dordrecht, 2002.CrossRefGoogle Scholar
  54. 54.
    G. Tsatsaronis, F. Cziesla, and Z. Gao. Avoidable Thermodynamic Inefficiencies and Costs in Energy Conversion Systems. Part 1: Methodology. In N. Houbak, B. Elmegaard, B. Qvale, and M.J. Moran, editors, Proceedings of ECOS 2003, Copenhagen, Denmark, volume II, pages 809–814, June 30–July 2, 2003.Google Scholar
  55. 55.
    G. Tsatsaronis, K. Kapanke, and A.M. Blanco Marigorta. Exergoeconomic estimates for a novel process with integrated CO 2 capture for the production of hydrogen and electric power. In C.A. Frangopoulos, C.D. Rakopoulos, and G. Tsatsaronis, editors, Proceedings of ECOS 2006, July 12–14, Aghia Pelagia, Crete, Greece, volume 3, pages 1581–1591, 2006.Google Scholar
  56. 56.
    G. Tsatsaronis, L. Lin, J. Pisa, and T. Tawfik. Thermoeconomic Design Optimization of a KRW-based IGCC power plant, Final Report submitted to Southern Company Services and the U.S. Department of Energy. DE-FC21-89MC26019, Center for Electric Power, Tennessee Technological University, 1991.Google Scholar
  57. 57.
    G. Tsatsaronis, T. Tawfik, L. Lin, and D.T. Gallaspy. Exergetic Comparison of two KRW-based IGCC Power Plants. Journal of Engineering Gas Turbines and Power, pages 219–299, 1994.Google Scholar
  58. 58.
    R. Turton, R. Bailie, W. Whiting, and J. Shaeiwitz. Analysis, Synthesis and Desing of Chemical Processes. Prentice Hall, New Jersey, USA, 1984.Google Scholar
  59. 59.
    Zsolt Ugray, Leon Lasdon, John Plummer, Fred Glover, Jim Kelly, and Rafael Martí. Scatter search and local NLP solvers: A multistart framework for global optimization. INFORMS Journal on Computing, 19(3):328–340, 2007.MathSciNetCrossRefMATHGoogle Scholar
  60. 60.
    G. Ulrich. A guide to chemical engineering process design and economics. Wiley, New York, USA, 1984.Google Scholar
  61. 61.
    W. Wagner. Properties of Water and Steam. Springer, Berlin, 1998.Google Scholar
  62. 62.
    T. Westerlund and R. Pörn. Solving pseudo-convex mixed integer optimization problems by cutting plane techniques. Optimization and Engineering, 3:253–280, 2002.MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Marc Jüdes
    • 1
  • Stefan Vigerske
    • 2
  • George Tsatsaronis
    • 3
  1. 1.Leibniz Universität HannoverHannoverGermany
  2. 2.Humboldt-Universität zu BerlinBerlinGermany
  3. 3.Institute for Energy EngineeringTechnische Universität BerlinBerlinGermany

Personalised recommendations