Stochastic Optimization of Power Generation and Storage Management in a Market Environment

Part of the International Series in Operations Research & Management Science book series (ISOR, volume 199)


This chapter provides an overview of practically applying mathematical optimization techniques to short-term and medium-term planning of a power generation system in a market environment. The considered power generating system may contain thermal plants (gas or coal fired), hydro power plants, new renewables, as well as dedicated energy storages (e.g., gas storages, hydro reservoirs). We argue that stochastic optimization is an appropriate modeling framework in order to take into account the uncertainty of input data (such as natural hydrologic inflows and energy market prices), market decision structures, as well as the optional character of power generating units and energy storages.


Electricity Market Scenario Tree Spot Market Stochastic Dynamic Programming Multistage Stochastic Program 
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.


  1. 1.
    APG: Austrian Power Grid (2013) Web page:
  2. 2.
    Birge JR, Louveaux F (1997) Introduction to stochastic programming. In: Springer series in operations research. Springer, New YorkGoogle Scholar
  3. 3.
    Boogert A, Dupont D (2008) When supply meets demand: the case of hourly spot electricity prices. IEEE Trans Power Syst 23:389–398CrossRefGoogle Scholar
  4. 4.
    Burger M, Klar B, Müller A, Schindlmayr G (2004) A spot market model for pricing derivatives in electricity markets. Quant Financ 4:109–122CrossRefGoogle Scholar
  5. 5.
    Burger M, Graeber B, Schindlmayr G (2007) Managing energy risk (Wiley Finance Series). Wiley, ChichesterGoogle Scholar
  6. 6.
    EEX: European Energy Exchange (2013) Web page:
  7. 7.
    Eichhorn A, Römisch W (2005) Polyhedral risk measures in stochastic programming. SIAM J Optimiz 16:69–95CrossRefGoogle Scholar
  8. 8.
    Eichhorn A, Heitsch H, Römisch W (2009) Scenario tree approximation and risk aversion strategies for stochastic optimization of electricity production and trading. In: Kallrath J et al (eds) Optimization in the energy industry, chap 14. Springer, Berlin, pp 321–346CrossRefGoogle Scholar
  9. 9.
    EPEX Spot: European Power Exchange (2013) Web page:
  10. 10.
    Faria E, Fleten SE (2011) Day-ahead market bidding for a Nordic hydropower producer: taking the Elbas market into account. Comput Manage Sci 8:75–101CrossRefGoogle Scholar
  11. 11.
    Fleten SE, Wallace SW (2009) Delta-hedging a hydropower plant using stochastic programming. In: Kallrath J et al (eds) Optimization in the energy industry, chap 22. Springer, Berlin, pp 507–524CrossRefGoogle Scholar
  12. 12.
    Föllmer H, Schied A (2004) Stochastic finance: an introduction in discrete time. In: De Gruyter studies in mathematics, vol 27, 2nd edn. Walter de Gruyter, BerlinGoogle Scholar
  13. 13.
    Garcés L, Conejo A (2010) Weekly self-scheduling, forward contracting, and offering strategy for a producer. IEEE Trans Power Syst 25:657–666CrossRefGoogle Scholar
  14. 14.
    GME: Gestore Mercati Energetici (2013) Web page:
  15. 15.
    Guigues V, Römisch W (2012) SDDP for multistage stochastic linear programs based on spectral risk measures. Oper Res Lett 40:313–318CrossRefGoogle Scholar
  16. 16.
    Heitsch H, Römisch W (2009) Scenario tree modeling for multistage stochastic programs. Math Program 118:371–406CrossRefGoogle Scholar
  17. 17.
    Heitsch H, Römisch W, Strugarek C (2006) Stability of multistage stochastic programs. SIAM J Optimiz 17:511–525CrossRefGoogle Scholar
  18. 18.
    Hull J (2011) Options, futures and other derivatives, 8th edn. Pearson, HarlowGoogle Scholar
  19. 19.
    Kovacevic RM, Pflug GC (2013) Electricity swing option pricing by stochastic bilevel optimization: a survey and new approaches. (preprint)
  20. 20.
    Kovacevic RM, Wozabal D (2013) A semiparametric model for EEX spot prices. IIE Transactions.  doi:10.1080/0740817X.2013.803640 Google Scholar
  21. 21.
    Löhndorf N, Wozabal D, Minner S (2013) Optimizing trading decisions for hydro storage systems using approximate dual dynamic programming. Operations Research 61:810–823CrossRefGoogle Scholar
  22. 22.
    Markowitz H (1952) Portfolio selection. J Financ 7:77–91Google Scholar
  23. 23.
    NordPool: Nord Pool Spot (2013) Web page:
  24. 24.
    Pereira MVF, Pinto LMVG (1991) Multi-stage stochastic optimization applied to energy planning. Math Program 52:359–375CrossRefGoogle Scholar
  25. 25.
    Pflug GC, Pichler A (2011) Approximations for probability distributions and stochastic optimization problems. In: Bertocchi M et al (eds) International series in operations research and management science, vol 163, chap 15. Springer, New York, pp 343–387Google Scholar
  26. 26.
    Pflug GC, Römisch W (2007) Modeling, measuring, and managing risk. World Scientific, SingaporeCrossRefGoogle Scholar
  27. 27.
    Philpott AB, Guan Z (2008) On the convergence of stochastic dual dynamic programming and related methods. Oper Res Lett 36:450–455CrossRefGoogle Scholar
  28. 28.
    PJM: Pjm Interconnection (2013) Web page:
  29. 29. Internetplattform zur Vergabe von Regelleistung (2013) Web page:
  30. 30.
    Rockafellar RT, Uryasev S (2002) Conditional value-at-risk for general loss distributions. J Bank Financ 26:1443–1471CrossRefGoogle Scholar
  31. 31.
    RTE: Réseau de Transport d’Electricité (2013) Web page:
  32. 32.
    Ruszczyński A (2003) Decomposition methods. In: Ruszczyński A, Shapiro A (eds) Handbooks in operations research and management science, vol 10, chap 3, 1st edn. Elsevier, Amsterdam, pp 141–211Google Scholar
  33. 33.
    Ruszczyński A, Shapiro A (eds) (2003) Stochastic programming. In: Handbooks in operations research and management science, vol 10, 1st edn. Elsevier, AmsterdamGoogle Scholar
  34. 34.
    Ruszczyński A, Shapiro A (2006) Conditional risk mappings. Math Oper Res 31:544–561CrossRefGoogle Scholar
  35. 35.
    Shapiro A (2011) Analysis of stochastic dual dynamic programming method. Eur J Oper Res 209:63–72CrossRefGoogle Scholar
  36. 36.
    Shapiro A, Tekaya W, Da Costa J, Soares M (2013) Risk neutral and risk averse stochastic dual dynamic programming method. Eur J Oper Res 224:375–391CrossRefGoogle Scholar
  37. 37.
    Weron R, Bierbrauer M, Trück S (2004) Modeling electricity prices: jump diffusion and regime switching. Physica A 336:39–48CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.VERBUND Trading AGViennaAustria

Personalised recommendations