Abstract
We present a multi-stage decision model, which serves as a building block for solving various electricity portfolio management problems. The basic setup consists of a portfolio optimization model for a large energy consumer, which has to decide about its mid-term electricity portfolio composition. The given stochastic demand may be fulfilled by buying energy on the spot or futures market, by signing a supply contract, or by producing electricity in a small plant. We formulate the problem in a dynamic risk management-based stochastic optimization framework, whose flexibility allows for extensive parameter studies and comparative analysis of different types of supply contracts. A number of application examples is presented to outline the possibilities of using the basic multi-stage stochastic programming model to address a range of issues related to the design of optimal policies. Apart from the question of an optimal energy policy mix for a large energy consumer, we investigate the pricing problem for flexible supply contracts from the perspective of an energy trader, demonstrating the wide applicability of the framework.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Bernhardt C, Klüppelberg C, Meyer-Brandis T (2008) Estimating high quantiles for electricity prices by stable linear models. J Energ Market 1(1):3–19
de Jong CM, Huisman R (2002) Option formulas for mean-reverting power prices with spikes. Research paper, Erasmus Research Institute of Management (ERIM), October 2002
Dupačová J, Gröwe-Kuska N, Römisch W (2003) Scenario reduction in stochastic programming. An approach using probability metrics. Math Program A 95(3):493–511
Eichhorn A, Römisch W (2008) Stability of multistage stochastic programs incorporating polyhedral risk measures. Optimization 57(2):295–318
Eichhorn A, Römisch W, Wegner I (2005) Mean-risk optimization of electricity portfolios using multiperiod polyhedral risk measures. IEEE Proceedings - St. Petersburg Power Tech, 2005
Escribano L, Pena JI, Villaplana P (2002) Modeling electricity prices: International evidence. Economics working papers, Universidad Carlos III, Departamento de Economa, 2002
Haarbrücker G, Kuhn D (2009) Valuation of electricity swing options by multistage stochastic programming. Automatica 45(4):889–899
Heitsch H, Römisch W (2003) Scenario reduction algorithms in stochastic programming. Computat Optim Appl 24(2–3):187–206
Hochreiter R, Pflug GC (2007) Financial scenario generation for stochastic multi-stage decision processes as facility location problems. Ann Oper Res 152:257–272
Hochreiter R, Pflug GC, Wozabal D (2006) Multi-stage stochastic electricity portfolio optimization in liberalized energy markets. In System modeling and optimization, vol. 199 of IFIP Int. Fed. Inf. Process. Springer, New York, pp. 219–226
Hollander M, Wolfe A (1973) Nonparametric statistical inference. Wiley, New York
Király A, Jánosi IM (2002) Stochastic modeling of daily temperature fluctuations. Phys. Rev. E 65(5):051102
Lucia JJ, Schwartz ES (2002) Electricity prices and power derivatives: evidence from the Nordic Power Exchange. Rev Derivatives Res 5(1):5–50
McNeil AJ, Frey R, Embrechts P (2005) Quantitative risk management. Princeton Series in Finance. Princeton University Press, NJ
Nolan J (2004) stable.exe. A program to fit and simulate stable laws. http://academic2.american.edu/~jpnolan/stable/stable.html
Pflug GC (2001) Scenario tree generation for multiperiod financial optimization by optimal discretization. Math Program B 89(2):251–271
Pflug GC, Broussev N (2009) Electricity swing options: behavioral models and pricing. Eur J Oper Res 197(3):1041–1050
Pflug GC, Römisch W (2007) Modeling, measuring and managing risk. World Scientific, Singapore
Rachev ST, Mittnik S (2000) Stable paretian models in finance. Wiley, New York
Rachev ST, Römisch W (2002) Quantitative stability in stochastic programming: the method of probability metrics. Math Oper Res 27(4):792–818
Rockafellar RT, Uryasev S (2000) Optimization of conditional value-at-risk. J Risk 2(3):21–41
Römisch W (2003) Stability of stochastic programming problems. In Stochastic programming, vol. 10 of Handbooks Oper. Res. Management Sci. Elsevier, Amsterdam, pp. 483–554
Ruszczyński A (2003) Decomposition methods. In: Ruszczyński A, Shapiro A (eds) Stochastic programming. Handbooks in operations research and management science, vol. 10. Elsevier, Amsterdam, pp. 141–211
Ruszczyński A, Shapiro A (eds) (2003) Stochastic programming. Handbooks in operations research and management science, vol. 10. Elsevier, Amsterdam
Schultz R, Nowak MP, Nürnberg R, Römisch W, Westphalen M (2003) Stochastic programming for power production and trading under uncertainty. In: Mathematics – Key technology for the future. Springer, Heidelberg, pp. 623–636
Sen S, Yu L, Genc T (2006) A stochastic programming approach to power portfolio optimization. Oper Res 54(1):55–72
Wallace SW, Ziemba WT (eds) (2005) Applications of stochastic programming. MPS/SIAM Series on Optimization, vol. 5. Society for Industrial and Applied Mathematics (SIAM), 2005
Weron R (2006) Modeling and forecasting electricity loads and prices: A statistical approach. Wiley, Chichester
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Hochreiter, R., Wozabal, D. (2010). A Multi-stage Stochastic Programming Model for Managing Risk-optimal Electricity Portfolios. In: Rebennack, S., Pardalos, P., Pereira, M., Iliadis, N. (eds) Handbook of Power Systems II. Energy Systems. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12686-4_14
Download citation
DOI: https://doi.org/10.1007/978-3-642-12686-4_14
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-12685-7
Online ISBN: 978-3-642-12686-4
eBook Packages: EngineeringEngineering (R0)