Energy Portfolio Optimization for Electric Utilities: Case Study for Germany

Part of the Energy Systems book series (ENERGY)


We discuss a portfolio optimization problem occurring in the energy market. Energy distributing public services have to decide how much of the requested energy demand has to be produced in their own power plant, and which complementary amount has to be bought from the spot market and from load following contracts. This problem is formulated as a mixed-integer linear programming problem and implemented in GAMS. The formulation is applied to real data of a German electricity distributor.


Power Plant Variable Cost Time Slice Power Rate Spot Market 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



We would like to thank Peter Miebach (Mühlheim an der Ruhr, Germany) for providing the real-world case to us and his engagement in improving the description of the real world situation in this paper. Panos M. Pardalos and Steffen Rebennack are partially supported by AirForce and CRDF grants. The support is greatly appreciated.


  1. Arroyo, J., & Conejo, A. (2000). Optimal response of a thermal unit to an electricity spot market. IEEE Transactions on Power Systems, 15(3), 1098–1104.CrossRefGoogle Scholar
  2. Atamtürk, A., & Savelsbergh, M. (2005). Integer-programming software systems. Annals of Operations Research, 140(1), 67–124.CrossRefGoogle Scholar
  3. Baldick, R. (1995). The generalized unit commitment problem. IEEE Transactions on Power Systems, 10(1), 465–475.CrossRefGoogle Scholar
  4. Beale, E., & Tomlin, J. (1969). Special facilities in a general mathematical programming system for non-convex problem using ordered sets of variables. In 5th International Conference on Operation Research (pp. 447–454). North-Holland.Google Scholar
  5. Brand, H., Weber, C., Meibom, P., Barth, R., & Swider, D. J. (2004). A stochastic energy market model for evaluating the integration of wind energy. In Tagungsband der 6. IAEE European Conference 2004 on Modelling in Energy Economics and Policy. Zurich.Google Scholar
  6. Bruce, A. M., Meeraus, A., van der Eijk, P., Bussieck, M., Dirkse, S., & Steacy, P. (2009). McCarl GAMS User Guide. GAMS Development Corporation.Google Scholar
  7. Bundesministerium für Wirtschaft und Technologie (2004). Gesetz für den Vorrang Erneuerbarer Energien (Erneuerbare-Energien-Gesetz – EEG).Google Scholar
  8. Bundesministerium für Wirtschaft und Technologie (2006). Bundeskabinett beschließt Entlastungen im Erneuerbare-Energien-Gesetz (EEG). Berlin.Google Scholar
  9. Carrion, M., & Arroyo, J. (2006). A computationally efficient mixed-integer linear formulation for the thermal unit commitment problem. IEEE Transactions on Power Systems, 21(3), 1371–1378.CrossRefGoogle Scholar
  10. Chowdhury, S., & Rahman, B. H. (1990). A review of recent advances in economic dispatch. IEEE Transactions on Power Systems, 5(4), 1248–1259.CrossRefGoogle Scholar
  11. Dhillon, K., & Dhillon, J. S. (2004). “Power system optimization”. India: Prentice Hall.Google Scholar
  12. Dillon, T. S., Edwin, K. W., Kochs, H.-D., & Taud, R. J. (1978). Integer programming approach to the problem of optimal unit commitment with probabilistic reserve determination. IEEE Transactions on Power Apparatus and Systems, PAS-97(6), 2154–2166.Google Scholar
  13. EEX - European Energy Exchange (2007). EEX Product Information Power. Leipzig.Google Scholar
  14. Erdmann, G., & Zweifel, P. (2007). Energieökonomik - Theorie und Anwendungen. Berlin: Springer.Google Scholar
  15. European Commission (2007). Germany - Energy mix fact sheet.Google Scholar
  16. GAMS (2009). The GAMS model library index.Google Scholar
  17. Gröwe-Kuska, N., & Römisch, W. (2005). Applications of stochastic programming. In S. W. Wallace & W. T. Ziemba (Eds.), Stochastic unit commitment in hydro-thermal power production planning, Chap. 30, MPS-SIAM Series in Optimization.Google Scholar
  18. Gröwe-Kuska, N., Kiwiel, K. C., Nowak, M. P., Römisch, W., & Wegner, I. (2002). Decision making under uncertainty: energy and power. In C. Greengard, & A. Ruszczynski (Eds.), IMA Volumes in Mathematics and its Applications (Vol. 128, pp. 39–70), Power management in a hydro-thermal system under uncertainty by Lagrangian relaxation. New York: Springer.Google Scholar
  19. Heuck, K., & Dettmann, K. -D. (2005). Elektrische Energieversorgung: Erzeugung, Übertragung und Verteilung elektrischer Energie für Studium und Praxis (6th ed.). Vieweg.Google Scholar
  20. Hobbs, B., Stewart, W., Bixby, R., Rothkopf, M., ONeill, R., and Chao, H. -p. (2002). The next generation of electric power unit commitment models, chapter why this book? New capabilities and new needs for unit commitment modeling (pp. 1–14).Google Scholar
  21. Kallrath, J., & Wilson, J. M. (1997). Business optimisation using mathematical programming. Houndmills, Basingstoke, UK: Macmillan.Google Scholar
  22. LINDO Systems (2003). Application survey paper: electrical generation unit commitment planning.Google Scholar
  23. Madlener, R., & Kaufmann, M. (2002). Power exchange spot market trading in Europe: theoretical considerations and empirical evidence. OSCOGEN Deliverable 5.1bMarch; Contract No. ENK5-CT-2000-00094.Google Scholar
  24. Madrigal, M., & Quintana, V. (2000). An analytical solution to the economic dispatch problem. IEEE Power Engineering Review, 20(9), 52–55.CrossRefGoogle Scholar
  25. Nowak, M. P., & Römisch, W. (2000). Stochastic lagrangian relaxation applied to power scheduling in a hydro-thermal system under uncertainty. Annals of Operations Research, 100(1), 251–272.CrossRefGoogle Scholar
  26. Österreichische Elektrizitätsstatistikverordnung (2007). 284. Verordnung des Bundesministers für Wirtschaft und Arbeit über statistische Erhebungen für den Bereich der Elektrizitätswirtschaft.Google Scholar
  27. Padhy, N. (2004). Unit commitment-a bibliographical survey. IEEE Transactions on Power Systems, 19(2), 1196–1205.CrossRefGoogle Scholar
  28. Philpott, A., & Schultz, R. (2006). Unit commitment in electricity pool markets. Mathematical Programming, 108(2), 313–337.CrossRefGoogle Scholar
  29. Rosenthal, R. E. (1997). A GAMS Tutorial.Google Scholar
  30. Rosenthal, R. E. (2008). GAMS – A user’s guide. Washington, DC, USA: GAMS Development Corporation.Google Scholar
  31. Schweppe, F. C., Caramanis, M. C., Tabors, R. D., & Bohn, R. E. (Eds.) (2002). Spot pricing of electricty (5th ed.). Boston, MA: Kluwer.Google Scholar
  32. Sen, S., & Kothari, D. P. (1998). Optimal thermal generating unit commitment: a review. International Journal of Electrical Power & Energy Systems, 20(7), 443–451.CrossRefGoogle Scholar
  33. Sheble, G. B., & Fahd, G. N. (1994). Unit commitment literature synopsis. IEEE Transactions on Power Systems, 9(1), 128–135.CrossRefGoogle Scholar
  34. Shiina, T., & Birge, J. R. (2004). Stochastic unit commitment problem. International Transactions in Operational Research, 11(1), 19–32.CrossRefGoogle Scholar
  35. Stadtwerke Saarlouis GmbH (2003). Jahreshöchstlast als viertelstündige Leistungsmessung.Google Scholar
  36. Takriti, S., Birge, J., & Long, E. (1996). A stochastic model for the unit commitment problem. IEEE Transactions on Power Systems, 11(3), 1497–1508.CrossRefGoogle Scholar
  37. Takriti, S., Krasenbrink, B., & Wu, L. S. -Y. (2000). Incorporating fuel constraints and electricity spot prices into the stochastic unit commitment problem. Operations Research, 48(2), 268–280.CrossRefGoogle Scholar
  38. Talaq, J. H., EI-Hawary, F., & EI-Hawary, M. E. (1994). A summary of environmental/economic dispatch algorithms. IEEE Transactions on Power Systems, 9(3), 1508–1516.CrossRefGoogle Scholar
  39. Verband der Netzbetreiber - VDN - e.V. beim VDEW (2006). VDN-Richtlinie – MeteringCode 2006. Berlin.Google Scholar
  40. Wallace, S. W., & Fleten, S. -E. (2003). Stochastic programming. In A. Ruszczynski & A. Shapiro (Eds.), Handbooks in operations research and management science, chapter Stochastic programming models in energy (Vol. 10, pp. 637–677). North-Holland.Google Scholar
  41. Wolsey, L. A., & Nemhauser, G. L. (1999). Integer and combinatorial optimization. Wiley-Interscience.Google Scholar
  42. Wood, A. J. & Wollenberg, B. F. (1996). Power generation, operation, and control (2nd ed.). New York: Wiley.Google Scholar
  43. Yalcinoz, T., & Köksoy, O. (2007). A multiobjective optimization method to environmental economic dispatch. International Journal of Electrical Power & Energy Systems, 29(1), 42–50.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  1. 1.Department of Industrial & Systems Engineering, Center for Applied OptimizationUniversity of FloridaGainesvilleUSA
  2. 2.Department of AstronomyUniversity of FloridaGainesvilleUSA

Personalised recommendations